BOSTON UNIVERSITYGRADUATE SCHOOL OF ARTS AND SCIENCESDissertation

A SEARCH FOR NUCLEON DECAYINTO MODES FAVORED BY SUPERSYMMETRY USINGSUPER-KAMIOKANDEbyMATTHEW ALLEN EARLB.A., The Johns Hopkins University, 1994M.A., Boston University, 1999

Submitted in partial ful�llment of therequirements for the degree ofDo tor of Philosophy2000

Approved by

First Reader James L. Stone, Ph.D.Professor of Physi sSe ond Reader Edward T. Kearns, Ph.D.Asso iate Professor of Physi sThird Reader Lawren e R. Sulak, Ph.D.Professor of Physi s

A knowledgmentsI would �rst like to give thanks to my advisor, Jim Stone, who involved me inthe Super{Kamiokande experiment early in my graduate studies and has given meex eptional advi e and support throughout my time at Boston University. I thank EdKearns for his day-to-day guidan e, advi e, and en ouragement of my work. Thanksto Larry Sulak who has always been enthusiasti and en ouraging of my studies inphysi s. I would also like to thank the rest of my thesis ommittee, Sekhar Chivukula,Steve Ahlen, and Bill Sko pol. They have always hallenged me with tough questionswhi h inspired me to think harder and s rutinize my work more thoroughly.I deeply appre iate the parti le astrophysi s group in whi h I work at BostonUniversity. The dis ussions, ollaboration, and omradary between us has been agreat experien e. Thanks to post-do s Ale Habig, Chris Walter, and Kate S holbergand fellow graduate students Shantanu Desai, Mark Messier, and Chris Orth.I am extremely fortunate to have joined the Super{Kamiokande experiment. Iwould like to thank spokesmen Yoji Totsuka, Jim Stone, and Hank Sobel for providingsu h ex eptional leadership. The atmospheri neutrino/proton de ay data analysisgroup in whi h I worked bene�tted from the superb leadership of T. Kajita and EdKearns and the hard work of a number of people. I would like to espe ially thank J.Kameda, K. Kobayashi, M. Etoh, Y. Hatakeyama, Y. Hayato, Y. Itow, K. Ishihara,S. Kasuga, C. M Grew, C. Mauger, B. Viren, D. Casper, and T. Barsz zak. Spe ialthanks to M. Shiozawa.I would like to thank my family who have always given me love and support forwhi h I am deeply grateful. My mom and dad have been extremely en ouragingthroughout my graduate areer. This work ould not have been ompleted withoutthem. Thanks to my dad for tea hing me his methodology for solving problems. Hehas been a role model for me. Thanks to my big brothers John, Jimmy, and Davidiii

for being big brothers. I have always looked up to them.Finally I would like to thank my wife, Diane. She has endured several of mylong trips to Japan at in onvenient moments and remained patient. Without herlove, support, and en ouragement this work would not have been possible. I am verygrateful for her.The Super{Kamiokande experiment was built from and operated by funding fromthe Japanese Ministry of Edu ation, S ien e, Sports, and Culture and the UnitedStates Department of Energy.

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A SEARCH FOR NUCLEON DECAY INTO MODES FAVORED BYSUPERSYMMETRY USING SUPER{KAMIOKANDE(Order No. )MATTHEW ALLEN EARLBoston University Graduate S hool of Arts and S ien es, 2000Major Professor: James L. Stone, Professor of Physi sABSTRACTThis dissertation presents results of a sear h for nu leon de ay into modes fa-vored by supersymmetri (SUSY) grand uni�ed theories (GUTs) using a 991 day(61.5 kiloton�year) exposure of the the Super{Kamiokande water Cherenkov dete -tor lo ated near Kamioka, Japan. SUSY GUTs predi t nu leon de ay with lifetimesranging from 1029 to 1035 years into modes with a kaon in the �nal state. Thede ay modes studied in this dissertation were p ! ��K+ , n ! ��K0 , p ! �+K0 ,and p ! e+K0 . No eviden e for nu leon de ay into any of these modes was found;therefore lower limits for the partial lifetime into these modes were set. The limitsat the 90% on�den e level are (17, 2.5, 12, and 4.4) �1032 years, respe tively. Thelimits set for p! ��K+ and p! �+K0 ex eed limits set by previous experiments byapproximately an order of magnitude. The limits for the n ! ��K0 and p! e+K0modes ex eed previous limits by approximately a fa tor of 3.v

ContentsA knowledgements iiiAbstra t vTable of Contents vList of Figures xList of Tables xx1 Introdu tion 12 Theoreti al Motivation 52.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1 Quarks and Leptons . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 For es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.3 Conservation Laws . . . . . . . . . . . . . . . . . . . . . . . . 72.1.4 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.5 SU(3) � SU(2)W � U(1)Y Des ription . . . . . . . . . . . . . 102.1.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Grand Uni� ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13vi

2.2.1 Running Coupling Constants . . . . . . . . . . . . . . . . . . 142.2.2 Minimal SU(5) . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.3 Supersymmetri GUTs . . . . . . . . . . . . . . . . . . . . . . 193 Experiments 263.1 Early Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Iron alorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 Soudan (1981-1990) . . . . . . . . . . . . . . . . . . . . . . . . 293.2.2 KGF (1980-1992) . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.3 NUSEX (1982-1988) . . . . . . . . . . . . . . . . . . . . . . . 303.2.4 Frejus (1984-1988) . . . . . . . . . . . . . . . . . . . . . . . . 303.2.5 Soudan 2 (1988-Present) . . . . . . . . . . . . . . . . . . . . . 303.3 Water Cherenkov dete tors . . . . . . . . . . . . . . . . . . . . . . . . 313.3.1 IMB/IMB-3 (1982-1991) . . . . . . . . . . . . . . . . . . . . . 313.3.2 Kamiokande (1983-1988) . . . . . . . . . . . . . . . . . . . . . 323.3.3 HPW (1983-1984) . . . . . . . . . . . . . . . . . . . . . . . . . 333.3.4 Super{Kamiokande (1996-Present) . . . . . . . . . . . . . . . 344 The Super{Kamiokande Dete tor 354.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1.1 Water Cherenkov Dete tor . . . . . . . . . . . . . . . . . . . . 354.1.2 Stru ture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1.3 Water Puri� ation System . . . . . . . . . . . . . . . . . . . . 384.2 Inner Dete tor Ele troni s . . . . . . . . . . . . . . . . . . . . . . . . 394.2.1 Photomultiplier Tubes . . . . . . . . . . . . . . . . . . . . . . 394.2.2 Front End Ele troni s . . . . . . . . . . . . . . . . . . . . . . 414.2.3 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42vii

4.3 Outer Dete tor Ele troni s . . . . . . . . . . . . . . . . . . . . . . . . 434.3.1 Photomultiplier Tubes . . . . . . . . . . . . . . . . . . . . . . 444.3.2 Front End Ele troni s: QTC modules . . . . . . . . . . . . . . 454.3.3 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.3.4 Data A quisition . . . . . . . . . . . . . . . . . . . . . . . . . 475 Calibration 485.1 Relative Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2 Absolute Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.3 Timing/Charge (TQ) Calibration . . . . . . . . . . . . . . . . . . . . 505.4 Water Attenuation Length . . . . . . . . . . . . . . . . . . . . . . . . 515.4.1 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.4.2 Cosmi -Ray Muons . . . . . . . . . . . . . . . . . . . . . . . . 535.5 Energy S ale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.5.1 LINAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.5.2 Mi hel Ele trons . . . . . . . . . . . . . . . . . . . . . . . . . 565.5.3 Stopping Muons . . . . . . . . . . . . . . . . . . . . . . . . . . 575.5.4 �0 Re onstru tion . . . . . . . . . . . . . . . . . . . . . . . . . 605.5.5 Summary of energy s ale . . . . . . . . . . . . . . . . . . . . . 616 Monte Carlo 636.1 Nu leon de ay Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . 636.1.1 Nu leon de ay kinemati s . . . . . . . . . . . . . . . . . . . . 636.1.2 Nu lear Intera tions . . . . . . . . . . . . . . . . . . . . . . . 666.2 Atmospheri Neutrino Monte Carlo . . . . . . . . . . . . . . . . . . . 696.2.1 Atmospheri Neutrino Flux . . . . . . . . . . . . . . . . . . . 706.2.2 Neutrino-nu leon Cross se tions . . . . . . . . . . . . . . . . . 71viii

6.2.3 Propagation of Pions Through Nu leus . . . . . . . . . . . . . 786.2.4 Normalization of Ba kground . . . . . . . . . . . . . . . . . . 796.3 Dete tor Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817 Sele tion of Contained Events 827.1 1st Redu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827.2 2nd Redu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.3 3rd Redu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.3.1 Through going muons . . . . . . . . . . . . . . . . . . . . . . 837.3.2 Stopping muons . . . . . . . . . . . . . . . . . . . . . . . . . . 847.3.3 Low energy event reje tion . . . . . . . . . . . . . . . . . . . . 847.3.4 Flasher reje tion . . . . . . . . . . . . . . . . . . . . . . . . . 857.3.5 Cable hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.4 Final Redu tion: ashs an and s anning . . . . . . . . . . . . . . . . 867.5 Final Event Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 868 Event Re onstru tion 888.1 Single ring �tting: a�t . . . . . . . . . . . . . . . . . . . . . . . . . . 888.2 Ring ounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918.3 Parti le identi� ation . . . . . . . . . . . . . . . . . . . . . . . . . . . 968.3.1 Ele tron expe ted PE distribution . . . . . . . . . . . . . . . . 978.3.2 Muon expe ted PE distribution . . . . . . . . . . . . . . . . . 988.3.3 Parti le identi� ation parameter . . . . . . . . . . . . . . . . . 998.4 Momentum determination . . . . . . . . . . . . . . . . . . . . . . . . 1018.5 muon/shower (MS) �t . . . . . . . . . . . . . . . . . . . . . . . . . . 1038.6 De ay ele tron ounting . . . . . . . . . . . . . . . . . . . . . . . . . 103ix

9 The Sear h for Nu leon De ay 1059.1 p! ��K+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1069.1.1 K+ ! �+�0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1069.1.2 K+ ! �+�� . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1109.1.3 Final Limit of p! ��K+ . . . . . . . . . . . . . . . . . . . . . 1199.2 n! ��K0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.2.1 KS ! �0�0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.2.2 KS ! �+�� . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1229.2.3 Final Limit of n! ��K0 . . . . . . . . . . . . . . . . . . . . . 1259.3 p! �+K0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1279.3.1 KS ! �0�0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1279.3.2 KS ! �+�� . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1309.3.3 Final Limit of p! �+K0 . . . . . . . . . . . . . . . . . . . . 1369.4 p! e+K0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1379.4.1 KS ! �0�0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1379.4.2 KS ! �+�� . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1399.4.3 Final Limit of p! e+K0 . . . . . . . . . . . . . . . . . . . . . 1459.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14710 Con lusion 15110.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15110.2 Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15210.3 Dis ussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153A Setting a Limit 155Bibliography 158x

List of Figures2.1 Pi ture of SU(3). The gluons g���, where � and � orrespond to the olor index, onne t di�erent olor states. . . . . . . . . . . . . . . . . 112.2 Simple pi ture of the Standard Model. The gluons mediate intera -tions between various olor states andW� bosons mediate intera tionsbetween the SU(2) eigenstates. . . . . . . . . . . . . . . . . . . . . . 132.3 Feynman diagrams for new intera tions predi ted in Grand Uni�edTheories. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 Feynman diagrams for the favored proton de ay in minimal SU(5),p! e+�0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5 Evolution of running oupling onstants in Minimal SU(5). Equa-tions 2.10 are solved to yield the uni� ation s ale MX and the weakmixing angle sin2 �W . The �i (i = 1; 2; 3) denote the ouplings forU(1)Y ,SU(2)L, and SU(3) , respe tively. . . . . . . . . . . . . . . . . 182.6 Evolution of running oupling onstants in SUSY. The ouplings mergeat a s ale about an order of magnitude larger than in minimal SU(5). 212.7 The Feynman diagram for d=5 intera tions predi ted in SUSY GUTs. 212.8 Feynman diagram for the favored proton de ay in Supersymmetri GUTs, p! ��K+ . For n! ��K0 , repla e the spe tator u quark witha d quark. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22xi

2.9 16 multiplet in SO(10). The �5 and 10 of SU(5) are ontained withinthe 16. In addition, there is a 1 whi h orresponds to a left-handedanti-neutrino, the anti-parti le of a right-handed neutrino. . . . . . . 232.10 Stru ture of the Pati-Salam right-left symmetri G(224) whi h is basedon a SU(2)L � SU(2)R � SU(4) symmetry. This model provides apla e for a right-handed neutrino. . . . . . . . . . . . . . . . . . . . . 244.1 Illustration of Cherenkov radiation. . . . . . . . . . . . . . . . . . . . 364.2 S hemati of the Super{Kamiokande dete tor. . . . . . . . . . . . . . 374.3 S hemati of a supermodule. . . . . . . . . . . . . . . . . . . . . . . . 384.4 Water puri� ation system. . . . . . . . . . . . . . . . . . . . . . . . . 394.5 S hemati view of a 50- m diameter photomultiplier tube used inSuper{Kamiokande. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.6 50- m photomultiplier tube quantum eÆ ien y as a fun tion of photonwavelength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.7 Layout of the ID ele troni s . . . . . . . . . . . . . . . . . . . . . . . 424.8 High and low energy trigger rate as a fun tion of elapsed days sin ethe start of data taking on April 1, 1996. . . . . . . . . . . . . . . . . 444.9 Blo k diagram of OD ele troni s. . . . . . . . . . . . . . . . . . . . . 454.10 Blo k diagram for a single hannel (or \daughter" ard) of a QTCmodule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.11 Cartoon of s ope tra es for di�erent stages in a single QTC hannel. . 475.1 Xe/s intillator ball alibration setup. . . . . . . . . . . . . . . . . . . 495.2 Relative gain distribution from Xe alibration. . . . . . . . . . . . . . 495.3 Sample single photoele tron distribution. . . . . . . . . . . . . . . . . 50xii

5.4 Timing alibration: Setup used to measure TQ maps for individualPMTs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.5 TQ map for a typi al PMT. . . . . . . . . . . . . . . . . . . . . . . . 525.6 Setup used to measure water attenuation length at di�erent wavelengths. 525.7 Attenuation length alibration for � = 420 nm. . . . . . . . . . . . . 535.8 Attenuation length vs. wavelength. The solid line shows the modelused in the Monte Carlo dete tor simulation. Points show the mea-surements using the N2 laser system. . . . . . . . . . . . . . . . . . . 545.9 log � Qlf(�)� versus l for osmi ray muons in a single run of Super{Kamiokande data taking. . . . . . . . . . . . . . . . . . . . . . . . . . 555.10 Re onstru ted momentum distributions for 16-MeV ele trons gener-ated by the ele tron LINAC for both data and Monte Carlo. Theagreement is about 1%. . . . . . . . . . . . . . . . . . . . . . . . . . . 565.11 Re onstru ted momentum distributions Mi hel ele trons for both dataand Monte Carlo. The Monte Carlo simulation is systemati ally 2:2%lower than the data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.12 Distributions of j~pQj vs. j~p�j for data and Monte Carlo low energy(E < 400 MeV) stopping muons. The momenta j~pQj and j~p�j arethe momenta al ulated from the number of PE dete ted and theCherenkov opening angle, respe tively. . . . . . . . . . . . . . . . . . 585.13 (a) Binned distributions of j~pQj=j~p�j vs. j~p�j for data and Monte Carlolow-energy stopping muons. (b) Per ent di�eren e between data andMonte Carlo (Data-MC)/Data. . . . . . . . . . . . . . . . . . . . . . 59xiii

5.14 Distributions of j~p�j vs. range for data and Monte Carlo stoppingmuons. The range is de�ned as the di�eren e between the muon en-tran e point and the vertex of the de ay ele tron. j~p�j was al ulatedusing the number of PEs dete ted. . . . . . . . . . . . . . . . . . . . 605.15 (a) Binned distributions of j~p�j vs. range for data and Monte Carlostopping muons. (b) Per ent di�eren e between data and Monte Carlo(Data-MC)/Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.16 Invariant mass distributions for �0s indu ed by atmospheri neutrinosfor both data and Monte Carlo. The agreement is about 3%. . . . . . 626.1 Fermi momentum distributions for s and p states in O16. . . . . . . . 646.2 E�e tive mass for nu leons in O16: . . . . . . . . . . . . . . . . . . . 656.3 Cross se tions for the K+p intera tion in the rest frame of the proton.Open triangles and ir les orrespond to data submitted to the Parti leData Group. Solid boxes and ir les orrespond to a partial waveanalysis by Hyslop et al. The line around 600 MeV illustrates the uto� momentum for K+ from p ! �K+ in the rest frame of thetarget proton. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.4 Flux of primary osmi rays used in Honda's al ulation. The topthree urves orrespond to al ulations for solar minimum (top), solaraverage (middle), and solar maximum (bottom) for Hydrogen. Simi-larly, the middle three orrespond to Helium and the bottom three toCNO. Points are from experimental measurements. . . . . . . . . . . 716.5 Neutrino ux in the middle of the solar y le at the Super{Kamiokandesite al ulated by Honda et al. The overall un ertainty is � 20%. . . 72xiv

6.6 Charged and neutral urrent quasi-elasti s attering ross se tions forboth �� and �. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736.7 Single-pion produ tion ross se tions. . . . . . . . . . . . . . . . . . . 756.8 Coherent-pion produ tion ross se tions. . . . . . . . . . . . . . . . . 766.9 Multiple-pion produ tion ross se tions. . . . . . . . . . . . . . . . . . 776.10 K produ tion ross se tions. These ross se tions are small omparedto those for single-� and multi-� produ tion. . . . . . . . . . . . . . . 786.11 � produ tion ross se tions. Like the ross se tions for K produ tion,they are small ompared to those for single and multi-� produ tion. . 796.12 Cumulative probabilities for absorption, inelasti s attering, hargeex hange, and no intera tion of positively harged pions traversing anO16 nu leus as a fun tion of the pion's momentum. . . . . . . . . . . 806.13 Di�erential ross se tions for �+-16O s attering. The points show theexperimental measurement of Ingram et al. and the histogram showsthe result of the Monte Carlo simulation. . . . . . . . . . . . . . . . . 818.1 A Q(�) distribution for a 525-MeV ele tron. . . . . . . . . . . . . . . 908.2 Vertex distributions for the 61 kiloton�year sub-GeV sample. Left�gure is for single-ring muons and right �gure is for multi-ring events. 918.3 Deviation of re onstru ted vertex from true vertex for various nu leonde ay Monte Carlo samples. . . . . . . . . . . . . . . . . . . . . . . . 928.4 Hough transform pro edure. After transforming the PMT oordinatesfrom (x; y; z) spa e to (�; �) spa e, evenly distribute the harge fromthe PMT in a ir le around it. The ir les overlap in the enter of theCherenkov ring orresponding to the dire tion of the tra k. . . . . . . 93xv

8.5 An example two-ring event and its hough transforms: a) the a tualevent b) tube hits in �-� spa e ) ontour plot of Hough map d) 3-dimensional plot of Hough transform. The two peaks in Hough spa e an learly be seen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 948.6 Number of rings for the 61-kton�year data sampel (points) and 40-yearatmospheri neutrino Monte Carlo (normalized to the 61-kton�yearlivetime). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 958.7 EÆ ien y urves as a fun tion of parti le momentum for pions and -rays in p ! ��K+ , n ! ��K0 , p ! �+K0 , and p ! e+K0 MonteCarlo samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 968.8 The expe ted angular photoele tron distribution orresponding to a525-MeV ele tron. This distribution takes into a ount dete tor e�e tslike geometry and light attenuation. . . . . . . . . . . . . . . . . . . . 988.9 The expe ted angular photoele tron distribution orresponding to a725-MeV muon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 998.10 The parti le identi� ation parameter for single ring sub-GeV events forthe 991-day exposure of Super{Kamiokande (points with error bars)and the (normalized) 40-year equivalent sample of atmospheri neu-trino Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1018.11 Conversion from photoele trons orresponding to a tra k to momen-tum for ele trons and muons. . . . . . . . . . . . . . . . . . . . . . . 102xvi

9.1 p ! ��K+ ; K+ ! �+�0 Monte Carlo event in unrolled view andfront-ba k view. The two -rays from the de ay of the �0 an be seen learly in both views. A ollapsed Cherenkov ring from the �+ anbe seen in the ba kwards hemisphere (right ir le) in the front-ba kview. The spike in the time histogram around 1250 ns is from thede ay ele tron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1089.2 Invariant mass distribution for events passing riteria A1 and A2 forp! ��K+ ;K+ ! �+�0 Monte Carlo and the 40-year equivalent sam-ple of atmospheri neutrino Monte Carlo. . . . . . . . . . . . . . . . 1099.3 Qba k vs. j~p j for p ! ��K+ ;K+ ! �+�0 and 40-year atmospheri neutrino Monte Carlo samples. The Qba k ut is asymmetri be auseit maximizes S/pN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1119.4 Qba k vs. j~p j distribution for 61-kton�year data. No events pass thesele tion riteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1119.5 Sample time of ight (TOF) subtra ted timing distribution for a p!��K+ ; K+ ! �+�� Monte Carlo event with prompt -ray emission. . 1139.6 Des ription of quantities used in the prompt -ray sear h. . . . . . . 1159.7 N12nshit distributions for p ! ��K+ ;K+ ! �+�� Monte Carlo, 40-yearequivalent Monte Carlo event samples, and 61-kton�year SK data.The p ! ��K+ ;K+ ! �+�� Monte Carlo was normalized to 2.3events/61 kton�year. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1169.8 Momentum spe trum for events passing riteria B1-B2. The pointswith error bars are the data, the solid line is the 90% C.L. upper limiton the ex ess of signal events with the atmospheri neutrino MonteCarlo events, and the dashed line is the same as the solid line with thesignal ex ess removed. . . . . . . . . . . . . . . . . . . . . . . . . . . 118xvii

9.9 n! ��K0 ; KS ! �0�0 Monte Carlo event. . . . . . . . . . . . . . . 1209.10 j~p sj vs. M s for events passing riteria C1-C2 for n ! ��K0 ; KS !�0�0 Monte Carlo and 40-year atmospheri neutrino Monte Carlo. . 1219.11 j~p sj vs. M s for events passing riteria C1-C2 for n ! ��K0 ; KS !�0�0 Monte Carlo and 40-year atmospheri neutrino Monte Carlo.These events also satisfy the requirement that at least one pair ofe-like rings re onstru ted to the �0 mass. . . . . . . . . . . . . . . . 1229.12 j~p sj vs. M s for events passing riteria C1-C2 and the �0 mass re-quirement for the 61-kton�year Super{Kamiokande data sample. Thenumber of events passing the sele tion riteria is onsistent with theexpe ted ba kground. . . . . . . . . . . . . . . . . . . . . . . . . . . 1239.13 n! ��K0 ; KS ! �+�� Monte Carlo event. . . . . . . . . . . . . . . 1249.14 j~p��j vs. M�� for events passing riteria D1-CD for n! ��K0 ; KS !�+�� Monte Carlo and 40-year atmospheri neutrino Monte Carlo. . 1259.15 j~p��j vs. M�� for events passing riteria D1-D2 the 61-kton�yearSuper{Kamiokande data sample. Like the sear h for n ! ��K0 ;KS ! �0�0 , the number of events passing the sele tion riteria is onsistent with the expe ted ba kground. . . . . . . . . . . . . . . . 1269.16 p ! �+K0 ; KS ! �0�0 Monte Carlo in front-ba k view. The fourEM showers from the s from the de ays of the �0s (left hemisphere)are balan ed by the � tra k (right hemisphere). Note the spike in thetiming histogram at about 1600 ns from the de ay ele tron of the �. 1289.17 Momentum vs. mass for events passing riteria E1-E3 for p! �+K0 ;KS ! �0�0 Monte Carlo and 40-year atmospheri neutrino MonteCarlo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129xviii

9.18 � momentum vs. e-like mass for events passing sele tion riteria E1-E5 for p! �+K0 ; KS ! �0�0 Monte Carlo and 40-year atmospheri neutrino Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . . 1309.19 Total momentum vs. total mass and � momentum vs. e-like mass forthe 61-kton�year data sample in sear hing for p! �+K0 ; KS ! �0�0 .The events in the left �gure have passed riteria E1-E3 and the eventsin the right �gure have passed E4-E5. . . . . . . . . . . . . . . . . . 1319.20 p ! �+K0 ;KS ! �+�� Monte Carlo event in unrolled view andfront-ba k view. The two ollapsed Cherenkov rings from the twopions from the de ay of the KS balan e the tra k from the muon.Note the two spikes in the timing histogram at about 1500 ns and1700 ns from the two de ay ele trons. . . . . . . . . . . . . . . . . . 1329.21 j~ptotj vs. Mtot for events passing riteria F1-F2 for p ! �+K0 ;KS !�+�� Monte Carlo and 40-year atmospheri neutrino Monte Carlo. . 1349.22 Invariant mass of the two pions for events passing sele tion riteria F1-F4 for p! �+K0 ; KS ! �+�� Monte Carlo and 40-year atmospheri neutrino Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . . 1349.23 j~ptotj vs. Mtot for events passing sele tion riteria F1-F2 for the 61-kton�year data sample. . . . . . . . . . . . . . . . . . . . . . . . . . . 1359.24 Distribution of j~ptotj vs. j~p�j for events passing sele tion riteria G1-G2for p ! �+K0 ; KS ! �+�� Monte Carlo and 40-year atmospheri neutrino Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . . 1369.25 Distribution of j~ptotj vs. j~p�j for events passing sele tion riteria G1-G2for the 61-kton�year data sample. . . . . . . . . . . . . . . . . . . . . 137xix

9.26 Momentum vs. mass for events passing riteria H1-H2 for p! e+K0 ;KS ! �0�0 Monte Carlo and 40-year atmospheri neutrino MonteCarlo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1399.27 Momentum vs. mass for events passing riteria H1-H2 the 61-kton�yearSuper{Kamiokande data sample. . . . . . . . . . . . . . . . . . . . . 1409.28 p ! e+K0 ; KS ! �+�� Monte Carlo event. The two lower energy ollapsed Cherenkov rings are from the �+ and �� from the KS de ay. 1419.29 Momentum vs. mass for events passing riteria I1-I2 for p ! e+K0 ;KS ! �+�� Monte Carlo and 40-year atmospheri neutrino MonteCarlo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1429.30 Invariant mass of the two pions for events passing sele tion riteria I1-I4 for p! e+K0 ; KS ! �+�� Monte Carlo and 40-year atmospheri neutrino Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . . 1429.31 a) Total momentum vs. total mass for the 61-kton�year data samplefor events passing sele tion riteria I1-I2. b) M�� for the data eventin the 61-kton�year data sample whi h passed sele tion riteria I1-I4. 1439.32 Distribution of j~ptotj vs. j~pej for events passing sele tion riteria J1-J3for p ! e+K0 ; KS ! �+�� Monte Carlo and 40-year atmospheri neutrino Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . . 1459.33 Data sear h for p! e+K0 ; KS ! �+�� with sele tion riteria J1-J5.Total momentum vs. total mass for the 61-kton�year data sample. . . 14610.1 Summary of limits set in this dissertation and previous limits. . . . . 152xx

List of Tables2.1 Quarks and Leptons in the Standard Model . . . . . . . . . . . . . . 62.2 Some mesons and their quark ontent. . . . . . . . . . . . . . . . . . 62.3 Gauge bosons in the Standard Model . . . . . . . . . . . . . . . . . . 72.4 Standard Model parti les and their supersymmetri partners. . . . . . 192.5 Summary of sele ted Grand Uni�ed Theories and their predi tions fornu leon de ay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1 Summary of indire t dete tion methods . . . . . . . . . . . . . . . . . 283.2 Summary of various parameters of Iron Calorimeters. . . . . . . . . . 313.3 Summary of Water Cherenkov Dete tors . . . . . . . . . . . . . . . . 344.1 50- m PMT hara teristi s. . . . . . . . . . . . . . . . . . . . . . . . 414.2 Trigger types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.1 De ay modes of N15� whi h have -rays as de ay produ ts. . . . . . . 669.1 Breakdown of ba kground ontributions to the de ay p ! ��K+ ;K+ ! �+�0 . Nnorm is the number normalized to the neutrino os- illation hypothesis (see se tion 6.2.4 for an explanation). The % isthe normalized per entage ontribution to the ba kground. . . . . . 112xxi

9.2 Breakdown of ba kground ontributions to the de ay p ! ��K+ ;K+ ! �+�� with a prompt- ray emission. (See table 9.1 for anexplanation of Nnorm and %.) . . . . . . . . . . . . . . . . . . . . . . 1179.3 Summary of three methods used to sear h for p! ��K+ . . . . . . . 1199.4 Breakdown of ba kground ontributions to the de ay n! ��K0 ; KS !�0�0 (see table 9.1 for an explanation of Nnorm and %.) . . . . . . . 1239.5 Breakdown of ba kground ontributions to the de ay n! ��K0 ; KS !�+�� . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1269.6 Summary of two methods used to sear h for n ! ��K0 (see table 9.1for an explanation of Nnorm and %.) . . . . . . . . . . . . . . . . . . 1279.7 Breakdown of ba kground ontributions to the de ay p ! �+K0 ;KS ! �0�0 (see table 9.1 for an explanation of Nnorm and %.) . . . 1339.8 Breakdown of ba kground ontributions to the de ay p ! �+K0 ;KS ! �+�� in the s enario where only two rings were re onstru ted(See table 9.1 for an explanation of Nnorm and %.) . . . . . . . . . . . 1389.9 Summary of three methods used to sear h for p! �+K0 . . . . . . . 1389.10 Breakdown of ba kground ontributions to the de ay p ! e+K0 ;KS ! �0�0 (see table 9.1 for an explanation of Nnorm and %.) . . . 1409.11 Breakdown of ba kground ontributions to the de ay p ! e+K0 ;KS ! �+�� for the two-ring s enario (see table 9.1 for an expla-nation of Nnorm and %.) . . . . . . . . . . . . . . . . . . . . . . . . . 1469.12 Summary of three methods used to sear h for p! e+K0 . . . . . . . 1479.13 Summary of K mesons. Values taken from the Parti le Data Book. . 1479.14 Summary of �nal results for sear hes for p ! ��K+ , n ! ��K0 , p !�+K0 , and p! e+K0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1489.15 Summary of the sele tion riteria used to sear h for p! ��K+ . . . . . 148xxii

9.16 Summary of the sele tion riteria used to sear h for n! ��K0 . . . . . 1499.17 Summary of the sele tion riteria used to sear h for p! �+K0 . . . . 1499.18 Summary of the sele tion riteria used to sear h for p! e+K0 . . . . 15010.1 Summary of limits studied in this dissertation for Super{Kamiokande,IMB, Kamiokande, and Soudan II. . . . . . . . . . . . . . . . . . . . 151

xxiii

Chapter 1Introdu tionThe goal of parti le physi s is to understand nature at its most fundamental level. Byexploring the world at ever de reasing distan e s ales, parti le physi ists have beenable to dig deeper and deeper into the subatomi world. Probing smaller distan eshas required in reasingly powerful parti le a elerators whi h serve as mi ros opeswhi h an see into the subatomi world. These powerful ma hines a elerate parti lesto high energies and provide a me hanism by whi h new parti les an be materializedand smaller distan es an be probed.Physi al observations hange when probing smaller distan es, or equivalently,higher energies. For instan e, by the mid 1930s it was known that atoms are made ofa small dense nu leus omposed of neutrons and protons around whi h ele trons orbit.At this time it was thought that protons were fundamental, however it was learnedin the 1960s that protons are omposed of smaller onstituents alled \quarks" [1℄.This was a omplished by probing protons with ele trons having suÆ iently highenergies [2℄. In this way, the understanding of parti le physi s be ame more a uratewhen looking at smaller distan e s ales.Through the years, physi ists have been able to build a elerators whi h ould1

2a elerate parti les to higher and higher energies and in doing so many ex iting dis- overies were made. After years of exploring the energy frontier with these ma hinesand developing theories based on these measurements, the Standard Model of parti lephysi s has been reated. This is the model that is widely a epted today. The ur-rent understanding is that there are a handful of fundamental parti les out of whi heverything is made. Protons and neutrons are omposed of the fundamental \up"and \down" quarks. Ele trons, whi h orbit nu lei omposed of protons and neutronsto make atoms, are themselves fundamental. Heavier versions of the up and downquarks and the ele tron also exist but are unstable and de ay before they an formsomething that we an tou h, see, or feel. There are also elusive neutrinos whi h arevery light and diÆ ult to dete t. Finally, there are four fundamental for es: strong,ele tromagneti , weak, and gravity.It is reasonable to ask the question: is this present understanding of naturalphenomena suÆ ient to des ribe physi s at even smaller distan es (or equivalently,higher energies)? Theoreti al predi tions and experimental data suggest that thefour for es behave di�erently at extremely short distan es. In fa t, these predi tionsstate that at distan es of more than 1013 times shorter than the urrent ability toprobe, the for es have the same strength: they are said to be \uni�ed." But how ansu h small distan es be probed? The energy required is about 1013 times more thanthe urrent te hnology allows. It is likely impossible to build a parti le a elerator apable of a hieving su h a large energy. This is where sear hing for proton de aybe omes useful.To understand why proton de ay is so useful, �rst think about the four for esin nature. For ea h of these, there are for e- arrying parti les whi h transmit thefor es. An analogy an be drawn to two people playing at h. By passing the ballba k and forth, the ball ex hanges a for e between the two people. By omparing

3the rate at whi h we an pass a golf ball ba k and forth to the rate at whi h we anpass a 50-lb. medi ine ball ba k and forth, it is easy to see that the latter has a mu hslower rate. In a similar way, in the subatomi world, heavier for e arriers result inpro esses whi h pro eed at a slower rate. Consider the de ay of the muon (a heavierversion of the ele tron) whi h is aused by the weak for e. Compared to the de ayof a parti le via the strong or ele tromagneti for e, the muon lifetime is extremelylong. This an be attributed to the ex hange of the heavy parti le whi h mediatesthe weak for e, the W boson.Let us now return to the theories where the four for es are uni�ed at a verysmall distan e s ale. In these theories, new for e arrying parti les whi h are notpart of the Standard Model exist whi h an ause protons to de ay. However themasses of these parti les are extremely large: more than 1013 times larger than theWboson. Therefore proton de ay is predi ted to be extremely rare and proton lifetimespredi ted to be extremely long.Sin e proton de ay is the result of a physi s pro ess whi h o urs at an extremelyshort distan e s ale, sear hing for it is an indire t probe of these short distan es (orequivalently, high energies). In this way proton de ay provides a method by whi hwe an probe energies whi h are unattainable by a elerator experiments.The experimental method to sear h for nu leon de ay is simple (nu leon is ageneri term for either a proton or a neutron residing in a nu leus of an atom). Avery large sample of nu leons is assembled and observed for a period of time with adete tor whi h an dete t the de ay produ ts of a single nu leon. This dissertationutilizes the Super{Kamiokande dete tor whi h sits deep underground in the Mozumimine of the Kamioka Mining and Smelting ompany in the Japanese Alps. Thevolume of the dete tor is water, whi h serves as the sour e of nu leons. The walls ofthe tank are lined with photomultiplier tubes whi h dete t the Cherenkov light from

4parti les passing through the volume of the tank. If a nu leon in a water mole ulede ays, its de ay produ ts will generate this radiation. The patterns of Cherenkovlight proje ted onto the walls of the dete tor and dete ted by the photomultipliertubes will have hara teristi s whi h will distinguish it as a nu leon de ay event.This dissertation presents the results of a sear h for nu leon de ay into modesfavored by a spe i� type of uni� ation theory: supersymmetri grand uni� ation.This theory is elaborate in that it postulates the existen e of an entirely new setof parti les. For every parti le in the Standard Model, it is postulated that thereexists a orresponding \superpartner." These parti les have not yet been observedhowever some of them have masses whi h are just above the urrent ability to probewith a elerators. Other \superpartners" are extremely heavy and ause nu leons tode ay into spe i� modes. Observation of nu leon de ay into these modes would be ahint of things to ome at the next generation a elerator, the Large Hadron Collider(LHC) in Europe, set to turn on within the next de ade. It would also provide awindow into an energy frontier whi h no ollider will ever be able to look dire tly.

Chapter 2Theoreti al Motivation2.1 The Standard Model2.1.1 Quarks and LeptonsQuarks and leptons are the fundamental spin-12 fermions in the Standard Model (seetable 1). The ele tron and its orresponding neutrino, with harges of -1 and 0, aresome familiar leptons. In ontrast to leptons, quarks are fra tionally harged funda-mental parti les whi h annot exist by themselves but omprise hadroni parti lessu h as protons, neutrons, and pions. For example, a proton is omposed of two\up" quarks and one \down" quark. A positively harged pion is a bound state ofone \up" quark and the anti-parti le of the \down" quark. Pions are examples ofmesons whi h in general are omposed of a quark and an anti-quark (see table 2.2for a list of some mesons and their quark ontent). Every fermion listed in table 2.1has a orresponding anti-parti le whi h has the same mass but opposite quantumnumbers. For example, the positron is the antiparti le of the ele tron with harge ofQ = +1. 5

6 parti le mass (MeV/ 2) harge Lepton no. Baryon no.�e 0 0 Le = 1 0First e� 0.511 �1 Le = 1 0Family up quark (u) a few MeV/ 2 23 0 13down quark (d) a few MeV/ 2 �13 0 13�� 0 0 L� = 1 0Se ond �� 105.7 �1 L� = 1 0Family harm quark ( ) 1:3� 103 23 0 13strange quark (s) � 100 �13 0 13�� 0 0 L� = 1 0Third �� 1:78� 103 �1 L� = 1 0Family top quark ( ) � 1:7� 105 23 0 13bottom quark (s) 4:2� 103 �13 0 13Table 2.1: Quarks and Leptons in the Standard ModelMeson Quark Content mass (MeV/ 2)�+ u �d 139.6�0 12(u�u� d �d) 135.0�� d�u 139.6K+ u�s 493.7K0 d�s 497.7�K0 s �d 497.7K� s�u 493.7Table 2.2: Some mesons and their quark ontent.2.1.2 For esFour fundamental for es are observed in nature: strong, ele tromagneti , weak, andgravity. The strong for e is responsible for holding nu lei together, ele tromagnetisma ounts for the for e between two harged parti les, and the weak for e mediatesde ay pro esses su h as beta de ay n ! pe� ��e. Gravity is the most familiar to us,but is the weakest and least understood of the four.The fundamental for es are mediated via the ex hange of gauge bosons whi h

7parti le For e mass (MeV/ 2) harge Relative Strengthgluons (g) strong 0 0 � 1photon ( ) ele tromagneti 0 0 � 1=137W bosons (W�) weak 80:4� 103 �1 � 10�5Z boson (Z0) weak 91:2� 103 0 � 10�5graviton gravity 0 0 � 10�38Table 2.3: Gauge bosons in the Standard Modelare transfered between parti les experien ing the for e. \Gluons" arry the strongfor e between quarks in nu lei. The light quantum, the photon, transmits the ele -tromagneti for e between harged parti les. The weak for e is mediated by the W�and Z0 bosons. Experimental eviden e for the gluons, W�, Z0, and exists. Itis postulated that gravity is mediated by a \graviton," however there is no dire texperimental eviden e for its existen e. Table 2.3 summarizes the properties of thefour for es.2.1.3 Conservation LawsQuantities whi h do not hange with time are designated as \ onserved." For exam-ple, energy, momentum, and angular momentum are three kinemati quantities thatare onserved in all intera tions. Another important quantity whi h is onserved inall intera tions is harge: the sum of all harges in the initial state of a rea tion mustequal the sum of all harges in the �nal state of a rea tion.The lepton and baryon quantum numbers whi h are outlined in table 2.1 are onserved in all observed intera tions. For instan e, the � de ay �! e via the ele -tromagneti intera tion does not o ur be ause it does not onserve lepton number.The initial state has L� = 1 and Le = 0 and the �nal state has L� = 0 and Le = 1.An example of a baryon number violating pro ess is the proton de ay p ! e+�0

8whi h has an initial state of B = 1 and a �nal state of B = 0. The idea of baryonnumber onservation was �rst proposed by Weyl in 1929 [3℄ when he postulated thatthe proton was the Dira ounterpart to the ele tron. As a result, the number ofele trons and protons remain onstant in an intera tion. After the dis overy of thepositron (the a tual ounterpart to the ele tron) the idea of baryon number on-servation was re�ned by St�u kelberg in 1938 [4℄ and again by Wigner in 1949 [5℄.With these proposals, protons and neutrons were assigned a \heavy harge" whi h orresponds to baryon number. This postulation of baryon number onservation ledto experiments whi h set out to test the proposal.2.1.4 SymmetryConserved quantities and symmetries in parti le physi s are intimately related. This an be seen using the Lagrangian formulation to des ribe a system. A physi al system an be des ribed by its Lagrangian, from whi h the lassi al equations of motion anbe derived. If the form of the Lagrangian remains un hanged after transforming the�elds in the Lagrangian (by a rotation or translation, for instan e), it is \symmetri "under the transformation. For ea h of these possible transformations for whi h theLagrangian remains invariant, there is an asso iated onservation law. Examplesare onservation of energy, momentum, and angular momentum whi h follow fromthe invarian e of the Lagrangian under general Lorentz spa e-time transformations.In addition to the onserved quantities asso iated with spa e-time transformationsthere are internal symmetries whi h are not dependent upon the spatial and temporal oordinates of the system. An example of an internal symmetry is isospin invarian ein nu lear intera tions.Physi ists typi ally utilize group theory to des ribe symmetries and onservation

9laws. To show how this works, onsider the group SU(2) whi h is used to des ribe thespin-12 system of quantum me hani s. The ommutation relations of the generators ompletely des ribe SU(2) [Li; Lj℄ = i�ijkLk (2.1)where �ijk is the ompletely antisymmetri tensor and (i; j; k) orrespond to the(x; y; z) oordinates. The Li matri es an be written in terms of the Pauli spinmatri es �i as Li = 12�i whi h are tra eless unitary matri es. It follows that anyarbitrary tra eless unitary matrix an be written asR = ei~��~L (2.2)where ~� is an arbitrary s aling ve tor. The Li's an generate any general transforma-tion within the spa e and are therefore alled \generators." The two physi al statesspin-up, j+i, and spin-down,j�i, are the orthogonal eigenstates of the system and onstitute a \spin-12 doublet." Any state in the system an be written as a linear ombination of these two eigenstates. Finally, there are two important operatorsL� = (L1 � iL2) (2.3)whi h represent mixing between states, L�j�i = j�i. The entire system may nowbe des ribed in terms of its \generator matrix" L and its \doublet" L = 12 2664 lz l+l� �lz 3775 ! 0BB� updown 1CCA (2.4)The diagonal elements of L represent the proje tion of the state while the o�-diagonal elements represent transformations between eigenstates. This is where an

10analogy an be drawn to a system in parti le physi s: the matri es Lz and L� an be ompared to \gauge bosons" (the Z andW� bosons, for example) and the \doublet" an be ompared to a physi al doublet of fermions (the ele tron and its neutrino,for example). This example an now be used to provide a basi des ription of theStandard Model of parti le physi s.2.1.5 SU(3) � SU(2)W � U(1)Y Des riptionThe Standard Model is based on the dire t produ t SU(3) �SU(2)L�U(1)Y gaugegroup. The group SU(3) des ribes the strong for e between the quarks. The quarkshave \ olor harge" and omprise a olor triplet having states arbitrarily labeledred, green, and blue. The gluons an be represented in the generator matrix Ggluonsand the system an be ompa tly writtenGgluons = 26666664 gr�r gr�g gr�bgg�r gg�g gg�bgb�r gb�g gb�b

37777775 ! 0BBBBBB� redgreenblue1CCCCCCA (2.5)

where gb�b = �gr�r � gg�g. This des ription is the analog SU(3) des ription of SU(2)des ribed in equation 2.4. The o� diagonal matrix elements of Ggluons represent the oupling of the di�erent olor states to one another. A pi torial representation of theSU(3) system is shown in �gure 2.1.Ele troweak theory is the uni� ation of ele tromagnetism and the weak for e. Itis governed by the dire t produ t SU(2)L�U(1)Y symmetry [6, 7, 8℄. The subs ript Lon SU(2) is the statement that only left-handed parti les are subje t to intera tions ofthis symmetry group, the so- alled \V -A" intera tion. Negle ting mass, left-handedparti les are parti les whose spin ve tor is in the opposite dire tion of its momentum

11g(bg)

g(gb) g(rb)g(br)

g(rg)

g(gr)

redgreen

blueFigure 2.1: Pi ture of SU(3). The gluons g���, where � and � orrespond to the olorindex, onne t di�erent olor states.ve tor. The subs ript Y on U(1) denotes a quantity alled \weak-hyper harge" whi his de�ned to be Y = 12 (Q� T3) (2.6)where Q is harge from ele tromagnetism and T3 is the eigenvalue for the 3rd om-ponent of weak isospin from SU(2)L. From equation 2.6 one an see that ele tro-magnetism and the weak intera tion are intimately related.If unbroken, the gauge theory of SU(2)L � U(1)Y is related to four masslessgauge bosons, W �1;2;3 from SU(2)L and a� from U(1)Y . This is not onsistent withobservations in nature whi h has one massless boson (the photon) and three massive(W� and Z bosons) gauge bosons. One way to resolve this is to introdu e a s alarparti le alled the Higgs boson. The Higgs generates masses for the W and Z bosonsand mixes the massless gauge bosons orresponding to the massive Z of the weakintera tion and the massless photon of ele tromagnetismZ� = �a� sin �W +W �3 os �W (2.7)

12 A� = a� os �W +W �3 sin �W (2.8)where � is the spa e-time Lorentz index, A� is the massless gauge �eld of ele tro-magnetism (the photon), and �W is the \weak mixing angle" whi h parameterizesthe relation between the weak and ele tromagneti for es. The oupling onstantsof SU(2)L and U(1)Y an then be expressed in terms of the �ne stru ture onstant�em of ele tromagnetism and �W .The parti les from table 2.1 form the weak doublets0BB� �ee 1CCAL 0BB� ud0 1CCAL ; 0BB� ��� 1CCAL 0BB� s0 1CCAL ; 0BB� ��� 1CCAL 0BB� tb0 1CCAL (2.9)The subs ript L denotes left-handedness. The d0,s0, and b0 in the weak doublets area tually admixtures of the olor d, s, and b mass eigenstates. These admixtures areparameterized by the Cabibbo-Kobayashi-Maskawa mixing matrix [9, 10℄.The quarks ome in both SU(3) olor triplets and SU(2)L weak doublets, how-ever the leptons ome only in SU(2)L weak doublets. They do not ome in SU(3) triplets and for this reason they are alled \ olor singlets" whi h means that they donot feel the \ olor" for e. There are also right-handed leptons, eR, �R, and �R, andright handed quarks. The right-handed leptons are both olor singlets and singletsunder SU(2)L while the right-handed quarks are olor triplets but singlets underSU(2)L. An important aspe t of the Standard Model is that a right-handed neutrino(or left-handed anti-neutrino) does not exist. A graphi al des ription of the �rstfamily of the SU(3) � SU(2)L � U(1)Y standard model is shown in �gure 2.2.

13+W

e

b

bd

u-

SU(2)

SU(3) gluons

r

eν

gd

ug

d

ru

Figure 2.2: Simple pi ture of the Standard Model. The gluons mediate intera tionsbetween various olor states andW� bosons mediate intera tions between the SU(2)eigenstates.2.1.6 ProblemsDespite the su ess of the Standard Model, there remain some unanswered questions.To name a few:� Why is nature des ribed by the dire t produ t SU(3) �SU(2)L�U(1)Y sym-metry group?� Why are the harges of quarks in units of 1=3 the ele tron harge?� Why do both quarks and leptons ome in weak doublets?Grand Uni� ation Theories (GUTs) attempt to explain these questions.2.2 Grand Uni� ationGrand Uni�ed Theories (GUTs) are an attempt to unify the for es in nature into asingle for e at some large energy s ale. This means that at some extremely smalldistan e s ale the for es in nature be ome indistinguishable from one another. Thisis des ribed quantitatively by the merging of the oupling onstants of the for es at

14this high energy s ale. When onstru ting su h theories one must hoose a symmetrygroup whi h ontains the observed SU(3)� SU(2)�U(1) stru ture of the StandardModel su h as SU(5) or SO(10). By examining the stru ture of the symmetry group,predi tions an be made and tested against experiment. Nu leon de ay is predi tedby all GUTs in whi h SU(3) �SU(2)L are uni�ed in a single group and is thereforea good experimental test of these theories.2.2.1 Running Coupling ConstantsThe oupling onstants of the strong and ele troweak intera tions are not a tually onstants but vary with in reasing energy s ales (or equivalently, de reasing distan es ales). One of the �rst hints of Grand Uni� ation was the apparent onvergen eof the three oupling onstants �1;2;3 at some extremely high energy s ale. Theevolution of �i's is des ribed quantitatively to �rst order by1�i (E) = 1�GUT + 16� bi logMXE (2.10)where �i (i = 1; 2; 3) are the oupling onstants of the U(1)Y , SU(2)L, and SU(3) intera tions. E is the energy s ale at whi h the measurements are made, �GUT isthe value of � when the ouplings meet, MX is the GUT energy s ale, and bi arethe oeÆ ients for the �rst order al ulations. The oeÆ ients bi are spe i� to thedi�erent theories and depend on the number and harges of the fermions.2.2.2 Minimal SU(5)The smallest gauge group whi h an ontain SU(3) � SU(2) � U(1) is SU(5). Thesimplest GUT based on this symmetry group is alled \Minimal SU(5)" and was�rst proposed by Georgi and Glashow in 1974 [11℄. The generator matrix is written

15asVSU(5) =

2666666666666664gr�r � 2p30a gr�g gr�b X1 Y1gg�r gg�g � 2p30a gg�b X2 Y2gb�r gb�g gb�b � 2p30a X3 Y3�X1 �X2 �X3 1p2W 3 + 3p30a W+�Y1 �Y2 �Y3 W� � 1p2W 3 + 3p30a

3777777777777775(2.11)and the fermions are ontained in the �5 and 10 representations (analogous to thedoublet in SU(2) and the triplet in SU(3))�5 =

0BBBBBBBBBBBBBB��dr�dg�dbe���e

1CCCCCCCCCCCCCCAL 10 =2666666666666664

0 �ub ��ug �ur �dr��ub 0 �ur �ug �dg�ug ��ur 0 �ub �dbur ug ub 0 e+dr dg db �e+ 03777777777777775L (2.12)

The SU(3)�SU(2)�U(1) stru ture of the Standard Model is ompletely ontainedin this des ription: the upper left 3 � 3 of VSU(5) ontain the gluons of SU(3) andthe bottom right 2� 2 ontain the W s of SU(2). The diagonal elements also ontainU(1)Y . Below the masses MX;Y the SU(3) � SU(2) � U(1) pi ture be omes valid:SU(5) is said to be \broken" to the SU(3)�SU(2)�U(1) stru ture of the StandardModel.An attra tive feature following from this theory is harge quantization. The pho-ton orresponds to the harge generator and is ontained in VSU(5). The generatorsof the group must be tra eless so applying the harge operator on the �5 implies the

16 ondition 3Q(d) = �Q(e+) (2.13)explaining why harges of quarks are in units of 1=3 the harge of the ele tron.d�����R )))((( X�����e+ u�����R )))((( Y �����e+ d�����R )))((( Y ����� ��u�����R )))((( X����� �u d�����R )))((( Y ����� �u

Figure 2.3: Feynman diagrams for new intera tions predi ted in Grand Uni�ed The-ories.In addition to the bosons of the Standard Model, VSU(5) ontains new X and Ygauge bosons with massesMX;Y whi h mediate new intera tions not ontained in theStandard Model (�gure 2.3). These intera tions do not onserve baryon or leptonnumber (B or L) but do onserve B�L and lead to nu leon de ay via the ex hangeof one of these massive bosons. Some examples of the favored proton de ay modein mimimal SU(5), p ! e+�0, are shown in �gure 2.4. The proton lifetime has thefollowing dependen e �p �p! e+�0� � 1�2GUT M4Xm5p (2.14)where mp is the mass of the proton and MX;Y is the mass of the new gauge boson

17duu e+�uuX- ))(- ��- udu e+�uuY- ))(- ��-uud

e+�ddX���R ���� _ _ _ _ _^ ^ ^ ^ �̂�����I-duu

e+�uuY���R ���� _ _ _ _ _^ ^ ^ ^ �̂�����I-Figure 2.4: Feynman diagrams for the favored proton de ay in minimal SU(5), p!e+�0.

whi h is lose to the s ale of the uni� ation of the oupling onstants. To make apredi tion for the proton lifetime,MX;Y must be estimated. This is a omplished byusing equation 2.10 to estimate the uni� ation s ale. The al ulation of the bi's forminimal SU(5) to �rst order areb3 = 33 � 4nfb2 = 22 � 4nf � 12b1 = � 4nf � 310 (2.15)where nf is the number of generations, or families. In the Standard Model thereare three families. Using the measured values for the oupling onstants �i, theuni� ation of the oupling onstants o urs aroundMX � 1015 GeV and is shown in�gure 2.5. This gives a predi tion for the proton lifetime into e+�0 of 1030�1:5 years

18[11℄. In addition to setting the uni� ation s ale, a predi tion for the weak mixingangle sin2 �W of 0:215� 0:005 is made.

log µ (GeV)

1/α

1/α3

1/α2

1/α1

Electroweak scale

GUT scale MX

Evolution of coupling constants in minimal SU(5)

0 2 4 6 8 10 12 14 16 180

10

20

30

40

50

60

70

80

Figure 2.5: Evolution of running oupling onstants in Minimal SU(5). Equations2.10 are solved to yield the uni� ation s ale MX and the weak mixing angle sin2 �W .The �i (i = 1; 2; 3) denote the ouplings for U(1)Y ,SU(2)L, and SU(3) , respe tively.Despite the aestheti ally pleasing simpli ity of minimal SU(5), experimental ob-servations have ex luded it. IMB set a limit of �(p ! e+�0) > 5:5 � 1032 years atthe 90% on�den e level [12℄ and Super{Kamiokande has re ently in reased this to1:6 � 1033 years (90% C.L.) [13℄. In addition, experimental observations reveal aweak mixing angle of 0:232 � 0:001, a signi� ant deviation from the predi tion of0:215� 0:005.

19Parti le Spin Superpartner SpinQuark (q) 1=2 \Squark" (~q) 0Lepton (l) 1=2 \Slepton" (~l) 0Photon ( ) 1 \Photino" (~ ) 1=2Gluon (g) 1 \Gluino" (~g) 1=2W 1 \Wino" ( ~W ) 1=2Higgs (H) 0 \Higgsino" ( ~H) 1=2Table 2.4: Standard Model parti les and their supersymmetri partners.2.2.3 Supersymmetri GUTsWhen al ulating the mass of the ele troweak Higgs boson assuming the existen eof a GUT, �rst order radiative orre tions depend on the large value of MX;Y . Thisleads to orre tions whi h are naturally mu h larger than the weak s ale. This is alled the \hierar hy problem." One way to re on ile this [14, 15℄ is to postulatean entirely new spe trum of parti les in su h a way that for every Standard Modelparti le there is a orresponding \superpartner." To e�e tively an el the radiative orre tions, the ontributions from the superpartners must be opposite in sign totheir orresponding Standard Model parti le. To a omplish this, the superpartnersmust have a spin whi h is 12 unit di�erent from the Standard Model partner. Thisis alled \supersymmetry": for every fermion in the Standard Model there existsa orresponding bosoni partner and for every boson in the Standard Model thereexists a orresponding fermioni partner (see table 2.4). Requiring the radiative orre tions to the Higgs mass to be manageable sets the s ale of the mass di�eren ebetween partners and superpartners���m2SUSY �m2SM ��� < O(1TeV2) (2.16)When in orporating the new spe trum of parti les into the al ulations for the

20evolution of the running oupling onstants, the onstants bi hange tob3 = 27 � 6nfb2 = 28 � 6nf � 3b1 = � 6nf � 95 (2.17)Putting these into equation 2.10, a larger uni� ation s ale is found (�gure 2.6). A omparison of the evolution of the ouplings in this model in orporating SUSY tothe non-SUSY model (�gure 2.5) reveals a higher uni� ation s ale for the SUSY aseby about an order of magnitude. MX;Y is predi ted to be about 1016 GeV omparedto about 1015 GeV in the non-SUSY ase. Sin e the de ay rate of the proton viathe ex hange of the X and Y gauge bosons s ales as � M�4X , the proton lifetimeinto e+�0 is suppressed by four orders of magnitude in SUSY GUTs ompared to thenon-SUSY Minimal SU(5). This is onsistent with the experimental non-observationof p! e+�0. In addition, the predi tion for sin2 �W be omes 0:236� 0:002 [16℄ whenin orporating SUSY, mu h loser to the experimental value. In orporating SUSYthen solves three problems en ountered in non-SUSY GUTs: the hierar hy problem,the disagreement between predi tion and measurement for sin2 �W , and the non-observation of the proton de ay p! e+�0.Despite the fa t that nu leon de ay via the ex hange of the heavy gauge bosonsis suppressed in SUSY GUTs, there are other intera tions in the SUSY Lagrangianwhi h an mediate nu leon de ay. The type having the most signi� ant ontributionis the dimension 5 (d=5) operator via the ex hange of the heavy supersymmetri olortriplet Higgsino [17, 18, 19℄. The Feynman diagram for this intera tion is shown in�gure 2.7. These operators have the property that transitions from one family in theinitial state to the same family in the �nal state are not allowed. For instan e, the

21

log µ (GeV)

1/α

1/α3

1/α2

1/α1

Electroweak scale

GUT scale MX

Evolution of coupling constants in SUSY SU(5)

0 2 4 6 8 10 12 14 16 180

10

20

30

40

50

60

70

80

Figure 2.6: Evolution of running oupling onstants in SUSY. The ouplings mergeat a s ale about an order of magnitude larger than in minimal SU(5).proton is omposed of quarks from the �rst family, two \up" quarks and one \down"quark. An intera tion via the d=5 operator requires the se ond or third family tobe in the �nal state. All quarks ex ept a strange quark are kinemati ally disallowed,meaning that an anti-strange quark must be the �nal state. The anti-strange quarkbinds with a spe tator u or d quark to form a K meson. The favored de ay modesare therefore p! ��K+ and n! ��K0 (�gure 2.8).q

~q

~H

~

l

qq

q

~WFigure 2.7: The Feynman diagram for d=5 intera tions predi ted in SUSY GUTs.

22~

~

u

u νµ

p d

u

su

d

~

K+

HW~

Figure 2.8: Feynman diagram for the favored proton de ay in Supersymmetri GUTs,p! ��K+ . For n! ��K0 , repla e the spe tator u quark with a d quark.Sin e the Higgsino is a fermioni propagator, the amplitude ontains only onepower of the Higgsino mass. Therefore the nu leon lifetime s ales as� jd=5 � � M2HXm2SUSYm5p (2.18)where MHX is the mass of the heavy olor triplet Higgsino, mp is the proton mass,mSUSY is the s ale of SUSY breaking, and � is a fa tor whi h depends on variousparameters. The many free parameters in the model allow a wide range of predi tionsfor the nu leon lifetime. Parameters su h as the mass of the olor triplet HiggsinoMHX , the masses of the various squarks and sleptons, the mass of the Wino, the SUSYbreaking s ale, CKM mixing fa tors, and the masses of the ele troweak Higgsinodoublet all ontribute to the al ulation. In the minimal SUSY SU(5) GUT [20, 21℄,the al ulation by Hisano, Murayama, and Yanagida [22℄ yields lifetimes for p !��K+ and n! ��K0 of around 1030�2 years.Other models have been proposed beyond those based on SU(5). More popularmodels have been proposed based on an SO(10) symmetry group [23, 24, 25℄. SO(N)is the group whi h des ribes orthogonal rotations in an N dimensional spa e. Animportant feature of SO(10) is that all of the fermions an be ontained in a singlerepresentation. This is di�erent from SU(5) where the fermions must be broken up

23into �5 and 10 multiplets. The multiplet for SO(10) is the 16 whi h ontains the 10and �5 16 = 10+ �5 + 1 (2.19)Noti e that there is an additional singlet 1 representation within the 16. This pro-vides a pla e for a right-handed neutrino �R whi h does not exist in the StandardModel or SU(5). A diagram of the 16 representation is shown in �gure 2.9 (diagramfrom [26℄).gur u

g

ubνL

-e d νLd

eur ub+

rdr db g

ug

db dFigure 2.9: 16 multiplet in SO(10). The �5 and 10 of SU(5) are ontained withinthe 16. In addition, there is a 1 whi h orresponds to a left-handed anti-neutrino,the anti-parti le of a right-handed neutrino.The SO(10) model by Babu, Pati, and Wil zek [27, 24℄ has drawn attentionin light of the re ent eviden e for neutrino mass from Super{Kamiokande [28, 29℄.Neutrino mass �ts ni ely into the SO(10) group stru ture on whi h this model isbased. This theory is based on early ideas by Pati and Salam [30, 31℄ whi h in-trodu ed the group G(224) whi h is shorthand for the left-right symmetri groupSU(2)L � SU(2)R � SU(4) . The features whi h distinguish this model from theStandard Model are the existen e of a right-handed SU(2)R group and a SU(4) of\extended olor" instead of SU(3) . The idea of extended olor is that in additionto the three olors from SU(3) in the Standard Model, there is an additional olorfor the leptons. The existen e of the SU(2)R provides a pla e for the right-handedneutrino. A pi ture of G(224) is shown in �gure 2.10 (diagram from [26℄).

24

db

ugur u bR

SU(4)c

SU(2)L

SU(2)g

ur uguνL

+e

νL

b

g

dr d

ddr-e db

Figure 2.10: Stru ture of the Pati-Salam right-left symmetri G(224) whi h is basedon a SU(2)L�SU(2)R�SU(4) symmetry. This model provides a pla e for a right-handed neutrino.An important feature of this theory is that to generate neutrino masses the exis-ten e of a new set of olor triplet �elds is required. These �elds generate a new setof d=5 operators whi h predi t omparable rates for p! ��K+ and p! �+K0 of�(p! �+K0) � (20% to 50%)� �p! ���K+� (2.20)Using the Super{Kamiokande measurement for the mass di�eren e squared �m2[29, 28℄ between the two neutrino mass eigenstates as an input parameter, a protonlifetime of no more than about 5� 1033 years [32℄ into p! ��K+ is predi ted. Thisis within the observable range of Super{Kamiokande.In on lusion, a few models and their predi tions are summarized in table 2.5.

25Model Authors Modes �N (years)Minimal SU(5) Georgi and Glashow [11℄ p! e+�0 � 1030Dimopoulos and Georgi [20℄, Sakai[18℄ p! ��K+Minimal SUSY SU(5) Lifetime Cal ulations: Hisano, n! ��K0 1028 to 1032Murayama, and Yanagida [22℄SUGRA SU(5) Nath and Arnowitt [33, 34℄ p! ��K+ 1032 to 1034SUSY SO(10) p! ��K+with anomalous Sha� and Tavartkiladze [25℄ n! ��K0 1032 to 1035 avor U(1) p! �+K0SUSY SO(10) Lu as and Raby [23℄ p! ��K+ 1033 to 1034 (p)n! ��K0 1032 to 1033 (n)SUSY SO(10) p! ��K+with G(224), � mass Babu, Pati, and Wil zek [27, 24, 32℄ n! ��K0 < 1034p! �+K0Table 2.5: Summary of sele ted Grand Uni�ed Theories and their predi tions fornu leon de ay.

Chapter 3ExperimentsThe experimental sear h for nu leon de ay began long before the idea of GrandUni�ed Theories. Instead of GUTs, the motivation for early experiments was totest baryon number onservation. It wasn't until the late 1970s that experimentswere proposed whi h would sear h spe i� ally for nu leon de ay predi ted by GUTs.Around this time the SU(3) � SU(2) � U(1) stru ture of the Standard Model wasbeginning to be a epted and it be ame feasible that minimal SU(5) was indeed the\theory of everything." If this were the ase, the proton should de ay via p! e+�0with a lifetime of 1030�1:5. In the early 1980s tra king alorimeters began to turnon to sear h dire tly for proton de ay followed a ouple of years later by the moremassive water Cherenkov dete tors.Be ause the lifetimes of the proton and bound neutron are expe ted to be ex-tremely long, it is important that nu leon de ay experiments observe a large numberof nu leons for a suÆ ient amount of time to a hieve the desired sensitivity to thelong nu leon lifetime. In addition, it is important that the dete tors are able todete t nu leon de ay events eÆ iently. In general nu leon de ay experiments are di-vided into two ategories: indire t and dire t dete tion. Indire t dete tion methods26

27are insensitive to the parti ular nu leon de ay mode while dire t dete tions methodssear h for de ay produ ts from the nu leon de ay in real time. To redu e ba kgroundindu ed by osmi ray muons whi h are the result of primary osmi rays striking theupper atmosphere, dire t dete tion nu leon de ay experiments are typi ally pla edat signi� ant depths below the surfa e of the earth.3.1 Early ExperimentsRadio hemi al and geo hemi al methods were initially used to sear h for nu leonde ay [35℄. These methods sear hed for daughter nu lei whi h ould be the resultof the de ay of a nu leon within a sample of parent nu lei. For this reason they aredesignated as indire t dete tion. The virtue of these types of experiments is theirinsensitivity to the parti ular de ay mode into whi h the nu leon de ays. The basi idea of radio hemi al experiments is that a nu leon de ay within a heavy parent nu- leus an leave a hole in the residual nu leus whi h an indu e spontaneous �ssion.A sear h for the resulting nu lei from the �ssion rea tion is then performed. Geo- hemi al methods assemble a pure sample of nu lei and periodi ally sear h it for rareisotopes whi h might be the result of the de ay of one of the nu leons in the nu leus.Sin e there are modest limits to the quantity of a sample whi h an be assembledand sear hed, these methods ould only rea h nu leon lifetime sensitivities of � 1026years. A summary of various radio hemi al and geo hemi al experiments is shownin table 3.1 [36℄.The �rst dire t dete tion experiment was by Reines, Cowan, and Goldhaber inthe 1950s using a dete tor designed to dete t neutrinos [37℄. It was 60 meters un-derground and was made of 300 liters of liquid s intillator. In addition to dete tingneutrinos, the large sour e of nu leons in the dete tor made it possible to also test

28Method nu leon lifetime AuthorsSpontaneous �ssion 232Th 1023 years Flerov et al. [43℄129Xe!128Xe 1025 years J.C. Evans and R.I. Steinberg [44℄39K!38K or 38Ar 1026 years R.I. Steinberg and J.C. Evans [45℄Table 3.1: Summary of indire t dete tion methods .baryon number onservation. The test was quite rude: the ount rate was he kedfor an ex ess over the expe tation from osmi ray muons resulting in a limit on theproton lifetime of 1022 years. The liquid s intillator method was improved over theyears [38, 39, 40, 41℄ ulminating in a total nu leon lifetime al ulated by Learned,Reines, and Soni in 1979 of �p > 1030 years at the 90% on�den e level [42℄.3.2 Iron alorimeterWith the hope that the rate of proton de ay via p ! e+�0 fell in the middle of therange predi ted by minimal SU(5), the �rst iron alorimeters were designed to havea sensitivity of nu leon lifetimes up to about 1031 years. The se ond wave dete torshad larger mass and therefore sensitivity to longer lifetimes. Iron alorimeters sear hdire tly for the de ay produ ts of the nu leon and are typi ally omposed of ironplates, whi h serve as a sour e of nu leons, interspersed with dete tors whi h tra kparti les traversing the dete tor. The virtue of iron alorimeters is their ex ellenttra king resolution. The drawba k is that instrumentation of iron is expensive, re-sulting in a high ost per kiloton. Also, nu lear e�e ts on the daughter parti les froma nu leon de ay are more ompli ated and prominent in iron ompared to oxygen.Table 3.2 summarizes the hara teristi s of various iron alorimeters.

293.2.1 Soudan (1981-1990)The �rst Soudan dete tor was situated in the Soudan mine whi h is lo ated in north-ern Minnesota. The dete tor was omposed of 432 on rete slabs ea h having 8proportional tubes. The on rete served as the sour e of nu leons and was loadedwith ta onite on entrate resulting in a on entration of 57% iron, 29% oxygen, 13% al ium, and 1.2% hydrogen. The dete tor was lo ated at about 2000 meters waterequivalent (m.w.e.) below the surfa e of the earth and had a total mass of 31.4metri -tons. Nu leon de ay was not observed by Soudan and they set a limit on theproton lifetime via p! e+�0 of 1.3�1030 years [46℄.3.2.2 KGF (1980-1992)The Kolar Gold Field (KGF) nu leon de ay experiment was lo ated in the KolarGold Mines in India [47℄. The dete tor had 34 layers of alternating 12-mm thi k ironplates interspersed with 10 m � 10 m proportional ounters. Its total mass was0.140 kilotons and it was pla ed extremely deep underground at a depth of m.w.e.in order to signi� antly redu e the ba kground from osmi -ray muons.Ex itement ame in the early 1980s when KGF reported an anomaly in theirdata whi h they interpreted to be aused by nu leon de ays [47, 48℄. The non-observation of nu leon de ay from every other experiment at the time refuted this laim. Based on the number of observed events they estimated the nu leon lifetime tobe �N � 6�1030 years. If this were the ase, Super{Kamiokande would be expe tedto see several hundreds of events from nu leon de ay after 1-2 years of livetime.

303.2.3 NUSEX (1982-1988)The NU leon Stability EXperiment (NUSEX) was lo ated at a depth of 4800 m.w.e.beneath Mont Blan in a highway tunnel onne ting Italy and Fran e [49℄. Thedete tor onsisted of a sandwi h of 134 layers of alternating 1 m � 3.5 m � 3.5 miron plates and streamer tubes of ross-se tion of 9 mm�9 mm. The total mass ofthe dete tor was 0.150 kiloton.3.2.4 Frejus (1984-1988)The Frejus nu leon de ay dete tor was lo ated in the Frejus highway onne tingModane, Fran e to Bardone hia, Italy [50℄. It onsisted of 912 layers of 3-mm thi kiron plates and ash tubes with 5 mm � 5 mm ross-se tion. Every 8 layers therewas a layer of Geiger tubes whi h provided a trigger for the ash tubes. Be ause ofthe long readout time of the ash tubes (2-3 se onds), the rate of osmi ray muons rossing the dete tor had to be small to minimize deadtime. This was a hieved bypla ing it at a depth of 4800 m.w.e. resulting in a muon rate of about 20 per hour.The mass of the dete tor was 0.9 kilotons.3.2.5 Soudan 2 (1988-Present)The Soudan 2 dete tor [51℄ is a larger version of the �rst Soudan dete tor [46℄. Thisiron alorimeter is lo ated in the Soudan iron mine in Northern Minnesota and has atotal mass of 0.974 kiloton. It is omposed of 224 (2.7 m � 1.0 m � 1.2 m) modulesea h of whi h is made of drift tubes layers interspersed with iron sheets. A ross-se tional view of a module reveals a \honey omb"-like stru ture. A virtue of Soudan2 is that the K+ from p! ��K+ an be dete ted dire tly. This is be ause it is highlyionizing and an therefore be tra ked in the dete tor. The tra ks of the subsequent

31Dete tor mass exposure depth (m.w.e.) nu leon lifetime(kiloton) (kton�year) sensitivity (years)KGF 0.140 0.126 [48℄ 6800 1030 to 1031NUSEX 0.150 0.130 [52℄ 5200 1030 to 1031Frejus 0.9 2.0 [53℄ 4800 1031 to 1032Soudan 1 0.031 0.3 [46℄ 2000 1030Soudan 2 0.974 4.4 [54℄ 2000 1031 to 1032Table 3.2: Summary of various parameters of Iron Calorimeters.de ay produ ts an be seen where the K+ stops. Being able to dire tly dete t theK+ and its de ay provides very powerful ba kground reje tion riteria.3.3 Water Cherenkov dete torsWater Cherenkov dete tors use Cherenkov radiation, an opti al sho k wave produ edby harged parti les traveling faster than the speed of light in the medium (se tion4.1.1), to tra k harged parti les passing through the dete tor. These dete tors aretanks of water instrumented with photomultiplier tubes (PMTs) whi h dete t the ashes of Cherenkov light. The water therefore serves as both the sour e of nu leonsand the tra king medium. Due to the relatively low ost of water, these dete tors an have a large mass, making them sensitive to longer proton lifetimes than iron alorimeter experiments. In addition, timing information an be obtained from thePMT pulses. A summary of various water Cherenkov dete tors is in Table 3.3.3.3.1 IMB/IMB-3 (1982-1991)Lo ated in the Fairport salt mine lose to Cleveland, Ohio, the Irvine Mi higanBrookhaven (IMB) water Cherenkov dete tor was designed to over the entire life-time range of the proton de ay p! e+�0 predi ted by minimal SU(5)[55℄. To a hieve

32a sensitivity to the partial lifetime predi ted by SU(5) [11℄ whi h is �=Bjp!e+�0 =4:5 � 10(29�1:7) years, it had a 3.3 kiloton �du ial mass ( orresponding to � 1033protons) with a ubi al shape (18 m � 17 m � 22.5 m). It operated in three di�erentoperation modes, the se ond having very brief duration. The major di�eren e be-tween the �rst and third phases was an upgrade in whi h the 2048 13- m PMTs wererepla ed with 20- m PMTs equipped with wavelength-shifter plates to in rease light olle tion eÆ ien y [56℄. These PMTs and wavelength-shifters are now used in theouter dete tor of Super{Kamiokande. Although it did not observe proton de ay, IMBhad some triumphs whi h in lude observation of neutrinos from Supernova 1987A on urrent with Kamiokande and the �rst hints of a de� it of muon neutrinos in thesample of atmospheri neutrinos.3.3.2 Kamiokande (1983-1988)Kamiokande was the prede essor to Super{Kamiokande. It was lo ated about 200 maway from the present lo ation of Super{Kamiokande in the Mozumi mine of theKamioka Mining and Smelting ompany in Gifu Prefe ture, Japan. A smaller ver-sion of Super{Kamiokande, Kamiokande was a ylindri al tank with total mass of3 kilotons. It was instrumented with 948 50- m diameter PMTs viewing a �du ialmass of 1 kiloton yielding a photo athode overage of 20%. This large photo athode overage in reased the sensitivity of Kamiokande to nu leon de ay modes with lowerCherenkov light yields, su h as p! ��K+ .Operation onsisted of two phases, Kamiokande I (1983-84) and Kamiokande II(1986-88). The upgrade to Kamiokande II was designed to dete t low-energy so-lar neutrinos and onsisted of three major hanges. The �rst was the installationof an anti- ounter used to veto in oming parti les. This anti- ounter was a water

33Cherenkov dete tor whi h surrounded the inner dete tor and was instrumented with123 PMTs. The se ond part of the upgrade was an improved water puri� ation sys-tem to remove the ba kground from radon gas. Finally, a new ele troni s system wasinstalled whi h made it possible to make multi-hit time and harge measurements.Like IMB, Kamiokande did not observe nu leon de ay, but did produ e signi� ants ienti� dis overies. Observation of neutrinos from Supernova 1987A, observationof a de� it of solar-neutrinos in the energy range of about 10 to 20 MeV, and the �rstsigns of a distortion in the zenith angle distribution of atmospheri neutrinos wereall very important advan es in the �eld of neutrino physi s. Although data analysisstopped in 1988, Kamiokande remained alive until 1997 in order to dete t neutrinosignals from stellar ollapse.3.3.3 HPW (1983-1984)The Harvard-Purdue-Wis onsin (HPW) water Cherenkov dete tor was lo ated ina mine near Park City Utah at a depth of about 1500 m.w.e [57℄. Unlike otherwater Cherenkov dete tors whi h have PMTs mounted on the walls of the dete tor,its 700 PMTs were mounted on verti al strings of hoops suspended in a ylindri altank of water whi h had a mass of 0.7 kilotons. The walls were lined with mirrorsto in rease light dete tion eÆ ien y. The ombination of the 3-d spa ing of PMTsand the mirrors made it diÆ ult to tra k parti les, so they were only able to quotelimits based on the number of ele trons from muon de ays. For example, the de ayp ! �K+ ; K+ ! �+�+�� would have two de ay ele trons from the de ay of the�+s to �+s.

34Dete tor mass (�du ial) exposure depth nu leon lifetime(in kilotons) (kton�years) (m.w.e) sensitivity (years)HPW .680 (.130/.180) 0.2 [57℄ 1500 1030Kamiokande (I/II) 3.0 3.76 [58℄ 2700 1031 to 1032IMB/IMB-3 8.0 (3.3) 7.6 [12℄ 1600 1031 to 1032Super{Kamiokande 50 (22.5) - 2700 1032 to 1034Table 3.3: Summary of Water Cherenkov Dete tors3.3.4 Super{Kamiokande (1996-Present)Super{Kamiokande is a massive 50 kiloton water Cherenkov dete tor with a �du ialmass of 22.5 kilotons. Its large mass provides a sensitivity to longer proton lifetimes.In addition, the 11146 50- m PMTs viewing the inner dete tor provide 40% photo- athode overage. This large overage makes it possible to eÆ iently tra k parti lestraversing the dete tor. Parti les an be distinguished eÆ iently between showeringparti les from ele trons or gamma-rays and non-showering parti les like muons, pi-ons, or protons. The large overage also provides an enhan ed ability to re onstru tmultiple tra ks in events with many parti les. It is also possible to dete t showeringparti les having energies as low as about 5 MeV. This is important when dete tingthe nu lear de-ex itation gamma-rays whi h an be produ ed when a nu leon in O16de ays.Data taking began in April 1996 and the dete tor has been running with anintegrated livetime of about 80% sin e then. More details of Super{Kamiokandeappear in Chapter 4.

Chapter 4The Super{Kamiokande Dete tor4.1 GeneralSuper{Kamiokande is lo ated in the Mozumi mine of the Kamioka Mining and Smelt-ing Company in Gifu Prefe ture, Japan. It sits at a depth of about 1000 meters (2700meters water equivalent) below the peak of Mount Ikenoyama. This shielding atten-uates the onstant rain of osmi ray muons by about �ve orders of magnitude, whi hresults in a muon dete tion rate of about 2 Hz. The total mass of 50 kilotons makesit the largest underground water Cherenkov dete tor to date.4.1.1 Water Cherenkov Dete torWhen a harged parti le travels faster than the speed of light in a medium, theele tromagneti waves it emits form a oherent sho k front known as Cherenkovradiation (�gure 4.1) [59℄. This radiation is emitted in a oni al shape with anglerelative to the dire tion of movement of the parti le (�C) given by os �C = 1n� (4.1)35

36where n is the index of refra tion of the medium and � = v= is the velo ity of theparti le relative to the speed of light.θc

Shock Front

ct/n

ctFigure 4.1: Illustration of Cherenkov radiation.The number of photons (N) emitted per unit path length (dx) per unit wavelength(d�) is d2Nd�dx = 2���2 1� 1�2n2(�)! (4.2)where � � 1137 is the �ne stru ture onstant. In the wavelength range where thePMTs of Super{Kamiokande are sensitive (� 300-600 nm), a parti le moving at� = 1 will emit about 300 photons/ m. The one of Cherenkov light emitted bythe parti le will proje t onto the PMT lined wall of Super{Kamiokande reating a ir ular pattern on the wall. Various kinemati variables su h as momentum, energy,and dire tion of parti les traversing the dete tor are re onstru ted on the basis ofthese patterns.

374.1.2 Stru tureSuper{Kamiokande is a ylindri al stainless steel water tank with a height of 41.4m and a diameter of 39.3 m (�gure 4.2). The dete tor is opti ally separated intotwo regions, the inner and outer dete tors (ID and OD). The ID has a diameter of33.8 m and a height of 36.2 m and is lined with 11,146 inward fa ing 50- m diameterPMTs overing 40% of the surfa e. The OD ompletely surrounds the ID with athi kness of 2.6 to 2.75 m and is lined with 1885 outward fa ing 20- m diameterPMTs re y led from the IMB dete tor. These PMTs are equipped with 60 m � 60 m wavelength-shifter plates to in rease the light dete tion eÆ ien y [56℄. By Fall1996, the death rate of the PMTs had stabilized to one every 11 days for the ODand one every 20 days for the ID. The total number of dead PMTs as of De ember1999 were 154 and 216 for the ID and OD, respe tively.

Figure 4.2: S hemati of the Super{Kamiokande dete tor.The ID and OD are separated by a 55- m thi k PMT support stru ture omposedof about 1000 \super modules," ea h of whi h supports 12 50- m ID PMTs and 2

38OD 20- m PMTs (�gure 4.3).tyvek8 inch

PMT

black sheet

20 inch

PMT

Figure 4.3: S hemati of a supermodule.In order to opti ally separate the ID and OD, the side of ea h super modulefa ing the inner dete tor is lined with a bla k plasti sheet. The side of the stru turefa ing the OD is lined with Tyvek, a re e tive material whi h also in reases the lightdete tion eÆ ien y of the OD.On top of the water tank are �ve ele troni s huts, alibration devi es in ludingan ele tron LINAC, and hundreds of kilometers of ables onne ting the PMTs tothe ele troni s. About 100 m from the top of the water tank is a ontrol room wherephysi ists monitor the many di�erent pro esses related to data taking.4.1.3 Water Puri� ation SystemThe main purposes of the water puri� ation system in Super{Kamiokande (�gure4.4) are to de rease the light attenuation and to remove radioa tive impurities su h

39as radon gas. Radon de ays are a major ba kground in the low energy analysis butdo not ontribute signi� antly to nu leon de ay analyses.Water is initially ir ulated through a �lter whi h removes dust with size �1 �m.It is then passed through stages to remove metal ions, ba teria, and any remainingoxygen or radon gases. Finally, the water is passed through \ultra-�lters" whi hremove smaller parti les with size �100 nm. The resulting attenuation length of thewater is about 100 m for 450 nm wavelength photons.m

Figure 4.4: Water puri� ation system.4.2 Inner Dete tor Ele troni s4.2.1 Photomultiplier TubesThe 50- m diameter photomultiplier tubes (PMTs) used in Super{Kamiokande wereoriginally designed for the Kamiokande dete tor by HAMAMATSU Corporation [60℄.

40ph

otos

ensi

tive

area

>46

0φ

<φ

520

7000

0~

720~

)20610(

φ 82

2

φ 25

410

φ 11

6ca

ble

leng

th

water proof structure

glass multi-seal

cable

(mm)Figure 4.5: S hemati view of a 50- m diameter photomultiplier tube used in Super{Kamiokande.A s hemati of the PMT is shown in �gure 4.5. They were designed to have largephotosensitive area, good timing resolution, ability to dete t single photoele trons,and stability over a long period of time. In order to have suÆ ient pre ision in vertexand dire tion re onstru tion in the low-energy solar neutrino analysis, improvementsin timing and energy resolution at the 1 photoele tron (PE) level were required. Thiswas a hieved by making hanges in the \Venetian blind" dynode stru ture [61℄. Thetiming resolution was redu ed to �2.5 ns. Furthermore, a lear single photoele tronpeak an be distinguished from dark noise (�gure 5.3). The quantum eÆ ien y hasa maximum of 22% at 390 nm wavelength and is signi� ant in the range of �300-600nm (�gure 4.6). Some parameters of PMTs are outlined in table 4.1.Magneti �elds a�e t the response of PMTs making it ne essary to ompensatefor the geomagneti �eld of 450 mG at the Super{Kamiokande site. A system of26 Helmholtz oils was onstru ted around the dete tor to a ount for this e�e tredu ing the magneti �eld to approximately 50 mG.

41

Figure 4.6: 50- m photomultiplier tube quantum eÆ ien y as a fun tion of photonwavelength. Diameter 50 mDynode Stru ture 11 stage Venetian BlindGain 107 at 2 kVQuantum eÆ ien y 22% at 390 nmMean Transit time 100 nsTiming Resolution 2:5 nsDark Noise Rate � 3 kHz at .25 PE levelTable 4.1: 50- m PMT hara teristi s.4.2.2 Front End Ele troni sAnalog Timing Modules (ATMs) are used to pro ess the analog signals from thePMTs. These modules are equipped with two hannels whi h enable them to storetwo su essive pulses from a PMT [62℄. This makes it possible to dete t ele trons frommuon de ays and to handle high rate situations su h as supernovae. Ea h hannel onsists of a time to amplitude onverter (TAC) to re ord timing information and a harge to analog onverter (QAC) to re ord the size of the PMT pulse. The full timerange is 1.6 �s with a timing resolution of 0.3 ns and the harge saturation level is600 pC, orresponding to about 300 PE, with a resolution of 0.2 pC.

42 The ATM modules are part of a TKO (Tristan KEK Online) system. In ea hof four ele troni s huts on the dete tor, there are 12 TKO rates. A TKO rate onsists of 20 ATMs, a GONG (GO NoGo) trigger ontrol module, and a SCH(Super Control Header). The SCH provides an interfa e between the TKO rateand its orresponding SMP (Super Memory Partner) residing in a VME rate in theele troni s hut. This SMP a ts as a bu�er for data before being read out to online omputer workstations. There are two workstations, ea h handling 6 SMP modules,in ea h of the four ele troni s huts. A s hemati of the system is shown in �gure 4.7.12 x ATM

20 inchPMT

x 20

SCHGONG

11200 PMTs1000 ATMs48 TKO,SMP, SCH9 workstations

TKO Crate

VME Crate

SMPx 6

Workstation

To Hitsum

From Trigger

x 6

2 per hut (4 huts) = 8

12 PMT per ATM20 ATM per TKO12 TKO per HUT12 SMP per HUT12 SCH per HUT

4 HUTS

2 workstations per HUT (plus one "central")Figure 4.7: Layout of the ID ele troni s

4.2.3 TriggerIn the ATM module, PMT signals are ampli�ed by a fa tor of 100 and are sent to adis riminator set at a threshold orresponding to �0.2 PE. If the signal ex eeds thisthreshold a re tangular pulse with a width of 200 ns and amplitude of -15 mV is sent

43Trigger type Threshold Nhit Energy RateLow Energy 320 mV 29 5 MeV 11 HzSuper Low Energy 222 mV 20 3.5 MeV 550 HzHigh Energy 340 mV 31 6 MeV 6 HzOuter Dete tor - 19 N/A 3 HzTable 4.2: Trigger typesto a summing ir uit. The output of this summing ir uit is alled a HITSUM. TheHITSUMs from ea h of the four huts are sent to the entral hut to another summing ir uit and a �nal HITSUM for the entire dete tor is generated. The trigger is basedon thresholds set on the �nal HITSUM outputThe dis riminator threshold for the �nal HITSUM varies depending on the fourtrigger types, high energy (HE), low energy (LE), super-low energy (SLE), and outerdete tor trigger (explained later). The HE trigger, whi h is required for all events aused by atmospheri neutrinos and proton de ays, is the most pertinent for thisdissertation. The LE and SLE triggers are important for the solar neutrino analysis.Table 4.2 summarizes the di�erent triggers. The high and low energy trigger ratesas a fun tion of elapsed time sin e data taking started on April 1, 1996 are shown in�gure 4.8.4.3 Outer Dete tor Ele troni sThe OD ele troni s onsists of 1885 20- m PMTs whi h are fed to the front endele troni s harge to time onverters (QTCs) via paddle ards. One paddle ardserves twelve PMTs. The output of the QTCs is sent to time-to-digital onverters(TDCs) whi h are read out with the aid of dual-port memory modules in a VME rate ontrolled by a Sun workstation. A box diagram of the OD ele troni s is shown

44

Elapsed days since April 1, 1996

Tri

gg

er r

ate

(Hz)

Low energy

High energy

0 200 400 600 800 1000 1200 14000

2

4

6

8

10

12

14

16

18

20

Figure 4.8: High and low energy trigger rate as a fun tion of elapsed days sin e thestart of data taking on April 1, 1996.in �gure 4.9.4.3.1 Photomultiplier TubesThe 1800 20- m diameter OD PMTs were re y led from the IMB dete tor. ThePMTs are opti ally oupled to 60- m � 60- m � 1- m wavelength-shifter plateswhi h are a ryli doped with bis-MSB [56℄. The bis-MSB absorbs Cherenkov photonsin the near ultraviolet region of the spe trum where the ux is larger and re-emitsphotons in the blue-green region where the PMTs are most sensitive. The wavelength-shifter plates redu e the timing resolution from �10 ns to �15 ns but in reases thelight olle tion eÆ ien y by �60%. The redu tion in timing resolution does notsigni� antly a�e t the ability of the OD to veto events and is a small pri e to payfor the in rease in light olle tion.

45

AcquisitionOD Data

(HITSUM)OD Trigger

FASTBUS

NIM

TDC

VME

20-cm PMT20x

2x4x12x

WorkstationSun

1877 LeCroyQTC

ModuleCardHV Paddle

Figure 4.9: Blo k diagram of OD ele troni s.4.3.2 Front End Ele troni s: QTC modulesThe QTC ( harge-to-time onverter) modules whi h ompose the front end ele -troni s of the OD were designed, built, and tested at Boston University. The QTCmodules are self-gated harge integrators whi h en ode timing information in therising edge of the output pulse and harge information in the width of the pulse.Ea h QTC module, omposed of 3 \mother ards" ea h serving 16 \daughter" ards,supports 48 hannels. There are 10 QTC modules residing in two NIM rates in ea hof the four ele troni s huts.A box diagram of a single QTC hannel is shown in �gure 4.10. A pulse fromthe 20- m PMT is sent through a dis riminator with threshold of about 0.25 PE.Pulses over threshold trigger the ir uit generating a 200-ns gate whi h is used asthe integrating window for the LeCroy MQT200 harge-to-time onverter hip. ThePMT pulse is also sent to the LeCroy MQT200 hip and integrated within the 200-nsgate. Finally, the output pulse from the LeCroy MQT200 is dis riminated and sentto the CE16V8 PAL. The PAL (programmable array logi ) hip onverts the pulse

46DelayLine

Trigger Circuit

PMT pulse

Threshold=0.25 PE CE16V8

PAL

LeCroy MQT2000

Charge to time Converter

Single Daughter Card Threshold

Discriminator

Discriminator

200 ns gate

OneShot

Qt

To Hitsum

TTL t/Q output pulse

to TTL-ECLconverterFigure 4.10: Blo k diagram for a single hannel (or \daughter" ard) of a QTCmodule.to TTL output and provides the logi for the rising edge of the �nal daughter ardoutput. Cartoon os illos ope tra es for various stages of the ir uit are shown in�gure 4.11.

4.3.3 TriggerIn addition to en oding harge and timing information from the PMTs, the QTCsgenerate the trigger for the OD. A single 200-ns width 25-mV square pulse is gener-ated for PMT signals whi h are above the initial dis riminator threshold of 0.25 PE.Ea h QTC module generates a HITSUM by summing these pulses. The HITSUMsfrom the individual QTC modules are sent to the entral hut where they are summed.This �nal sum is a global HITSUM. The OD is triggered when there are 19 or morehits within a 200-ns time window. The OD trigger rate is about 3 Hz.

47

∆ t Q~

Input PMT pulse

200-ns gate

Delayed PMT pulse

Output fromLeCroy MQT200

After Discriminator

Discriminator Threshold

Final DaughterCard Output

Time (ns)200 400 600 800 1000

200 mV

1 V

1 V

tFigure 4.11: Cartoon of s ope tra es for di�erent stages in a single QTC hannel.4.3.4 Data A quisitionThe ECL output of the QTC modules is sent to a LeCroy 1877 Time-to-Digital onverter (TDC). Ea h quadrant hut houses �ve 1877 modules whi h are ontainedin a single FASTBUS rate. Ea h TDC hannel an digitize a maximum of 16 pulseedges in a window of up to 32 �s. Ea h QTC output pulse has two edges, meaningthat ea h hannel an digitize a maximum of 8 hits in 32 �s. Digitization takesanywhere between 2 to 5 �s. More details of the OD DAQ may be found in referen e[63℄.The width of the digitization window and its lo ation relation to trigger time anbe adjusted. At the start of dete tor operation the full width of 32 �s was used withthe dete tor trigger entered in the window. The width was redu ed to 16 �s withthe dete tor trigger o urring 10 �s into the window in September 1996. This smallerwindow redu ed the amount of data from the OD and helped solve the problem ofafter-pulses overriding real pulses.

Chapter 5Calibration5.1 Relative GainThe relative gains of individual PMTs are alibrated with the aid of the Xe ballsetup shown in �gure 5.1. A Xe ash lamp generates UV light whi h is passed viaopti al �ber to a s intillator ball in the dete tor. The s intillator shifts the UV lightto visible and di�uses it throughout the dete tor. The output spe trum peaks atabout 440 nm. The relative gain of the i-th PMT is given byGi = 1f (�i) QiQ0 r2i exp�riL� (5.1)where Qi is the harge dete ted at the i-th PMT, f(�i) is the PMT angular a eptan edepending on the angle � between the axis of symmetry of the PMT and the dire tionof the in oming photon, ri is the distan e from the s intillator ball to the i-th PMT,L is the attenuation length of the water, and Q0 is a normalization fa tor. The highvoltage for ea h PMT is adjusted so that the distribution of Gi for the 11146 PMTshas minimum spread (�gure 5.2). 48

49Xe Flash Lamp

UV filter ND filter

Optical fiber

Pho

toD

iode

Pho

toD

iode

ADC

Monitor

PMT

Scintilator

Trigger20inchPMT

SK TANK

Scintilator Ball

Figure 5.1: Xe/s intillator ball alibration setup.

corrected Q

0

250

500

750

1000

1250

1500

1750

2000

0 200 400 600 800 1000 1200 1400 1600 1800 2000

x 102

11146 PMTs

σ= 7.%

Figure 5.2: Relative gain distribution from Xe alibration.5.2 Absolute GainSignals from the PMTs are measured in units of pi oCoulombs (pC). Absolute gain alibration is the pro ess of determining the onversion of pC to photoele trons(PE). This requires a low energy sour e in order to generate single photoele trons.A Cf252 sour e surrounded by Ni wire is ontained in a plasti ase. Spontaneous�ssion of Cf produ es neutrons whi h are aptured on Ni subsequently emitting -

50rays with varying energies, the most ommon being 9 MeV. The -rays produ ean ele tromagneti shower from whi h Cherenkov radiation is generated. Single PEdistributions are made for ea h PMT and are used to onvert from raw harge in pCto PE. A sample single PE distribution is shown in �gure 5.3.

Figure 5.3: Sample single photoele tron distribution.5.3 Timing/Charge (TQ) CalibrationTiming alibration for the PMTs is performed with the aid of the N2 laser systemshown in �gure 5.4. The 337-nm output wavelength of the laser is slightly lower thantypi al Cherenkov radiation, therefore it is shifted to 384 nm with the aid of a dye.The intensity of the light is varied with the aid of an opti al �lter and the laser pulseshave a width of about 4 ns. Light from the laser is transmitted via opti al �ber toa di�using ball whi h is suspended in the enter of the Super{Kamiokande dete tor.Time vs. harge maps (TQ maps) are generated for ea h PMT using this setup andare used to shift the relative time o�set for the PMTs. These maps are used in the

51Super Kamiokande inner tank

diffuser ball

20’PMT

variableattenuation filter

optical fiberN lasergenerator

monitor PMT

trigger elec.

DAQelec.

sig.

optical fiber

sig.

sig.

sig.20’PMT

2

=384nmλ

diffuser tip(TiO )LUDOX 2Figure 5.4: Timing alibration: Setup used to measure TQ maps for individualPMTs.Monte Carlo dete tor simulation. A typi al TQ-map is shown in �gure 5.5.

5.4 Water Attenuation Length5.4.1 LaserThe attenuation length of the water is measured at di�erent wavelengths with thelaser setup shown in �gure 5.6. Mono hromati light produ ed with wavelengthsfrom 337 nm to 600 nm from a dye module pumped by a N2 laser is split into twobeams, one of whi h is transmitted via opti al �ber to a di�user ball whi h has beenlowered into Super{Kamiokande. The other beam is sent to a 2-in h diameter PMTwhi h monitors the beam intensity. A CCD amera at the top of the tank measuresthe light intensity from the di�user ball, ICCD, for various depths of the ball, ld.Several measurements are taken at ea h depth and wavelength. The attenuation

52Typical TQ map

880

890

900

910

920

930

940

950

960

970

980

Q (p.e.)

T (

nse

c)

Figure 5.5: TQ map for a typi al PMT.

Optical Fiber (70m)

CCD camera

<< SK Tank >>

Beam Splitter (50:50)

Lens

Integrating Sphere

<< laser box >>

Diffuser Ball

2inch PMT

DYE / N2 laser

Figure 5.6: Setup used to measure water attenuation length at di�erent wavelengths.length for ea h wavelength L(�) is al ulated by �tting the fun tionlog ICCDIlaser = A� ldL(�) (5.2)where A is a onstant. A sample distribution of ICCD=Ilaser is shown for � = 420 nmin �gure 5.7. Final results for all measurements are shown in �gure 5.8. The pointsrepresent the results of the measurements and the solid lines represent a model whi hin ludes Rayleigh s attering, Mie s attering, and absorption. Rayleigh s attering is

53the s attering of a photon with an entire water mole ule and has a 1=�4 wavelengthdependen e. Mie s attering is the s attering of photons with parti les within thewater and has no wavelength dependen e. Absorption is more pronoun ed for longerwavelength photons. The model shown by the solid lines in �gure 5.8 is used in theMonte Carlo dete tor simulation.

Figure 5.7: Attenuation length alibration for � = 420 nm.5.4.2 Cosmi -Ray MuonsCosmi -ray muons are also used to measure the attenuation length of water in Super{Kamiokande. Although it is impossible to make a wavelength dependent measure-ment from them, it is ni e to use a natural sour e to double- he k the measurementfrom the N2 laser method. Another virtue is that it is not ne essary to halt regulardata taking to make the measurement.

54

10-3

10-2

10-1

200 300 400 500 600 700

Mie scattering

Rayleigh scattering

absorptiontotal

Dec.-3,4-96 Dec.-14-96Dec.-17-96 Dec.-27-96Jan.-18-97 Mar.-6-97

wavelength (nm)

atte

nuat

ion

coef

ficie

nt(1

/m)

Figure 5.8: Attenuation length vs. wavelength. The solid line shows the model usedin the Monte Carlo dete tor simulation. Points show the measurements using the N2laser system.The harge dete ted at the i-th PMT an be writtenQi = A f(�i)li e � liL (5.3)or equivalently log Qilif(�i)! + onst = � liL (5.4)where A is some normalization onstant, f(�) is the same as the in equation 5.1, l isthe path length of the photon to the PMT, and L is the attenuation length. Figure5.9 shows log � Qlf(�)� versus l for a sample run. The �tted slope of the line is themeasurement for L. This measurement is done ontinuously to dete t any overallvariations in attenuation lengths.

55200

300

400

500

0 1000 2000 3000 4000 5000

192.0 / 19

P1 5.987 0.4609E-03

P2 -0.9487E-04 0.4444E-06RUN 3106

l (cm)

log(

Ql/f

(θ))

Figure 5.9: log � Qlf(�)� versus l for osmi ray muons in a single run of Super{Kamiokande data taking.5.5 Energy S aleAn important part of nu leon de ay analyses is hoosing sele tion riteria usingMonte Carlo samples. Many of these riteria are dependent on the energies of theparti les. For this reason, it is important to orre tly model the energy depositionand the dete tor response for parti les traversing the dete tor in the Monte Carlosimulation. Energy s ale alibration is performed by omparing data and MonteCarlo for ele trons from a LINAC, de ay ele trons from stopping osmi ray muons,stopping osmi ray muons themselves, and �0s produ ed in atmospheri neutrinointera tions. Ea h sour e provides a alibration in a di�erent energy range.5.5.1 LINACAn ele tron linear a elerator (LINAC) is used to alibrate the dete tor for thelow-energy solar neutrino analysis [64℄. The LINAC generates ele trons whi h areinje ted verti ally into Super{Kamiokande via a beam pipe whose end an be pla edat various depths in the dete tor. A series of magnets ontrol the dire tion and

56energy of the beam. Beam energies an be tuned to values between 5 MeV and 16MeV. The high-energy analysis uses only the 16-MeV data for energy alibration.Figure 5.10 shows the re onstru ted momentum for 16-MeV ele trons generated bythe LINAC for both data and Monte Carlo. The mean is 17.26 MeV for the data ompared to 17.45 MeV for the Monte Carlo, orresponding to an agreement of about1%.

Momentum (MeV/c)

Nev

ent

data

Monte Carlo

LINAC energy calibration16-MeV electrons

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35 40Figure 5.10: Re onstru ted momentum distributions for 16-MeV ele trons generatedby the ele tron LINAC for both data and Monte Carlo. The agreement is about 1%.5.5.2 Mi hel Ele tronsEle trons from the de ays of stopping muons are also a good energy alibrationsour e. De ay ele trons (Mi hel ele trons) were sele ted by requiring1. dwall > 2 m2. 1.8 �s < �t < 8:0 �s

573. Goodness > 0.54. N IDhit (50 ns) > 40where dwall is the re onstru ted distan e from the vertex to the wall (see se tion8.1), �t is the time from the muon to the de ay ele tron, goodness is de�ned inequation 8.1, and N IDhit (50 ns) is the number of hits in the ID within a 50-ns timewindow. The Mi hel spe trum for data and Monte Carlo is shown in �gure 5.11.The Monte Carlo is systemati ally lower than data by about 2:2%.

Momentum (MeV/c)

Nev

ent

data

Monte Carlo

Michel electron energy spectrum

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60 70 80Figure 5.11: Re onstru ted momentum distributions Mi hel ele trons for both dataand Monte Carlo. The Monte Carlo simulation is systemati ally 2:2% lower than thedata.5.5.3 Stopping MuonsCosmi ray muons whi h stop in the dete tor are used for energy alibration usingboth their opening angle and the distan e they traveled (range). Muons with energies

58greater than 1 GeV are used for range al ulations and muons with energies less than500 MeV are used for opening angle al ulations. The two regimes provide energys ale determinations for two energy regions.

Momentumθ (MeV/c)

Mo

men

tum

Q (

MeV

/c)

Low energy stopping muons: data

150

175

200

225

250

275

300

325

350

375

400

150 175 200 225 250 275 300 325 350 375 400Momentumθ (MeV/c)

Mo

men

tum

Q (

MeV

/c)

Low energy stopping muons:Monte Carlo

150

175

200

225

250

275

300

325

350

375

400

150 175 200 225 250 275 300 325 350 375 400Figure 5.12: Distributions of j~pQj vs. j~p�j for data and Monte Carlo low energy (E <400 MeV) stopping muons. The momenta j~pQj and j~p�j are the momenta al ulatedfrom the number of PE dete ted and the Cherenkov opening angle, respe tively.For low energy stopping muons (E� < 500 MeV), the Cherenkov opening angle an be used to al ulate the energy sin e it depends on the momentum a ording tothe equation os �C = 1n� = 1nvuut1 + mj~p�j!2 (5.5)The Cherenkov angle for a sample of low-energy stopping muons is determined usingthe method des ribed in se tion 8.3 and the momentum is al ulated (j~p�j) usingequation 5.5. The momentum is also re onstru ted from the number of PEs de-te ted (j~pQj) using the method des ribed in se tion 8.4. This provides two separatemeasurements of the momentum whi h an be ompared.The distributions of j~pQj vs. j~p�j for data and Monte Carlo are shown in �gure

59

Momentumθ

Mo

mQ/M

om

θa) Momentum ratio

dataMonte Carlo

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

150 175 200 225 250 275 300 325 350 375 400Momentumθ

(Dat

a-M

C)/

Dat

a

b) % difference of ratio

-5

-4

-3

-2

-1

0

1

150 175 200 225 250 275 300 325 350 375 400Figure 5.13: (a) Binned distributions of j~pQj=j~p�j vs. j~p�j for data and Monte Carlolow-energy stopping muons. (b) Per ent di�eren e between data and Monte Carlo(Data-MC)/Data.5.12. The ratio j~pQj=j~p�j vs. j~p�j in bins of width of 50 MeV/ is shown in �gure5.13a and the per ent di�eren e between data and Monte Carlo with this binning isshown in �gure 5.13b. The distributions agree within 2%.The range of the muon is found by al ulating the distan e between the entran epoint of the muon and the �tted vertex of the de ay ele tron. Both verti es have aresolution of about 50 m. The range gives a measurement of the momentum of themuon. This measurement is then ompared to the momentum measurement (j~p�j)from the number of PEs dete ted. Figure 5.14 shows the distribution of j~p�j=rangevs. range for stopping muons in the data and Monte Carlo simulated stopping muons.The data displayed in �gure 5.14 were then binned into 500-MeV bins from 700 MeVto 3500 MeV (the �rst bin has a width of 300 MeV). This distribution is shown in�gure 5.15a and the per ent di�eren e, (Data-MC)/Data, is shown in �gure 5.15b.The dis repan y between data and Monte Carlo is at most 3%.

60

Range (cm)

Mo

men

tum

/ran

ge

(MeV

/c/c

m)

Stopping muons: data

1

1.5

2

2.5

3

3.5

4

0 500 1000 1500 2000 2500 3000 3500 4000Range (cm)

Mo

men

tum

/ran

ge

(MeV

/c/c

m)

Stopping muons: Monte Carlo

1

1.5

2

2.5

3

3.5

4

0 500 1000 1500 2000 2500 3000 3500 4000Figure 5.14: Distributions of j~p�j vs. range for data and Monte Carlo stoppingmuons. The range is de�ned as the di�eren e between the muon entran e pointand the vertex of the de ay ele tron. j~p�j was al ulated using the number of PEsdete ted.5.5.4 �0 Re onstru tionAtmospheri neutrino intera tions sometimes reate �0s in Super{Kamiokande whi hde ay immediately (� � 10�16 s) via �0 ! with a bran hing ratio of 98:8%. Theinvariant mass of the �0 is a useful energy quantity for alibration whi h may be al ulated using the kinemati relationm�0 = q2E1E2 (1 � os �12) (5.6)where E1 and E2 are the energies of the two -rays and �12 is the angle between theirmomenta. Comparing the invariant mass distributions for data and Monte Carloprovides an idea of how well the energy s ale is modeled in the simulation.These events are sele ted by requiring1. Two EM showers

61

Range (cm)

Mo

men

tum

/ran

ge

(MeV

/c/c

m)

a) Range of stopping muons

dataMonte Carlo

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

0 500 1000 1500 2000 2500 3000 3500 4000Range (cm)

(Dat

a-M

C)/

Dat

a

b) % difference in range

-5

-4

-3

-2

-1

0

1

0 500 1000 1500 2000 2500 3000 3500 4000Figure 5.15: (a) Binned distributions of j~p�j vs. range for data and Monte Carlo stop-ping muons. (b) Per ent di�eren e between data and Monte Carlo (Data-MC)/Data.2. no de ay ele trons3. j~ptotj < 400 MeVwhere j~ptotj is the sum of the momenta of the two rings. Figure 5.16 shows there onstru ted mass for data and Monte Carlo. The distributions agree within about3%.5.5.5 Summary of energy s aleBased on the sour es outlined in the previous se tions, the energy s ale is reprodu edin the Monte Carlo with a deviation of no more than 3%. The sour es provide alibrations over a wide range of energies varying from 16 MeV to several GeV. Thisis within the energy range relevant to nu leon de ay studies.

62

µdata=146.2

σdata=16.7

µMC=141.9

σMC=15.6

dataMonte Carlo

Atmospheric neutrino π0

Massγγ (MeV/c2)

Nev

ent

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300Figure 5.16: Invariant mass distributions for �0s indu ed by atmospheri neutrinosfor both data and Monte Carlo. The agreement is about 3%.

Chapter 6Monte Carlo6.1 Nu leon de ay Monte CarloMonte Carlo simulations of nu leon de ay are a riti al omponent of nu leon de aysear hes. Simulations of spe i� de ay modes provide a predi tion for the signature ofthe events. Together with the predi tion of ba kground from atmospheri neutrinos,the signal simulation provides a method by whi h sele tion riteria for spe i� de aymodes are hosen. Dete tion eÆ ien y is then estimated by passing the nu leonde ay Monte Carlo sample through the sele tion riteria. This se tion des ribes thepro ess of generating a nu leon de ay Monte Carlo sample.6.1.1 Nu leon de ay kinemati sNu leon de ay events are found by dete ting the de ay produ ts of the nu leon.The kinemati s of the de ay produ ts are determined by the initial kinemati s of thenu leon. The quantities hara terizing the initial state of a nu leon de ay pro ess arethe nu leon's initial momentum and lo ation in the nu leus. The former determinesthe energy and momenta of the de ay produ ts while the latter is a starting point63

64for tra king the produ ts through the nu leus.Nu leons bound in oxygen have a non-zero momentum alled \Fermi momentum."The Fermi momentum spe tra for the angular momentum states l = 0 (\s-wave")and l = 1 (\p-wave") in O16 are shown in �gure 6.1. These distributions are basedon �ts to measurements of ele tron-C12 s attering by Hiramatsu et al. [65℄. Thenu leon's binding energy also results in mass distributions whi h are displa ed fromthe mass of a free nu leon (�gure 6.2). Initial momentum and mass are randomlydrawn from these distributions for nu leons in O16. In addition to the nu leons boundin O16, there are two additional protons from the hydrogen in H2O. These protonsare unbound within a nu leus; they have negligible initial momentum and their massis that of a free proton.p-waves-wave

Fermi momentum (MeV/c)0 100 200 300

0

2

4

6

8

Figure 6.1: Fermi momentum distributions for s and p states in O16.After the e�e tive mass and initial momentum are al ulated, the kinemati sof the de ay produ ts are al ulated in the nu leon's rest frame. This dissertationstudies only two body de ays making the kinemati s of these events simple. Momenta~pfinal of outgoing parti les are equal and opposite in the rest frame of the nu leon

65s-wave contribution

p-wave contribution

Effective nucleon mass in 16O

Masseff (MeV/c2)

Rel

ativ

e d

ensi

ty

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

850 860 870 880 890 900 910 920 930 940 950Figure 6.2: E�e tive mass for nu leons in O16:and have a magnitude ofj~pfinalj = 12mnu hm2nu � �m21 +m22�i (6.1)where mnu is the e�e tive mass of the nu leon and m1 and m2 are the masses of theoutgoing parti les. A random dire tion is sele ted in the rest frame of the nu leonand a Lorentz boost orresponding to the initial momentum of the nu leon is appliedto the de ay produ ts.The initial position of the nu leon is drawn randomly from the Woods-Saxondensity distribution [66℄ for nu lei�(r) = �(0)1 + exp ( r�ab ) (6.2)where a = 1:07A1=3 = 2:69 fermi for O16, 2b = 0:82 fermi is the thi kness of thenu lear surfa e, and r is the distan e from the enter of the nu leus.

66 Hole Resulting parti les p Probabilityp3=2 N15, -ray 6.32 MeV= 41%p3=2 N15, -ray 9.93 MeV= 3%s1=2 N14,neutron, -ray 7.03 MeV= 2%s1=2 C14,proton, -ray 7.01 MeV= 2%Table 6.1: De ay modes of N15� whi h have -rays as de ay produ ts.De aying nu leons in the p3=2 and s1=2 shells of O16 leave the residual N15 nu leusin an ex ited state whi h immediately de ays, sometimes emitting de-ex itation -rays. This pro ess was studied by Ejiri [67℄ and the results from his analysis areused in the Monte Carlo simulation. Possible de-ex itation s hemes of N15 and theirprobabilities are summarized in table 6.1.6.1.2 Nu lear Intera tionsThe de ay produ ts of a nu leon bound in oxygen an intera t hadroni ally with theremaining protons and neutrons in the residual N15 nu leus before exiting. Intera -tions pertinent to the de ay modes in this dissertations are K+N elasti s attering,K0N elasti s attering, K+N inelasti s attering, and K0N inelasti s attering via harge ex hange.The K+p rea tion an pro eed elasti ally or inelasti ally. Inelasti ities are dueto a K+p ! K+� resonan e. The distribution for total and elasti ross-se tionsbased on data submitted to the parti le data group [68℄ is shown in �gure 6.3. Apartial wave analysis for the s attering amplitudes was performed by Hyslop et al.by doing a global �t to many data samples [69℄ and is also shown in �gure 6.3.The line around 600 MeV/ represents the maximum momentum of the K+ fromp ! ��K+ in the rest frame of a target proton within the residual nu leus. Below800 MeV/ or so K+p s attering is mostly elasti , therefore a K+ from the proton

67de ay p ! ��K+ will only experien e elasti s attering with protons in the residualnu leus. Sin e proton de ays via p ! ��K+ are identi�ed through the dete tion ofthe daughter parti les of the K+ de ay at rest, K+p s attering will not a�e t thedete tion eÆ ien y of the proton de ay mode p! ��K+ .

pkaon (MeV/c)

σ (m

b)

total cross-section

elastic cross-section

total cross-section: Hyslop et. al.

elastic cross-section: Hyslop et. al.

0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

14

16

18

20

Figure 6.3: Cross se tions for the K+p intera tion in the rest frame of the proton.Open triangles and ir les orrespond to data submitted to the Parti le Data Group.Solid boxes and ir les orrespond to a partial wave analysis by Hyslop et al. Theline around 600 MeV illustrates the uto� momentum for K+ from p! �K+ in therest frame of the target proton.The harge ex hange rea tion K+n! K0p an redu e the eÆ ien y for dete tingp! ��K+ events. It is important to estimate what fra tion of K+ are lost due thise�e t. The rea tion was measured for low momentum kaons (250 to 600 MeV/ ) byGlasser et al. [70℄ yielding ross se tions ranging from 2.0 � 0.18 mb at 250 MeV/ K+ momentum to 6.4 �0:56 mb at 590 MeV/ K+ momentum. To estimate the

68fra tion of K+ lost due to this e�e t, a Monte Carlo simulation was performed. K+were started at random points in the nu leus a ording to the Woods-Saxon densitydistribution (equation 6.2) with random momenta drawn from the Fermi momentumdistribution. They were then stepped through the nu leus in 0.07-fm in rements. Atea h point the nu lear density and ross-se tion for K+n ! K0p harge-ex hangewere al ulated from whi h an intera tion probability was al ulated. The K+ wasstepped through until it rea hed 4 fm, the outer edge of the nu leus. If there wasan intera tion, Pauli blo king was taken into a ount by requiring the momentum ofthe re oil nu leon to be greater than the top of the Fermi surfa e (pF )pre oil > pF (r) = �h 3�22 �(r)! (6.3)where �(r) is the same as de�ned in equation 6.2. On the basis of this simulation,it is estimated that 4% of K+ from p! ��K+ proton de ays are lost due to hargeex hange.Be ause of isospin symmetry, the K0N rea tions have essentially the same mag-nitude as the K+N rea tions. For this reason, it is estimated that approximately4% of K0 from n ! ��K0 , p ! �+K0 , and p ! e+K0 are lost due to the hargeex hange rea tion K0p ! K+n. Elasti s attering was estimated to have a smalle�e t and was negle ted.Intera tions of pions in nu lei are not important for the Monte Carlo simulationof nu leon de ay modes studied in this dissertation, but they are important for theestimation of ba kground from atmospheri neutrinos to these de ay modes. Detailsof these nu lear intera tions will be des ribed in the following se tion.

696.2 Atmospheri Neutrino Monte CarloAtmospheri neutrinos are produ ed in ollisions of osmi rays with air mole ulesin the atmosphere of Earth. Primary osmi rays intera t hadroni ally with airmole ules reating ��,K�, K0, and other mesons. Neutrinos are then produ edthrough the de ay hains of these mesons�+ ! �+ �� (6.4)�+ ! e+ ��� �e (6.5)�� ! �� ��� (6.6)�� ! e� �� ��e (6.7)K+ ! �+ �� (63:5% B.R.) (6.8)K+ ! �+ �0 (21:2% B.R.) (6.9)� � �The ratio of K produ tion to � produ tion varies with energy of the primary osmi ray. It is 7% and 11% for 10 and 100-GeV primaries, respe tively.Be ause the ross se tions for neutrinos to intera t with matter is extremely small,they an travel uns athed through the earth and intera t with a nu leon in the waterof Super{Kamiokande via the weak intera tion. A generi intera tion is�l +N ! l +N 0 +X (6.10)where N and N 0 are the initial and �nal state nu leons, l is the outgoing leptonasso iated with �l, andX are other possible hadroni parti les su h as pions. Be ausesome of these intera tions result in topologies similar to those of nu leon de ays,

70they present a hallenging ba kground to nu leon de ay sear hes. It is ne essary tounderstand and predi t this ba kground as pre isely as possible.6.2.1 Atmospheri Neutrino FluxThe �rst step in predi ting the atmospheri neutrino ba kground is al ulating the ux of atmospheri neutrinos at Super{Kamiokande. The al ulation by Honda[71℄[72℄ was used in this dissertation. The neutrino os illation analysis also uses theBartol al ulation [73℄ as a ross he k. The al ulations agree within a few per ent,and therefore the Honda al ulation is suÆ ient for this analysis. A summary ofHonda's al ulation will be given in this se tion.Primary osmi rays are omposed of mainly hydrogen and helium nu lei withabundan es of � 95% and 5%, respe tively. Cal ulation of the ux of these primariesis done in two energy regimes, lower energy (0:01-100 GeV) and higher energy (100-1000 GeV).Low energy osmi rays are a�e ted by solar a tivity. Higher solar a tivity (solarmaximum) in uen es lower energy osmi rays in su h a way that the ux at earth issmaller. The solar y le has a period of 11 years with the last solar minimum in 1996and the next solar maximum in 2001. The middle of the solar y le was used in the ux al ulation of atmospheri neutrinos. The earth's magneti �eld also a�e ts the ux in su h a way that there is a de� it of low energy osmi rays (p < 50 GeV= ) oming from the east. This has been observed in Super{Kamiokande by a de� it ofneutrinos with momenta ranging from 400 MeV/ to 3000 MeV/ [74℄.In the higher energy regime (> 100 GeV) the spe trum is �t to a power law� = A� E100GeV� (6.11)

71where A is a normalization fa tor having units of ux, m�2 se �1 steradian�1 GeV�1.The �ts are (A = 6:65, = �2:75) for hydrogen nu lei and (A = 3:28, = �2:64)for helium nu lei. The resulting uxes for H,He, and CNO nu lei are shown in �gure6.4. The �nal neutrino ux al ulated at the Super{Kamiokande site is shown in�gure 6.5. The overall un ertainty in the absolute ux is � 20%.-1

-1G

eV)

(mse

csr

Flux

-1-2

4

Kinetic Energy per Nucleon (GeV)10

-110

010

110

210

310

-4

10 -3

10 -2

10 -1

100

10 1

10 2

10 3

10

Figure 6.4: Flux of primary osmi rays used in Honda's al ulation. The top three urves orrespond to al ulations for solar minimum (top), solar average (middle),and solar maximum (bottom) for Hydrogen. Similarly, the middle three orrespond toHelium and the bottom three to CNO. Points are from experimental measurements.6.2.2 Neutrino-nu leon Cross se tionsOn e the ux of atmospheri neutrinos at Super{Kamiokande has been estimated,their intera tion rate in the dete tor needs to be al ulated. In the simulation, thefollowing harged and neutral urrent neutrino intera tions are taken into a ount1. Quasi-elasti s attering

72

Eν

Flu

x E

ν2 (m

-2 s

-1 s

r-1 G

eV)

νe + νe

νµ + νµ

__

Atmospheric neutrino flux:Honda calculation

10-2

10-1

1 101

10

10 2

10 3

10 4

Figure 6.5: Neutrino ux in the middle of the solar y le at the Super{Kamiokandesite al ulated by Honda et al. The overall un ertainty is � 20%.2. Single pion produ tion3. Multiple pion produ tion4. Coherent pion produ tion5. �,K produ tion6. Deep inelasti s atteringThis se tion summarizes the ross se tions for ea h of these pro esses. Fermi momen-tum in O16 is taken into a ount for �N s attering using the distribution in �gure 6.1.In addition, Pauli blo king is taken into a ount by requiring that the re oil nu leonin the s attering is greater than the Fermi surfa e momentum (equation 6.3).

73Quasi-elasti Charged urrent and neutral urrent quasi-elasti rea tions are al ulated using stan-dard V � A theory. A detailed al ulation was done by Llewellyn-Smith [75℄. The ross se tions are shown in �gure 6.6. Quasi-elasti intera tions are typi ally hara -terized in Super{Kamiokande by their single tra k either from the outgoing lepton in�N ! lN 0 harged urrent intera tions or a re oil proton above Cherenkov thresholdin �N ! �N neutral urrent intera tions.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

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ν charged current elastic scattering

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Neutrino energy (GeV)

σ (1

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free protons

protons bound in O16

neutrons bound in O16

Neutrino energy (GeV)

anti-ν charged current

elastic scattering

νp → l+ n

Anti-neutrino energy (GeV)

σ (1

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elastic scattering

free protons

bound nucleons

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Figure 6.6: Charged and neutral urrent quasi-elasti s attering ross se tions forboth �� and �.Be ause quasi-elasti intera tions typi ally do not indu e multi-ring events, theydo not ontribute signi� antly to ba kgrounds of nu leon de ays whi h produ e mul-tiple parti les. The only nu leon de ay mode studied in this dissertation to whi h

74quasi-elasti s attering ontributes to the ba kground signi� antly is p ! ��K+ ;K+ ! �+�� whi h is hara terized by a 236-MeV/ mono hromati muon. Thequasi-elasti rea tions produ es a large but ontinuous ba kground. One way to �ndthe proton de ay p! ��K+ ; K+ ! �+�� is to sear h for a peak above ba kgroundin the muon momenta spe trum.Meson Produ tionMeson produ tion indu ed by atmospheri neutrinos is the most hallenging ba k-ground to nu leon de ay. Be ause of their potential for multiple tra ks, these events an mimi nu leon de ay events. Most of the mesons produ ed in atmospheri neu-trino intera tions are pions. Pion produ tion an be generally lassi�ed into twotypes, single-� and multi-� produ tion. Although the e�e t is small ompared topion produ tion, K+, K0, and � produ tion is in luded in the Monte Carlo simula-tion.Single-� produ tion begins to be ome important at a neutrino energy of about 1GeV. The model by Rein and Sehgal [76℄ is used to al ulate the ross se tions andsubsequent rates in Super{Kamiokande of single-� produ tion. This model uses thefa t that neutrinos with energies above 1 GeV intera ting with nu leons an generateresonan es whi h subsequently de ay, emitting pions�N ! lN� ! lN 0� (6.12)where N is the target nu leon, N� is the resonant state, l is the outgoing lepton,and N 0 is the �nal state nu leon. Fourteen resonan es are in luded in the simulationand both harged urrent and neutral urrent s enarios are in luded. Plots of rossse tion are shown in �gure 6.7.

75

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1ν Charged current single π production

νp → l- p π+

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Neutrino energy (GeV)

σ (1

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ν Neutral current single π production

νn → ν n π0

νp → ν p π0

νn → ν p π-νp → ν n π+

Neutrino energy (GeV)

σ (1

0-38 m

b)

0 2 4 6 8 10 12 14 16 18 2000.020.040.060.080.1

0.120.140.160.180.2

Figure 6.7: Single-pion produ tion ross se tions.The dominant resonan e in the region below 1.4 GeV is the �(1232) resonan e.For this resonan e, the angular distribution for the resulting pion is determined usingRein and Sehgal's al ulation [76℄. The angular distributions for the resulting pionsfor other resonan es are assumed to be isotropi .Coherent s attering o urs when a neutrino s atters o� of the O16 nu leus as awhole rather than a nu leon within it. These rea tions an indu e only single pionprodu tion. The model used is outlined in referen es [77, 78℄. Coherent s attering is lean in that pions are produ ed outside the O16 nu leus so nu lear intera tions donot play a part. Cross se tion plots for oherent s attering are shown in �gure 6.8.Deep inelasti s attering with multiple � produ tion at �N invariant masses ofthe neutrino-nu leon system above 2 GeV is in luded using a model based on the

76Coherent π production

νO16 → ν O16 π0νO16 → l- O16 π+

Neutrino energy (GeV)

σ (1

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b)

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Figure 6.8: Coherent-pion produ tion ross se tions.GRV94 al ulations of the parton distribution fun tions of the nu leus [79℄. Forinvariant masses from 1.4 GeV to 2.0 GeV, the model by Rein-Sehgal is used [77℄.The ross se tions for multiple � produ tion are shown in �gure 6.9.The mean number of pions, �n� produ ed in multiple pion produ tion intera -tions was studied at Fermilab with the 15-foot hydrogen bubble hamber [80℄. Themultipli ity was �t to the data�n� = 0:09 + 1:83 lnW 2 (6.13)where W is the �N invariant mass of the system. The forward-ba kward asymmetryof the pion produ tion was determined by the BEBC experiment [81℄ and is given

77

0 2 4 6 8 10 12 14 16 18 2002468

101214 Charged Current multiple π production

ν

anti-ν

Neutrino energy (GeV)

σ (1

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ν

anti-ν

Neutrino energy (GeV)

σ (1

0-38 m

b)

0 2 4 6 8 10 12 14 16 18 200

1

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Figure 6.9: Multiple-pion produ tion ross se tions.by the relation �nf��nb� = 0:35 + 0:41 lnW 20:50 + 0:09 lnW 2 (6.14)Finally, neutral urrent ross se tions of deep inelasti s attering are al ulated fromthe harged urrent ross se tions using the relations outlined in referen e [82, 83℄.Produ tion of K+, K0, and � mesons is in luded based on the model of Rein andSehgal [76, 84℄. Although these intera tions may seem as if they would ontributeto the ba kground to nu leon de ay modes with kaons in the �nal state, their rossse tions are rather small ompared to those for single-pion and multi-pion produ tion.In addition, K produ tion is a ompanied by a � baryon whi h de ays into eitherp�� or n�0. Figure 6.10 shows the various ross se tions for K produ tion and �gure6.11 shows the various ross se tions for � produ tion.

78

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.01

.02

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.05ν Charged current single K production

νn → l- Λ K+

anti-ν p → l+ Λ K0

Neutrino energy (GeV)

σ (1

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ν Neutral current single K production

νn → ν Λ K0

νp → ν Λ K+

anti-ν n → anti-ν Λ K0

anti-ν p → anti-ν Λ K+

Neutrino energy (GeV)

σ (1

0-38 m

b)

0 2 4 6 8 10 12 14 16 18 200.

.002

.004

.006

.008

Figure 6.10: K produ tion ross se tions. These ross se tions are small omparedto those for single-� and multi-� produ tion.6.2.3 Propagation of Pions Through Nu leusNu lear intera tions of pions before es aping the nu leus a�e ts the estimation ofba kground for nu leon de ay. To estimate this e�e t, pions are propagated throughthe nu leus after they are reated in simulated atmospheri neutrino intera tions.The starting point of the pion is determined using the Woods-Saxon density distri-bution (equation 6.2), and the pion is stepped through the nu leus from that pointin 0.07-fm in rements. At ea h step, the ross se tions for harge ex hange, pionabsorption, and inelasti s attering are al ulated using the model by Oset et al.[85℄. The probability of ea h of these intera tions for positively harged pions isshown in �gure 6.12 [86℄. The model used was he ked using experimental data from

79

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0.020.040.060.080.1

0.120.140.160.180.2

ν Charged current single η production

νn → l- p η0

anti-ν p → l+ n η0

Neutrino energy (GeV)

σ (1

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b)

ν Neutral current single η production

νn → ν n η0

νp → ν p η0

anti-ν n → anti-ν n η0

anti-ν p → anti-ν n η0

Neutrino energy (GeV)

σ (1

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b)

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0.005

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Figure 6.11: � produ tion ross se tions. Like the ross se tions for K produ tion,they are small ompared to those for single and multi-� produ tion.�+-O16 s attering [87℄ and �+-C12 s attering [88℄ and a omparison of data [87℄ andMonte Carlo for the di�erential ross se tions of �+-O16 s attering for three momenta(p = 213; 268; 353 MeV) is shown in �gure 6.13. Finally, Pauli blo king is taken intoa ount by requiring the re oil nu leon to be above the Fermi surfa e (equation 6.3).6.2.4 Normalization of Ba kgroundUsing the neutrino ux al ulation des ribed in se tion 6.5 and the ross se tions forvarious neutrino intera tions des ribed in se tion 6.2.2, a �nal 40-year equivalent sam-ple of atmospheri neutrino Monte Carlo was generated. It has been well known forsome time that there is a de� it of events indu ed by muon neutrinos [89, 90, 51, 91℄.

80

pπ (MeV/c)

Cu

mu

lati

ve P

erce

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absorption

inelastic scatt.

Charge exchange

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0 50 100 150 200 250 300 350 400 450 500Figure 6.12: Cumulative probabilities for absorption, inelasti s attering, hargeex hange, and no intera tion of positively harged pions traversing an O16 nu leusas a fun tion of the pion's momentum.To estimate the a tual number of ba kground events, the ux was normalized basedon the observed de� it of muon neutrinos [29, 28℄ and the observed number of ele tronneutrinos. This normalization assumes that muon neutrinos os illate to tau neutri-nos and ele tron neutrinos do not parti ipate in os illation. Therefore, the ele tronneutrino events are used as an overall normalization. Charged urrent ba kgroundevents indu ed by ele tron neutrinos were given a weight of 1.17 while the harged urrent events indu ed by muon neutrinos were given a weight of 0.74. All neutral urrent events were weighted by 1.17. Finally the 40-year sample (898 kton�years)was normalized to the 61-kton�year sample of Super{Kamiokande exposure.

81Scattering angle (degrees)

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dia

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eV)

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0 20 40 60 80 100 120 140 160 180Figure 6.13: Di�erential ross se tions for �+-16O s attering. The points show theexperimental measurement of Ingram et al. and the histogram shows the result ofthe Monte Carlo simulation.6.3 Dete tor SimulationThe GEANT [92℄ program developed at CERN was used in the dete tor simulation ofparti les traversing the dete tor. The program handles the physi s pro esses, dete torgeometry and response, and run and event ontrol. Hadroni intera tions above 500MeV were simulated using the CALOR [93℄ program whi h was also developed atCERN. For energies less than 500 MeV a ustom program was used [86℄.The number of Cherenkov photons generated by a parti le at ea h wavelength issampled from the Poisson distribution whose mean is given by equation 4.2. Theyare emitted at an angle relative to the dire tion of the path of the parti le givenby 4.1. On e the photons are emitted, they an undergo Rayleigh s attering, Mies attering, or absorption. Measurements with an N2 laser of these ontributions issummarized in se tion 5.4. Figure 5.8 shows with solid lines the model used in thedete tor simulation and with points the results of the measurement.Signals are generated for photons whi h strike the fa e of a PMT using the quan-tum eÆ ien y urve shown in �gure 4.6 and the single PE distribution for thatparti ular PMT (�gure 5.3).

Chapter 7Sele tion of Contained EventsApproximately 5 � 105 \high-energy" triggers are re orded in Super{Kamiokandeper day, orresponding to about 10 gigabytes of data. Most are either low energyevents aused by radioa tivity or osmi ray muons. These data are not interestingto nu leon de ay or atmospheri neutrino analyses and must be removed from thesample.7.1 1st Redu tionThe large size of the unredu ed data set requires the �rst step of redu tion to qui klyredu e the sample signi� antly. The riteria are:1. NODhit (800 ns) < 50 hits2. N IDhit (300 ns) > 200 PE3. time to previous event > 100 �se where NODhit (�t) (N IDhit (�t)) is the number of OD (ID) hits within a time window ofwidth �t. The �rst riterion removes osmi ray muons. The se ond removes low82

83energy events where 200 PE orresponds to an ele tron with an energy of about 23MeV. The third riterion removes events aused by de ay ele trons from stopping osmi ray muons. This redu tion redu es the data set by a fa tor of �100 to �4000events/day.7.2 2nd Redu tionThe 2nd redu tion is designed further to eliminate low energy events and osmi -raymuons. The sele tion riteria are:1. Qmax=Q(300 ns) < 0:52. NODhit (500 ns) < 50 or NODhit (500 ns) > 25 and Qtot < 105 PEwhere Qmax is the largest harge re orded by a single PMT, Q(�t) is the total harge re orded by the ID in a time window of �t, and Qtot is the total number ofPE dete ted by the ID. The �rst riterion removes noise events whi h have one largea idental hit. The se ond is a further redu tion of osmi ray muon events. Thedata rate after this redu tion is �400 events/day.7.3 3rd Redu tionAt this stage the event rate is small enough so detailed uts requiring more ompu-tation time are applied to the sample. The third redu tion onsists of six steps.7.3.1 Through going muonsThrough going muons enter the dete tor at some point and leave at some other point.Candidates are �rst sele ted by requiring that

84 1. Qmax � 230 PE2. N IDhit � 1000where N IDhit is the total number of hit PMTs in the ID. After events pass these riteria,a muon �tter is applied and a dire tion is �t by estimating the entering and exitingpoints of the muon. The entering point is de�ned as the position of the earliest hitPMT with at least two hit PMTs next to it. The exiting point is de�ned as the entral point where the PMTs are saturated. If the sum of OD hits within an 8-mradius and 800-ns time window (\OD luster") of the proje ted entering or exitingpoint of the muon is greater than 9, the event is lassi�ed as a \through-going muon"and dis arded.7.3.2 Stopping muonsStopping muons are osmi ray muons whi h enter the dete tor but stop and de ayinstead of exiting. A rough guess for the entran e point (vertex) of the muon is takento be the earliest hit PMT with at least two hit neighboring PMTs. This vertex isre�ned and a dire tion is �t by maximizing the sum of harge in a one with openingangle of 44 degrees whose axis orresponds to the dire tion of the muon. After avertex and dire tion are found goodness Gtot is al ulated using equation 8.6. Eventswith Gtot > 0:5 having greater than 9 hits in the OD luster proje ted ba k from the�tted dire tion are lassi�ed as a stopping muon and dis arded.7.3.3 Low energy event reje tionEvents are reje ted if they satisfy one of the following riteria::1. N IDhit � 500 and N IDhit (50 ns) < 50

852. Gpoint < :5where G is de�ned in equation 8.1. These low energy events are �rst �t using thelow energy vertex �tter. This �tter uses a grid sear h to maximize the goodness ofvertex �t of tubes within a 50-ns timing window. If the goodness is < 0.5, the eventis reje ted. If the number of hits in the 50-ns time window is < 50, the event is alsoreje ted. In the low energy analysis, nhit is onverted to energy. Roughly 5 hits =1-MeV. Therefore, ele trons with energies of less than about 10 MeV are reje ted bythis ut.7.3.4 Flasher reje tionPMTs an sometimes have a breakdown in the dynode hain whi h ause them toemit light whi h an trigger the dete tor. These PMTs are alled \ ashers." Su hevents typi ally have a wide timing distribution with many hits o uring well afterthe main trigger. Events aused by parti les traversing the dete tor typi ally havehits with times of no more than 100 ns later than the main trigger. Flashing eventsare reje ted by satisfying one of the following riteria:1. N slidemin (100 ns) > 142. N slidemin (100 ns) > 9 and N IDhit < 800where N slidemin (�t) is the minimum number of hits o uring in a sliding window ofwidth �t from about 200 ns to 800 ns after the dete tor triggers.7.3.5 Cable holeThe ables whi h supply power to and transmit signals from the PMTs are bundledtogether and leave the tank through 12 \ able holes." Four of the bundles make the

86OD insensitive in these regions. When data taking began in April 1996, osmi -raymuons would sometimes pass through the OD into the ID through one of the four able-bundles. This would ause the ID to trigger with no signal in the OD. In April1997, \veto-hats" were installed above ea h of the four troublesome able-bundles toredu e the rate of muons passing through the bundles without being dete ted by theOD. These are 2 m � 2.5 m s intillation ounters whi h if �re, the stopping muon�tter is applied and the event is reje ted if the re onstru ted vertex is within 4 mfrom the lo ation of the \veto-hat" that �red.7.4 Final Redu tion: ashs an and s anningAfter the third redu tion, the event rate is about 30 events/day. Unfortunately this isnot a pure atmospheri neutrino/nu leon de ay sample. There still remain impuritiesfrom osmi -ray muons and ashing PMTs. \Flashs an" is a program whi h usesspatial orrelations between hit PMTs in separate events to redu e the number of ashers [29℄. This program redu es the number of events that must be s anned byphysi ists from about 30 events/day to about 17 events/day. The remaining eventsars s anned by physi ists to further eliminate any remaining ontamination from ashers or osmi -ray muons.7.5 Final Event SampleThe �nal event rate of fully ontained events after the fourth redu tion is about15-events/day. The rate of events with verti es re onstru ting within the �du ialvolume of the dete tor, de�ned as 2 m from the dete tor wall, is 8.3 events/day. Theestimated probability to lose a fully ontained atmsopheri neutrino or nu leon de ay

87event through the redu tion steps is less than 0.1%. In the 61-kton�year data sampleused in this dissertation, 7940 ontained events were re orded in the �du ial volumeof the dete tor.

Chapter 8Event Re onstru tionEvent re onstru tion is the pro ess of determining the various event hara teristi ssu h as vertex, number of parti les traversing the dete tor, the dire tions and mo-menta of these parti les, and the number of de ay ele trons. This hapter des ribesthe pro edure for determining the various event hara teristi s.8.1 Single ring �tting: a�tThe �rst step in event re onstru tion is vertex �tting. The vertex is de�ned as thelo ation of the neutrino intera tion or nu leon de ay. Using timing information, apoint �t is performed by maximizing the goodness of �t de�ned asGpoint = 1Nhit Xi exp (ti � �t)22a2�2 ! (8.1)where Nhit is the number of hit PMTs onsidered in the �t, �t is the average time-of- ight subtra ted time, � is the typi al timing resolution (2.5 ns), a = 1:5 is a fa torused to a ount for s attered light, and ti is the time of ight subtra ted time from88

89the vertex to the ith PMT ti = 1v(di; qi)di (8.2)where di is the distan e from the ith PMT to the vertex, and v(di; qi) is the velo ityof light whi h depends on di and qi, the harge dete ted at the i-th PMT.After the point �t, a dire tion is al ulated.by optimizing the fun tionGdir = R �edge0 Q(�)d�sin �edge exp �(�edge � �C)2�2 ! (8.3)where Q(�) is the distribution of harge as a fun tion of angle relative to the trialdire tion (the Q(�) distribution for a 525-MeV ele tron is shown in �gure 8.1) and�C is the maximum Cherenkov angle for when a parti le's velo ity � = 1. �edge isthe angle � losest to and greater than �peak where the se ond derivative of the Q(�)distribution is equal to 0. For trial dire tions, Gdir is al ulated. The dire tion andopening angle �edge are found by maximizing Gdir.The method des ribed above only gives a rough estimate of the vertex and dire -tion of the tra k. It does not take into a ount the �nite tra k length of the parti le.This is a omplished by de�ning two goodnesses, GI and GO whereGI =Xi 1�2i exp �(ti � �t)22a2��2 ! (8.4)GO =Xi 1�2i max "exp �(ti � �t)22a2��2 ! ; 0:8 exp (�� onst(ti � �t))# (8.5)where a = 1:5 a ounts for s attered light, �i is the timing resolution of the i-thPMT, �� is the average of the �i's, ti is the residual time of the i-th PMT, �t is theaverage of the ti's, and � onst = 1=(20 ns) is the average di�eren e in time betweendire t and s attered light. The fa tors GI and GO orrespond to dire t and s attered

90

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electron direction

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Figure 8.1: A Q(�) distribution for a 525-MeV ele tron.light, respe tively. In GI , only PMTs with angles �i < �edge or with times ti < �t arein luded. For GO, tubes with angles �i > �edge and times ti > �t are in luded. The�nal goodness is de�ned as Gtot = GI +GOPi �i (8.6)The goodness is al ulated for varying verti es and dire tions. A �nal vertex anddire tion is the point where the goodness is maximized.The distributions of verti es for single-ring muons with momenta in the range ofp ! ��K+ ; K+ ! �+�� and sub-GeV multi-ring for the 61-kton�year data sampleis shown in �gure 8.2. Sub-GeV events are de�ned as events having visible energyless than 1.33 GeV. These are the only samples pertinent to nu leon de ay analysessin e nu leon de ays are often hara terized by multiple rings with a maximum total

91

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Figure 8.2: Vertex distributions for the 61 kiloton�year sub-GeV sample. Left �gureis for single-ring muons and right �gure is for multi-ring events.energy of not more than 1 GeV. The verti es are uniformly distributed throughoutthe dete tor volume. To test the vertex resolution, the verti es of re onstru tedMonte Carlo events are ompared to the \true" vertex. Distributions of deviationsfrom the true vertex are shown for various nu leon de ay Monte Carlo samples in�gure 8.3. In general, the vertex resolution is better than 25 m. The only deviationfrom this is for the p ! ��K+ ; K+ ! �+�� events whi h have less Cherenkov lightyield.8.2 Ring ountingRing ounting is the method by whi h the tra ks of parti les are found in eventswith more than one parti le traversing the dete tor. Tra ks are also referred to as\rings." This is based on the pattern of Cherenkov light dete ted on the walls of thedete tor. Ring ounting is an important aspe t of a nu leon de ay analysis be ausemost nu leon de ay modes have multiple parti les.The �rst step to ring ounting is to onvert the harge distribution in the dete tor

92δvertex (cm)

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0 20 40 60 80 100 120 140 160 180 200Figure 8.3: Deviation of re onstru ted vertex from true vertex for various nu leonde ay Monte Carlo samples.to a Hough transform [94℄. The pro edure for generating a Hough transform is asfollows:1. Transform the oordinates of the PMTs from (x; y; z) to (�; �) spa e, relativeto the vertex position.2. Distribute the harge from ea h PMT evenly in a ir le whose enter is thePMT in (�; �) spa e (see �gure 8.4). The radius of the ir le orresponds tothe Cherenkov angle.The idea behind the Hough transform is that the ir les overlap in su h a waythat the point of maximum intensity in the Hough spa e o urs in the enter of theCherenkov ring pattern. The peaks in Hough spa e therefore orrespond to dire tionsof the parti les. A sample event and its Hough transform is shown in �gure 8.5.Four Hough transforms are reated using di�erent harge distributions whi h willbe des ribed later. The three highest peaks from ea h of the four transforms are put

93

Circles overlapin center of ring correspondingto direction of particle

Hit PMT

Not-hit PMT

PMT corresponding to circle

PMT arrayFigure 8.4: Hough transform pro edure. After transforming the PMT oordinatesfrom (x; y; z) spa e to (�; �) spa e, evenly distribute the harge from the PMT in a ir le around it. The ir les overlap in the enter of the Cherenkov ring orrespondingto the dire tion of the tra k.into a list of \trial" rings. There is also a list of rings whi h have already been foundwhi h will be referred to as \�xed" rings. Ea h of the trial dire tions is tested to seeif it is a ring. The testing pro edure is as follows:1. Perform harge separation on the �xed rings and the trial ring and omputethe likelihood Ltrial. Charge separation is performed by al ulating a likelihoodbetween the a tual harge distribution in the dete tor and the expe ted hargedistributions for varying momenta of the list of rings. Charge is assigned tothe rings at the point of maximum likelihood.2. Perform harge separation only on �xed rings and ompute the likelihoodLfixed.3. Compare the likelihood di�eren e �L = Ltrial � Lfixed. The trial ring withthe greatest �L whi h is greater than 0 is added to the list of �xed rings.The pro edure is then repeated from s rat h starting with reating the Houghtransforms. If �L < 0 for all trial rings, the pro edure is stopped.

94Super-KamiokandeRun 5490 Event 68424798-01-15:02:49:57

Inner: 2057 hits, 4630 pE

Outer: 8 hits, 5 pE (in-time)

Trigger ID: 0x07

D wall: 527.4 cm

Fully-Contained

Charge(pe) >15.013.1-15.011.4-13.1 9.8-11.4 8.2- 9.8 6.9- 8.2 5.6- 6.9 4.5- 5.6 3.5- 4.5 2.6- 3.5 1.9- 2.6 1.2- 1.9 0.8- 1.2 0.4- 0.8 0.1- 0.4 < 0.1

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Figure 8.5: An example two-ring event and its hough transforms: a) the a tual eventb) tube hits in �-� spa e ) ontour plot of Hough map d) 3-dimensional plot ofHough transform. The two peaks in Hough spa e an learly be seen.

95Now the four Hough transforms used to �nd the rings will be des ribed. The�rst is reated with the observed harge of the event with the expe ted harge of the�xed rings removed. The se ond is reated with the fra tion of harge not assignedto any of the �xed rings. The third transform is reated with any harge inside a one of 50Æ opening angle of any �xed rings removed. Finally there is the \ lean"Hough transform whi h uses the �rst transform. A ir le is entered on ea h point inthe �rst transform and the pla e on that ir le where the maximum harge o urs isentered in the \ lean" spa e. The purpose of this is to make the peaks in the Houghspa e more pronoun ed. For ea h of the four variations, a separate map is made forCherenkov angles ranging from 24 degrees to 46 degrees in steps of two degrees.

Number of rings

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Figure 8.6: Number of rings for the 61-kton�year data sampel (points) and 40-yearatmospheri neutrino Monte Carlo (normalized to the 61-kton�year livetime).The results of the ring ounting for the 61-kton�year data sample and the 40-yearatmospheri neutrino Monte Carlo is shown in �gure 8.6. The performan e of the

96ring ounting was he ked using the \truth" information from the various nu leonde ay Monte Carlo samples. EÆ ien y urves as a fun tion of parti le momentumare shown in �gure 8.7 for the various nu leon de ay samples. For the p ! e+K0and p ! �+K0 Monte Carlo samples with KS ! �0�0 , the eÆ ien y to dete t the -rays from the �0 be omes better than 95% for p more than about 175 MeV/ . Atp =75 MeV/ , the eÆ ien y is estimated to be �20%. For p! ��K+ ; K+ ! �+�0 ,the eÆ ien y to dete t the -rays begins to de line at p =75 MeV/ and at p =50MeV/ , the eÆ ien y is estimated to be �30%.p→νK K→π+π0 MC

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150 200 250 300 350 400 450 500Figure 8.7: EÆ ien y urves as a fun tion of parti le momentum for pions and -raysin p! ��K+ , n! ��K0 , p! �+K0 , and p! e+K0 Monte Carlo samples.8.3 Parti le identi� ationParti les are identi�ed in Super{Kamiokande as either showering (e-like) or non-showering (�-like). Showering parti les orrespond to ele tromagneti showers in-du ed by either ele trons, positrons, or -rays. Non-showering parti les are aused

97by heavier parti les like muons, pions, and protons whi h do not indu e ele tro-magneti showers. Tra ks are identi�ed as either e-like or �-like by omparing theirdistribution of harge with the expe ted harge distributions for ele trons or muons.For single ring events, the opening angle of the Cherenkov ring is also onsidered.8.3.1 Ele tron expe ted PE distributionThe expe ted PE distribution for ele trons at a distan e of 16.9 -m from the ele tron'svertex is �rst estimated for the ideal ase in whi h there is no light s attering or at-tenuation. This provides a template harge distribution, Q(pe; �), for ele trons whi hdepends on the momentum of the ele tron, pe, and the opening angle, �, between theele tron's dire tion and the dire tion of Cherenkov photon. Based on vertex, dire -tion, and the estimated momentum of parti les dete ted in Super{Kamiokande, thistemplate harge distribution is altered for geometri al and dete tor e�e ts yieldingthe expe ted PE distribution Qeexp(i) at the i-th PMTQeexp(i) = Q(pe; �i) �16:9 mli �1:5 exp liL! f(�) (8.7)where �i is the angle between the i-th PMT and the dire tion of the ele tron, li is thedistan e between the i-th PMT and the point of emission of Cherenkov light, L isthe water attenuation length, and f(�) is the angular a eptan e of the PMT. Theexponential fa tor takes into a ount water attenuation and the fa tor (16:9-m=l)1:5takes into a ount the di�eren e in dispersion between the ideal ase al ulated for16.9-m path length and the a tual ase of l path length. A sample expe ted PEdistribution for a 525-MeV ele tron is shown in �gure 8.8. This is to be omparedwith the a tual angular harge distribution shown in �gure 8.1.

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Figure 8.8: The expe ted angular photoele tron distribution orresponding to a 525-MeV ele tron. This distribution takes into a ount dete tor e�e ts like geometry andlight attenuation.8.3.2 Muon expe ted PE distributionThe expe ted PE distribution for �-like events takes into a ount the de reasingCherenkov angle when heavier parti les lose energy when traversing the dete tor.The distribution is given byQ�exp(i) = 24 �� sin2 �ili �sin �i + li d� dr � +QÆ(i)35 exp liL! f(�) (8.8)where �� is a normalization fa tor, li(sin �i + li d� dr ) a ounts for the de rease inCherenkov angle with path length, and QÆi is the ontribution from delta-ray pro-du tion. The parameters li, L, �i, and f(�) are the same as in equation 8.7. Asample expe ted angular PE distribution for a 725-MeV muon is shown in �gure 8.9.

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Figure 8.9: The expe ted angular photoele tron distribution orresponding to a 725-MeV muon.8.3.3 Parti le identi� ation parameterAfter the expe ted harge distributions are generated for the showering and non-showering s enarios, they are ompared to the a tual harge distribution dete ted inSuper{Kamiokande and a likelihood is al ulated for the two.L(e; �) =Yi P (ti; Qobs(i); Qe;�exp(i)) (8.9)where i represents the i-th PMT lying within an angle of 1:5 �C relative to thedire tion of the parti le. To a ount for s attered light the probability fun tiondepends on the time ti of the PMT.P e;� = p (Qe;�exp;dire t(i); Qobs(i)) �30 ns < t� t0 < 2� + 5 ns= p (Qe;�exp;dire t(i); 0) p(Qe;�exp;s att(i); Qobs(i)) otherwise (8.10)

100The �rst is the probability fun tion used for dire t Cherenkov light and the se ondis used for s attered light. The p (Qexp; Qobs) is the probability to observe Qobs PEwith and expe tation of Qexp. For Qobs < 20 PE, this is derived from the measuredsingle-PE distribution. For Qobs � 20 PE it is a Gaussianp(Qexp; Qobs) = 1p2�� exp �(Qexp �Qobs)22�2 ! (8.11)where �2 = 1:22Qexp + (0:1Qexp)2. The se ond fa tor a ounts for the un ertaintyin the relative gain of the PMT. The fa tor of 1.2 a ounts for the a tual un ertaintyin the PMT resolution ompared to the ideal ase.For single ring events, the opening angle of the Cherenkov ring is taken intoa ount. Heavier parti les like pions, muons, and protons with � < 1 generateCherenkov ones with smaller opening angles . Based on the re onstru ted momen-tum an expe ted Cherenkov angle, �exp, is determined. From this, a probability is omputed P e;�� = A exp �(�e;�exp � �obs)2�2� ! (8.12)where �� is the un ertainty in the Cherenkov angle.The probabilities for the showering and non-showering s enarios and openingangle are then ombined into a total probabilityP e;�tot = P e;�� P e;� nring = 1= P e;� nring > 1 (8.13)The �nal parti le identi� ation parameter is based on a log likelihood method:PID = q� log10 P �tot �q� log10 P etot (8.14)

101The distributions of the parti le identi� ation parameter for the sub-GeV single ringsample is shown in �gure 8.10.

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Figure 8.10: The parti le identi� ation parameter for single ring sub-GeV eventsfor the 991-day exposure of Super{Kamiokande (points with error bars) and the(normalized) 40-year equivalent sample of atmospheri neutrino Monte Carlo.8.4 Momentum determinationTo determine the momentum of a parti le, the total harge orresponding to theparti le is al ulated by summing the harge from PMTs satisfying the following riteria:1. �i < 70Æ2. �50 ns < t0 � tresidi < 250 nswhere �i is the angle between the dire tion of the parti le and the i-th PMT, tresidi isthe time-of- ight subtra ted time of the PMT, and t0 is the average of the residual

102times. These riteria reje t any s attered light. On e the harge is known, a on-version to momentum is applied. This onversion is based on the energy alibrationsour es des ribed in se tion 5.5. The onverstion for ele trons and muons is shown in�gure 8.11. The resolution in the momentum determination for ele trons and muonsis estimated to be �e = 240:6 + 2:6qj~pej35% (8.15)�� = 241:7 + 0:7qj~p�j35% (8.16)where ~pe and ~p� are the momenta of the ele tron and muon, respe tively. Themomentum for harged pions is al ulated using both the opening angle of the tra kand the number of PE belonging to the tra k.

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Figure 8.11: Conversion from photoele trons orresponding to a tra k to momentumfor ele trons and muons.

1038.5 muon/shower (MS) �tFor single ring events, the vertex is re�ned using \MS-�t" (\muon/shower" �t). Inaddition to timing information, MS-�t uses the Cherenkov light patterns for e-likeand �-like tra ks (see se tion 8.3 for a des ription of these patterns). The timinginformation provides a good �t in the dire tion perpendi ular to the tra k of theparti le. The vertex is re�ned in the dire tion parallel to the tra k of the parti leby maximizing the likelihood de�ned in equation 8.13 for verti es o�set from theoriginal vertex.8.6 De ay ele tron ountingEle trons from muon de ay an o ur either in the same event as the main trigger or an produ e a trigger themselves. These two s enarios have separate sear h methods.For de ays o uring within the main trigger, the main trigger is found by sear hingthe time-of- ight (TOF) subtra ted timing distribution for the maximum peak. Fromthis point, de ays are sear hed by looking for the maximum number of hits within a30-ns sliding time window. De ay ele trons are tagged by requiring that1. t > 100 ns2. t < 800 ns3. N30 nshit � 604. Gpoint > 0.5Where t denotes the time of the de ay ele tron, N30 nshit is the number of hits withinthe 30-ns time window, and goodness Gpoint is de�ned with equation 8.1. The �rsttwo riteria re e t the fa t that the dete tion eÆ ien y de reases when the de ay is

104too lose to the main peak and when it is too lose to the end of the gate. Criteria3 and 4 ensure that the hit tubes are from an ele tron.De ays o uring in separate triggers are sele ted by requiring1. tsub < 20 �s2. t > 1:2 �s3. N30 nshit � 404. Gpoint > 0.5The �rst riterion reje ts after-events whi h o ur many muon lifetimes after theinitial event. The se ond riterion ensures that the dete tion eÆ ien y remains on-stant over the entire time window. Finally riteria 3 and 4 ensure a good �t of theCherenkov ring from the ele tron.From Monte Carlo studies, the eÆ ien ies to dete t de ay ele trons from �+ and�� are estimated to be 80% and 63%, respe tively. These eÆ ien ies were he kedusing stopping osmi -ray muons and were found to be a urate to within 1:5%.

Chapter 9The Sear h for Nu leon De ayThe strategy for a nu leon de ay analysis is straightforward. Monte Carlo eventsof the de ay mode being studied are generated with the aid of methods using nu- lear physi s (see se tion 6.1) and dete tor response to parti les traversing Super{Kamiokande. This gives a pi ture of how nu leon de ay into that spe i� mode willlook inside the dete tor. In addition, Monte Carlo events for the ba kground indu edby atmospheri neutrinos are generated. In this dissertation, a 40-year equivalentsample of atmospheri neutrino Monte Carlo was used to estimate the ba kground.Based on the simulated signal and simulated ba kground, sele tion riteria are gen-erated. After the sele tion riteria are de ided upon, they are applied to real datafrom Super{Kamiokande to sear h for nu leon de ays.This hapter des ribes the sear h for nu leon de ay via p ! ��K+ , n ! ��K0 ,p ! �+K0 , and p ! e+K0 using a 61-kton�year (991-days) exposure of Super{Kamiokande. Ea h se tion des ribes a parti ular de ay mode in detail, however atthe end of the hapter there are tables summarizing the sele tion riteria and resultsof the sear hes. 105

1069.1 p! ��K+The K+ in the de ay p ! ��K+ has a � of only �.6, whi h is below Cherenkovthreshold in water. Therefore it an not be observed dire tly in Super{Kamiokande.However, andidate events are observed indire tly through the de ay produ ts of theK+. The major de ay modes are K+ ! �+�� and K+ ! �+�0 with bran hingratios of 63.5% and 21.2%, respe tively. Be ause the hadroni ross-se tion for lowmomentum kaons to intera t inelasti ally is small, more than 90% of them stop beforede aying. The sear h for p! ��K+ then be omes a sear h for K+ de ays at rest.9.1.1 K+! �+�0The �0 and �+ from the K+ de ay at rest have equal and opposite momenta of ap-proximately 205 MeV/ . The -rays from the de ay of the �0 ompletely re onstru tthis momentum. The �+, barely over Cherenkov threshold with � � :86, produ es asmall amount of Cherenkov radiation whi h an be dete ted in the dire tion oppositethat of the �0. To quantify this, \ba kwards harge" (Qba k) is de�ned as the sum ofthe PEs measured by the PMTs whi h lie within a one of 40Æ opening angle whoseaxis is the opposite dire tion of the re onstru ted dire tion of the �0. This hargeis orre ted for light attenuation in the water and the angular dependen e of photona eptan e of the PMTs. In addition, the �+ de ays into a muon (�+ ! �+�� ;lifetime � = 2:6 � 10�8 ns) whi h de ays into a positron (�+ ! e+�e��� ; lifetime� = 2:2 � 10�6 ns). Dete tion of the positron is possible. A sample event displayof a Monte Carlo event in \unrolled" and \front-ba k" views is shown in �gure 9.1.The \unrolled" view is the ylindri al stru ture of Super{Kamiokande with the topfolded up, the bottom folded down, and the sides rolled out. The \front-ba k" viewis a hemispheri al view with PMTs plotted in the �-� oordinate system relative to

107the re onstru ted vertex position. In the \front-ba k" view of �gure 9.1, the -raysfrom the �0 de ay an be seen in the left hemisphere and a ollapsed Cherenkov ringfrom the �+ an be seen in the right hemisphere.Based on the nu leon de ay Monte Carlo simulation and the 40-year equivalentatmospheri neutrino Monte Carlo simulation, the following sele tion riteria werede ided upon:A1. two e-like ringsA2. one de ay ele tronA3. 85 MeV/ 2 < M < 185 MeV/ 2A4. 175 MeV/ < j~p j < 250 MeV/ A5. 40 PE < Qba k < 100 PEwhere j~p j is the sum of the momenta of the two e-like rings andM is the invariantmass of the two e-like rings whi h is al ulated using the kinemati relationm2 = E2 � ~p 2 (9.1)The invariant mass distributions for both p ! ��K+ ;K+ ! �+�0 and atmospheri neutrino Monte Carlo events whi h passed riteria A1 and A2 are shown in �gure9.2. Criteria A1, A3, and A4 sear h for the �0 with the mono hromati momentumexpe ted. Criterion A3 is entered around the �0 mass of about 135 MeV/ 2. Crite-rion A2 is a sear h for the de ay of the �+ into muon into positron and riterion A5sear hes for Cherenkov light from the �+. For p! ��K+ ; K+ ! �+�0 Monte Carloevents, the resolution of vertex �tting was estimated to be �28 m (�gure 8.3) and66% of the events were identi�ed as having two rings.

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Figure 9.1: p ! ��K+ ; K+ ! �+�0 Monte Carlo event in unrolled view and front-ba k view. The two -rays from the de ay of the �0 an be seen learly in both views.A ollapsed Cherenkov ring from the �+ an be seen in the ba kwards hemisphere(right ir le) in the front-ba k view. The spike in the time histogram around 1250ns is from the de ay ele tron.

109It is appropriate to now des ribe the two methods used to de ide upon the se-le tion riteria depending on the kinemati s of the event (A3, A4, and A5). Thesemethods were used to de ide upon sele tion riteria in all modes. Criteria A3 and A4were hosen by �nding the enter of the signal distribution and sele ting symmetri uts so that approximately 95% of the events passed. This method assumes a atba kground distribution. Criterion A5 was hosen by maximizing S=pN , where Sis the number of signal events passing and N is the number of ba kground eventspassing. In general, initial kinemati riteria were determined using the �rst method.Final kinemati uts on parameter spa es with signi� ant ba kground were de idedupon using the se ond method, while parameter spa es with little ba kground the�rst method was used to determine �nal kinemati riteria.

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0 50 100 150 200 250 300Figure 9.2: Invariant mass distribution for events passing riteria A1 and A2 for p!��K+ ;K+ ! �+�0 Monte Carlo and the 40-year equivalent sample of atmospheri neutrino Monte Carlo.By passing the p ! ��K+ ;K+ ! �+�0 Monte Carlo events through sele tion riteria A1-A5, the dete tion eÆ ien y was determined to be 31%. The major on-

110tribution to the ineÆ ien y was the dete tion of two -rays from the de ay of the �0.In luding the kaon bran hing ratio of 21:2% into �+�0, the total dete tion eÆ ien yfor this mode was estimated to be 6:8%.The sele tion riteria were applied to the sample of 40-year equivalent atmo-spheri neutrino Monte Carlo and the number of ba kground events expe ted in the61-kton�year exposure of Super{Kamiokande was estimated to be 1.7 events. Thisnormalized ba kground was estimated using the methods des ribed in se tion 6.2.4(all quoted ba kground estimates will be normalized a ording to this pro edure).Figure 9.3 shows the distribution of Qba k vs. j~p j for p! ��K+ ;K+ ! �+�0 MonteCarlo and the 40-year sample of atmospheri neutrino Monte Carlo for events passingsele tion riteria A1-A3.The breakdown of the types of neutrino intera tions whi h appear in the ba k-ground estimate is shown in table 9.1. Most of the ba kground is from single-� andmulti-� produ tion. The major ontribution of the multi-� produ tion is in the lowerenergy s heme of 1.4 GeV to 2.0 GeV neutrino-nu leon invariant mass. The in omingneutrino energy of the ba kground is typi ally between 600 MeV and 2 GeV.The sele tion riteria for this de ay mode were applied to the 61-kton�year datasample. Figure 9.4 shows the results of the �nal two uts. No events pass. Basedon the estimated dete tion eÆ ien y and ba kground estimation, a lower limit onthe partial lifetime of p ! ��K+ of 6:0 � 1032 yr at the 90% C.L. was set. For anexplanation on setting a limit see appendix A.9.1.2 K+! �+��The �+ from the de ay K+ ! �+�� at rest has a mono hromati momentum of236 MeV/ , a region highly ontaminated by atmospheri neutrinos. However, if a

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112 Ba kground for p! ��K+ ; K+ ! �+�0intera tion �e + ��e �� + ���Nnorm % Nnorm %quasi-elasti - - - -single-� 3.5 11.8% 5.2 20.5%CC multiple-� 2.3 9.0% 5.2 20.5%K prod. - - - -� prod. - - - -quasi-elasti - - - -single-� 1.2 4.6% - -NC multiple-� 3.3 13.0% 3.5 13.8%K prod. - - - -� prod. 1.2 4.6% - -TOTALS 11.5 45% 13.9 55%Table 9.1: Breakdown of ba kground ontributions to the de ay p ! ��K+ ; K+ !�+�0 . Nnorm is the number normalized to the neutrino os illation hypothesis (seese tion 6.2.4 for an explanation). The % is the normalized per entage ontributionto the ba kground.nu leon whi h is not in the outermost nu lear shell of O16 de ays, the remaining N15nu leus is left in an ex ited state. This ex ited state of N15 an de ay in di�erentways. Table 6.1 lists the modes whi h have a -ray in the �nal state. The ase wherea proton of O16 in the p3=2 state de ays leading to a prompt 6.3-MeV -ray emissionfrom the ex ited N15 is the most prominent with a probability of 41%[67℄.Due to the K+ lifetime of 12 ns, the signal from its de ay produ ts will be delayedrelative to the signal from the de-ex itation of the N15. The timing resolution inSuper-Kamiokande enables these two signals to be learly separated within an event.A timing distribution orre ted for time of ight for a p! ��K+ ; K+ ! �+�� MonteCarlo event with the N15 de ay emitting a prompt 6.3-MeV -ray is shown in �gure9.5.The sear h for the de ay mode p ! ��K+ ;K+ ! �+�� was performed by �rstsear hing for a muons with a mono hromati momentum of 236 MeV/ . The sele tion

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800 850 900 950 1000 1050 1100 1150 1200Figure 9.5: Sample time of ight (TOF) subtra ted timing distribution for a p !��K+ ; K+ ! �+�� Monte Carlo event with prompt -ray emission. riteria for su h events were determined to be:B1. one �-like ringB2. one de ay ele tronB3. 215 MeV/ < j~p�j < 260 MeV/ B4. \proton" event reje tionCriteria B1-B3 are a sele tion of a 236-MeV/ mono hromati muon. Criterion B4reje ts events whi h are aused by neutral urrent rea tions where a large amount ofmomentum is transferred to a proton, eje ting it from the O16 nu leus. These re oilprotons an have momenta that are above Cherenkov threshold making them visible

114in the dete tor. The Cherenkov rings produ ed by su h protons appear to be �-like,however they have a smaller opening angle. Therefore when they are �t as muonsthe vertex is shifted a large amount and the -rays from the nu lear deex itationasso iated with su h rea tions an appear at an earlier time. These events anbe reje ted by al ulating a goodness of �t. Cherenkov rings from protons have adi�erent hara teristi than muons and this an be parameterized by the goodnessof �t. More details of the proton reje tion riterion an be found in referen e [95℄.After sele tion riteria B1-B4 are applied, events are lassi�ed into two groups,\prompt dete tion" and \no prompt dete tion." These are independent eventsamples from whi h limits an be drawn and ombined.To des ribe the sear h for the prompt -ray, three quantities must be de�ned.The �rst is t0 whi h is a referen e time asso iated with the dete tion of the muon.The se ond is t1 whi h is the time before t0 from whi h to begin a ba kwards sear hin time for the earlier hits from the prompt ray. Finally, twin is the width of thetiming window in whi h hits are summed. A graphi al des ription of these threequantities is shown in �gure 9.6.The referen e point t0 orresponding to the muon was found by sear hing for thepoint in time when: dNhitdt �����t=t0 = max "dNhitdt # (9.2)After t0 was found, PMTs whi h were within a one of 50Æ opening angle relative tothe dire tion of the muon were removed. Removing these tubes enabled the sear hfor the prompt to start at an earlier time. With the remaining tubes, a ba kwardss an of dNhit=dt was made starting at t0. The starting time t1 was then de�ned asthe �rst point less than t0 where dNhit=dt = 0. On e t1 was found, a time window ofwidth twin = 12 ns was slid ba kwards starting with its trailing edge at t1. The hits

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tmaxFigure 9.6: Des ription of quantities used in the prompt -ray sear h.falling within twin were summed and the maximum number of hits falling within twinwas then de�ned as N12 nshit . This de�ned the �nal sele tion riterion:B5. N12 nshit > 7Passing the p! ��K+ ;K+ ! �+�� prompt Monte Carlo and 40-year atmospheri neutrino Monte Carlo through riteria B1-B5 the dete tion eÆ ien y and ba kgroundwere estimated to be 9.3% and 1 event, respe tively. The eÆ ien y in ludes allbran hing ratios. Passing the 61-kton�year data through this redu tion yielded noevents, therefore a lower limit on the partial lifetime of p ! ��K+ was set to be8:2�1032 years at the 90% on�den e level. Figure 9.7 shows N12nshit for the normalized40-year sample of atmospheri neutrino Monte Carlo, p! ��K+ ;K+ ! �+�� MonteCarlo normalized to 2.3 events/61-kton�year in the signal region, and 61-kton�yr

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0 5 10 15 20 25 30 35 40 45 50Figure 9.7: N12nshit distributions for p ! ��K+ ;K+ ! �+�� Monte Carlo, 40-year equivalent Monte Carlo event samples, and 61-kton�year SK data. The p !��K+ ;K+ ! �+�� Monte Carlo was normalized to 2.3 events/61 kton�year.sample of data.The events passing riteria B1-B2 but failing B5 were then sear hed for an ex esswithin the momentum range around the mono hromati momentum of the muon.The method of estimating the ex ess was developed by Y. Hayato [95℄. The numberof events in three momentum regions, 200 to 215 MeV/ , 215 to 260 MeV/ , and 260to 300 MeV/ were summed separately for p ! ��K+ ; K+ ! �+�� Monte Carlo,atmospheri neutrino Monte Carlo, and the 61-kton�yr data sample. The �2 methodwas applied to �t normalization parameters for the MC samples to the data. The �2

117Ba kground for p! ��K+ ; K+ ! �+��prompt -ray sear hintera tion �e + ��e �� + ���Nnorm % Nnorm %quasi-elasti - - 4.4 30.8%single-� - - 2.2 15.4%CC multiple-� - - - -K prod. - - 0.7 4.9%� prod. - - - -quasi-elasti - - 2.3 16.1%single-� - - 1.2 8.3%NC multiple-� 1.2 8.3% 2.3 16.1%K prod. - - - -� prod. - - - -TOTALS 1.2 8.3% 13.1 91.7%Table 9.2: Breakdown of ba kground ontributions to the de ay p ! ��K+ ; K+ !�+�� with a prompt- ray emission. (See table 9.1 for an explanation of Nnorm and%.)fun tion was de�ned as:�2 = 3Xi=1 hNdatai � �aNatm�i + bNpdki �i2Ndatai (9.3)where a and b are the normalization parameters for atmospheri neutrino and protonde ay Monte Carlo samples and Ndatai , Npdki , and Natm�i are the numbers of eventsof real data, proton de ay MC, and atmospheri neutrino MC, respe tively, in ea hmomentum region i.The minimum �2 = 0:853 was in the unphysi al region where the ex ess of protonde ay signal was estimated to be negative, bNpdk2 = �26:76. The minimum �2 inthe physi al region was 3.49 where bNpdk2 = 0. The 90% on�den e level upperlimit on the number of events from proton de ay was obtained by requiring that�290%C:L:��2min = 7:3 using the method outlined in referen e [96℄. The 90% on�den e

118level on the upper limit of the number of events from proton de ay was obtained tobe 15.6. The �tted momentum spe trum for events passing riteria B1 and B2is shown in �gure 9.8 whi h shows the 61-kton�year data, the �tted atmospheri neutrino Monte Carlo, and the 90% C.L. on the ex ess of signal added to the �ttedatmospheri neutrino Monte Carlo. Using this spe trum �tting method the lowerlimit on the partial lifetime of p ! ��K+ was found to be 4:3 � 1032 years (90%C.L.).

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119Method eÆ ien y N expBG Nobs s90 �=B (90% CL)K+ ! �+�0 6.8% 1.7 0 2.3 6:0� 1032 yearsK+ ! �+�� prompt 9.3% 1.0 0 2.3 8:2� 1032 yearsK+ ! �+�� spe trum �t 33% 137 128 15.6 4:3� 1032 years ombined 49% - - 6.2 1:7� 1033 yearsTable 9.3: Summary of three methods used to sear h for p! ��K+ .9.1.3 Final Limit of p! ��K+Table 9.3 summarizes the sear h for p! ��K+ via the three methods: K+ ! �+�0 ,K+ ! �+�� prompt , and K+ ! �+�� spe trum �tting. No eviden e for p !��K+ was found in these data, therefore the three limits were ombined using themethod des ribed in appendix A. The ombined lower limit of the partial lifetimefor p ! ��K+ using the three methods was 1:7 � 1033 years at the 90% C.L. This an be ompared to previous limits of 1:8� 1032 years set by IMB [12℄ and 1:0� 1032years set by Kamiokande [58℄.9.2 n! ��K0The K0 is a linear superposition of the CP eigenstates KS and KL by whi h it de ays.In this dissertation, only de ays of KS were studied be ause the lifetime of KL is longenough so that it has a very high probability of intera ting in water before de aying.Su h intera tions destroy the signature of these events. Two de ay modes of KS wereused, KS ! �0�0 and KS ! �+�� .9.2.1 KS ! �0�0The de ay KS ! �0�0 is hara terized by four ele tromagneti showers from thede ays of the two �0s. A sample n ! ��K0 ;KS ! �0�0 event is shown in �gure

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Times (ns)Figure 9.9: n! ��K0 ; KS ! �0�0 Monte Carlo event.9.9. The KS de ays in ight and the energies and momenta from the s ompletelyre onstru t its mass and momentum. The sele tion riteria were sele ted to be:C1. three or four e-like ringsC2. no de ay ele tronsC3. 400 MeV/ 2 < M s < 600 MeV/ 2C4. 200 MeV/ < j~p sj < 400 MeV/ Criteria C1, C3, and C4 sear h for the KS with momentum in the proper range.Invariant mass was al ulated as in equation 9.1. Criterion C2 re e ts the fa t thatthese events have no de ay ele trons. Plots of j~p sj vs. M s for n! ��K0 ; KS ! �0�0and atmospheri neutrino Monte Carlo are shown in �gure 9.10. The signal region

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0 100 200 300 400 500 600 700 800 900Figure 9.10: j~p sj vs. M s for events passing riteria C1-C2 for n! ��K0 ; KS ! �0�0Monte Carlo and 40-year atmospheri neutrino Monte Carlo.has a signi� ant expe ted ba kground of 14 events. To redu e this ba kground, theinvariant mass of ombinatori pairs of rings were re onstru ted. For an event tobe a epted, it must have at least one of the pairs re onstru t to the �0 mass (85MeV/ 2 < m < 185 MeV= 2). This �0 onstraint will be labeled riterion C5.Revised plots of j~p sj vs. M s for n! ��K0 ; KS ! �0�0 and atmospheri neutrinoMonte Carlo samples are shown in �gure 9.11.By passing the two Monte Carlo samples through the sele tion riteria, the dete -tion eÆ ien y and ba kground for n! ��K0 ; KS ! �0�0 were estimated to be 6.1%and 11, respe tively. The dete tion eÆ ien y in ludes the KS ! �0�0 bran hingratio of 31.4% and the probability of 1=2 for the K0 to be in the KS state. From nowon, all dete tion eÆ ien ies quoted will in lude all bran hing ratios. A breakdown ofthe ba kground indu ing neutrino intera tions is outlined in table 9.4. By imposingthe �0 onstraint the ba kground de reased by 21% from 14 to 11 events while the de-te tion eÆ ien y de reased by only 6% from 6:5% to 6:1%. Passing the data through

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0 100 200 300 400 500 600 700 800 900Figure 9.11: j~p sj vs. M s for events passing riteria C1-C2 for n! ��K0 ; KS ! �0�0Monte Carlo and 40-year atmospheri neutrino Monte Carlo. These events alsosatisfy the requirement that at least one pair of e-like rings re onstru ted to the �0mass.the sele tion riteria yielded 5 events (�gure 9.12), onsistent with the ba kgroundexpe ted from atmospheri neutrinos. The �nal limit of n! ��K0 ; KS ! �0�0 was al ulated using the method outlined in appendix A and was found to be 2.8�1032years at the 90% C.L.9.2.2 KS ! �+��The hara teristi for n ! ��K0 ; KS ! �+�� is its two low energy ollapsedCherenkov rings from the two pions. A sample event is shown in �gure 9.13. Thesele tion are straight-forward:D1. two �-like ringsD2. one de ay ele tron

123

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0 100 200 300 400 500 600 700 800 900Figure 9.12: j~p sj vs. M s for events passing riteria C1-C2 and the �0 mass require-ment for the 61-kton�year Super{Kamiokande data sample. The number of eventspassing the sele tion riteria is onsistent with the expe ted ba kground.Ba kground for n! ��K0 ; KS ! �0�0intera tion �e + ��e �� + ���Nnorm % Nnorm %quasi-elasti 1.2 0.7% - -single-� 48.0 28.6% 2.2 1.3%CC multiple-� 26.9 16.0% 7.4 4.4%K prod. - - - -� prod. 1.2 0.7% 1.5 0.9%quasi-elasti - - - -single-� 4.7 2.8% 5.8 3.5%NC multiple-� 16.4 9.8% 36.3 21.6%K prod. 1.2 0.7% - -� prod. 2.3 1.4% 12.9 7.7%TOTALS 101.8 60.6% 66.1 39.4%Table 9.4: Breakdown of ba kground ontributions to the de ay n ! ��K0 ; KS !�0�0 (see table 9.1 for an explanation of Nnorm and %.)

124 Resid(ns)

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Super-KamiokandeRun 999999 Event 17

98-06-10:16:32:10

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ap ver: 6

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Times (ns)Figure 9.13: n! ��K0 ; KS ! �+�� Monte Carlo event.D3. 450 MeV/ 2 < M�� < 550 MeV/ 2D4. 200 MeV/ < j~p��j < 400 MeV/ The invariant mass (M��) and momentum (j~p��j) were al ulated with the assump-tion that the two �-like rings were from a �+ and ��. This is be ause pions andmuons with the same momentum have di�erent Cherenkov light yields. The momen-tum al ulation of the two ases (� or �) will therefore be di�erent. Plots of j~p��j vs.M�� for n ! ��K0 ; KS ! �+�� and atmospheri neutrino Monte Carlo are shownin �gure 9.14. Based on these samples, the dete tion eÆ ien y and ba kground wereestimated to be 2.0% and 2.0 events, respe tively. The breakdown of the types ofintera tions whi h aused the ba kground is outlined in table 9.5. Passing the datathrough D1-D4 yielded 4 events, slightly higher than the expe ted ba kground but

125within statisti al error (�gure 9.15). The limit set for n ! ��K0 using the de ayKS ! �+�� was 0.5�1032 years at the 90% C.L.

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0 100 200 300 400 500 600 700 800 900 1000Figure 9.14: j~p��j vs. M�� for events passing riteria D1-CD for n ! ��K0 ; KS !�+�� Monte Carlo and 40-year atmospheri neutrino Monte Carlo.9.2.3 Final Limit of n! ��K0A summary of the two methods used to sear h for n ! ��K0 is shown in table 9.6.Unfortunately this de ay mode has a high expe ted ba kground and therefore thesensitivity to dete t it is less than that of other modes. This is unfortunate sin e itis one of the more favored modes of SUSY GUTs. The two methods were ombinedand a �nal limit for n! ��K0 was al ulated to be 2.5�1032 years at the 90% C.L.This an be ompared to previous limits of 0:27 � 1032 years set by IMB [12℄ and0:86� 1032 years set by Kamiokande [58℄.

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0 100 200 300 400 500 600 700 800 900 1000Figure 9.15: j~p��j vs. M�� for events passing riteria D1-D2 the 61-kton�year Super{Kamiokande data sample. Like the sear h for n ! ��K0 ; KS ! �0�0 , the numberof events passing the sele tion riteria is onsistent with the expe ted ba kground.Ba kground for n! ��K0 ; KS ! �+��intera tion �e + ��e �� + ���Nnorm % Nnorm %quasi-elasti - - 1.5 5.1%single-� - - 21.5 73.1%CC multiple-� - - 2.2 7.5%K prod. - - 0.7 2.4%� prod. - - - -quasi-elasti - - - -single-� - - 1.2 4.1%NC multiple-� - - - -K prod. - - 2.3 7.8%� prod. - - - -TOTALS 0 0% 29.4 100%Table 9.5: Breakdown of ba kground ontributions to the de ay n ! ��K0 ; KS !�+�� .

127Method eÆ ien y N expBG Nobs s90 �=B (90% CL)KS ! �0�0 6.1% 11 5 3.5 2:8� 1032 yearsKS ! �+�� 2.0% 2.0 4 6.1 0:5� 1032 years ombined 8.1% - - 5.4 2:5� 1032 yearsTable 9.6: Summary of two methods used to sear h for n ! ��K0 (see table 9.1 foran explanation of Nnorm and %.)9.3 p! �+K0Unlike the modes p ! ��K+ and n ! ��K0 where one of the de ay produ ts is aninvisible neutrino, the mode p! �+K0 is ompletely visible. The only ex eption iswhen the KS de ays asymmetri ally in the de ay KS ! �+�� and one of the pionsis below Cherenkov threshold. Being able to re onstru t all parti les provides manykinemati handles to separate signal from ba kground.9.3.1 KS ! �0�0A p ! �+K0 ; KS ! �0�0 event would ideally re onstru t to four e-like rings, one�-like ring, and one de ay ele tron. This is hardly ever the ase, so uts were hosenbased on a Monte Carlo simulation of p ! �+K0 ; KS ! �0�0 events. A sampleevent is shown in �gure 9.16. The initial sele tion riteria were hosen to be:E1. one �-like ringE2. two to four e-like ringsE3. zero or one de ay ele tronIn addition to sele tion riteria E1-E3, p ! �+K0 ; KS ! �0�0 events havea very distin tive kinemati signature. All parti les (� and s) are ompletelyvisible, making it possible to ompletely re onstru t these events. Based on the

128Super-KamiokandeRun 999999 Event 178198-11-01:10:38:28

Inner: 3173 hits, 6273 pE

Outer: 2 hits, 1 pE (in-time)

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D wall: 630.3 cm

Fully-Contained

Resid(ns) > 22 20- 22 17- 20 14- 17 11- 14 8- 11 5- 8 2- 5 0- 2 -2- 0 -5- -2 -8- -5 -11- -8 -14- -11 -17- -14 < -17

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Times (ns)Figure 9.16: p! �+K0 ; KS ! �0�0 Monte Carlo in front-ba k view. The four EMshowers from the s from the de ays of the �0s (left hemisphere) are balan ed by the� tra k (right hemisphere). Note the spike in the timing histogram at about 1600 nsfrom the de ay ele tron of the �.p! �+K0 ;KS ! �0�0 and 40-year atmospheri neutrino ba kground Monte Carlosamples, addition sele tion riteria were de ided upon:E4. 750 MeV= 2 < Mtot < 1000 MeV= 2E5. j~ptotj < 300 MeV= E6. 400 MeV= 2 < M s < 600 MeV= 2E7. 150 MeV= < j~p�j < 400 MeV= Criterion E4 requires that the visible tra ks re onstru t the 938-MeV/ 2 mass ofthe proton. Criterion E5 is a momentum uto� due to the Fermi momentum in

129O16 (�gure 6.1). Criterion E6 al ulates the invariant mass of all e-like rings usingequation 9.1. For proton de ay events via p ! �+K0 , this should re onstru t tothe mass of the K0. Criterion E7 sear hes for the momentum of the muon. Be auseof the kinemati power to reje t mu h of the ba kground, all sele tion riteria were hosen based only on the p! �+K0 ;KS ! �0�0 Monte Carlo sample. Distributionsof total momentum (j~ptotj) vs. total invariant mass (Mtot) for p! �+K0 ;KS ! �0�0and 40-year atmospheri neutrino Monte Carlo for events passing sele tion riteriaC1-C3 are shown in �gure 9.17. Distributions of j~p�j vs. M s for events passingsele tion riteria C1-C5 for the two Monte Carlo samples are shown in �gure 9.18.

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0 200 400 600 800 1000 1200Figure 9.17: Momentum vs. mass for events passing riteria E1-E3 for p ! �+K0 ;KS ! �0�0 Monte Carlo and 40-year atmospheri neutrino Monte Carlo.By applying sele tion riteria E1-E7 to the p ! �+K0 ; KS ! �0�0 and atmo-spheri neutrino Monte Carlo samples the dete tion eÆ ien y and ba kground wereestimated to be 6:1% and 1 event, respe tively. The breakdown of the types of neu-trino intera tions whi h aused the ba kground is in table 9.7. Applying the sele tion riteria to the 61-kton�year data sample yielded no events (�gure 9.19) therefore a

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0 100 200 300 400 500 600 700 800Figure 9.18: � momentum vs. e-like mass for events passing sele tion riteria E1-E5for p ! �+K0 ; KS ! �0�0 Monte Carlo and 40-year atmospheri neutrino MonteCarlo.lower limit on the partial lifetime of the proton into p! �+K0 was set to be 5:4�1032years at the 90% C.L.9.3.2 KS ! �+��In p! �+K0 ; KS ! �+�� events either both pions are above Cherenkov thresholdor the KS de ays asymmetri ally and one pion is below Cherenkov threshold. Theformer ase provides a lean signature of 3 lower energy Cherenkov rings (�gure 9.20)from whi h kinemati variables of the event an be re onstru ted. The sele tion riteria for this ase were hosen to be:F1. three ringsF2. one or two de ay ele tronsF3. 750 MeV= 2 < Mtot < 1000 MeV= 2

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0 100 200 300 400 500 600 700 800Figure 9.19: Total momentum vs. total mass and � momentum vs. e-like mass forthe 61-kton�year data sample in sear hing for p ! �+K0 ; KS ! �0�0 . The eventsin the left �gure have passed riteria E1-E3 and the events in the right �gure havepassed E4-E5.F4. j~ptotj < 300 MeV= F5. 450 MeV/ 2 < M�� < 550 MeV/ 2Criterion F1 requires no parti le type be ause approximately 37% of the p! �+K0 ;KS !�+�� events lassi�ed as having three rings identi�ed all three as e-like. Sin e the ef-� ien y to dete t three rings was only 20%, any additional parti le type requirementwould signi� antly redu e an already small eÆ ien y. Furthermore, the kinemati sof these events provides a powerful ba kground reje tion. The remaining sele tion riteria are straight-forward. On e again, riteria F3 and F4 sear h for the protonmass and the ut-o� from Fermi momentum. Criterion F5 sear hes for the kaon mass.In order to al ulate these kinemati quantities, the tra k orresponding to the muonmust be hosen sin e momentum and energy determination depends upon whetherthe parti le is a muon, pion, or a light showering parti le. The muon was hosen as

132Super-KamiokandeRun 999999 Event 1798-11-01:10:38:26

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Super-KamiokandeRun 999999 Event 17

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Super-KamiokandeRun 999999 Event 1798-11-01:10:38:26

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Figure 9.20: p! �+K0 ;KS ! �+�� Monte Carlo event in unrolled view and front-ba k view. The two ollapsed Cherenkov rings from the two pions from the de ay ofthe KS balan e the tra k from the muon. Note the two spikes in the timing histogramat about 1500 ns and 1700 ns from the two de ay ele trons.

133Ba kground for p! �+K0 ; KS ! �0�0intera tion �e + ��e �� + ���Nnorm % Nnorm %quasi-elasti - - - -single-� 2.3 16.2% 0.7 5.2%CC multiple-� 2.3 16.2% 3.0 21.1%K prod. - - - -� prod. - - - -quasi-elasti - - - -single-� - - 1.2 8.4%NC multiple-� - - 4.7 33.1%K prod. - - - -� prod. - - - -TOTALS 4.6 32% 9.6 68%Table 9.7: Breakdown of ba kground ontributions to the de ay p ! �+K0 ; KS !�0�0 (see table 9.1 for an explanation of Nnorm and %.)the most energeti tra k and by he king the \truth" information of the Monte Carlowas determined to be orre tly hosen with an eÆ ien y of approximately 90%. Themomentum for this tra k was al ulated by assuming it was a muon. The momentumfor the other two tra ks were al ulated by assuming they were pions. Figure 9.21shows the distributions of j~ptotj vs. Mtot for signal and ba kground Monte Carlo sam-ples. The invariant mass of the two pions was al ulated for events passing sele tion riteria F1-F4. This distribution for the two Monte Carlo samples is shown in �gure9.22.Based on the two Monte Carlo samples the dete tion eÆ ien y and ba kgroundwere estimated to be 2.8% and 0.2 events, respe tively. The low eÆ ien y an be at-tributed to asymmetri de ay of the KS where one pion is below Cherenkov thresholdand the ineÆ ien y of the ring- ounting algorithm at low energies. The two ba k-ground events whi h passed were muon indu ed multiple pion produ tion in theinvariant mass range of 1.4 GeV < W < 2.0 GeV. Applying sele tion riteria F1-F5

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135to the 61-kton�year data sample yielded no events (�gure 9.23) therefore a lower limiton the lifetime of p! �+K0 was set to be 2.5�1032 years at the 90% C.L.

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0 200 400 600 800 1000 1200Figure 9.23: j~ptotj vs. Mtot for events passing sele tion riteria F1-F2 for the 61-kton�year data sample.p ! �+K0 ; KS ! �+�� events with asymmetri KS de ays do not have thekinemati power of those events where all three tra ks were re onstru ted. Howeversome kinemati variables an be re onstru ted. The momentum of the muon andthe total momentum of the event an be used as onstraints. On e again, the muontra k was hosen to be the most energeti tra k. The following sele tion riteria wereused to sear h for these types of eventsG1. two �-like ringsG2. two de ay ele tronsG3. j~ptotj < 300 MeV= G4. 250 MeV= < j~p�j < 400 MeV=

136The distribution of j~ptotj vs. j~p�j is shown in �gure 9.24. The dete tion eÆ ien y andba kground were estimated to be 5.3% and 1.3, respe tively. The main ontributionto the ba kground was harged urrent single pion produ tion. A breakdown of theintera tions ontributing to the ba kground is in table 9.8. Applying the sele tion riteria G1-G4 to the data yielded no events (�gure 9.25). The lower limit on thepartial lifetime into p! �+K0 was then set to be 4:7� 1032 years (90% C.L.).

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0 100 200 300 400 500 600Figure 9.24: Distribution of j~ptotj vs. j~p�j for events passing sele tion riteria G1-G2for p! �+K0 ; KS ! �+�� Monte Carlo and 40-year atmospheri neutrino MonteCarlo.9.3.3 Final Limit of p! �+K0Table 9.9 summarizes the sear h for p! �+K0 using the three methods. On e again,no eviden e for p! �+K0 was found, therefore the three limits were ombined. The ombined lower limit of the partial lifetime using the three methods was 1:2 � 1033years at the 90% C.L. This an be ompared to previous limits of 1:3 � 1032 yearsset by IMB [12℄ and 1:2� 1032 years set by Kamiokande [58℄.

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0 100 200 300 400 500 600Figure 9.25: Distribution of j~ptotj vs. j~p�j for events passing sele tion riteria G1-G2for the 61-kton�year data sample.9.4 p! e+K09.4.1 KS ! �0�0The de ay p ! e+K0 ; KS ! �0�0 is hara terized by �ve EM showers from thee+ and the four s from the de ays of the �0s. These events are ompletely visible,so total invariant mass and total momentum an be re onstru ted. The followingsele tion riteria were hosen:H1. three to �ve e-like ringsH2. no de ay ele tronsH3. 750 MeV/ 2 < Mtot < 1000 MeV= 2H4. j~ptotj < 300 MeV=

138 Ba kground for p! �+K0 ; KS ! �+��2-ring s enariointera tion �e + ��e �� + ���Nnorm % Nnorm %quasi-elasti - - 0.7 3.8%single-� - - 15.5 84.2%CC multiple-� - - 2.2 12.0%K prod. - - - -� prod. - - - -quasi-elasti - - - -single-� - - - -NC multiple-� - - - -K prod. - - - -� prod. - - - -TOTALS 0 0% 18.4 100%Table 9.8: Breakdown of ba kground ontributions to the de ay p ! �+K0 ; KS !�+�� in the s enario where only two rings were re onstru ted (See table 9.1 for anexplanation of Nnorm and %.)Method eÆ ien y N expBG Nobs s90 �=B (90% CL)KS ! �0�0 6.1% 1.0 0 2.3 5:4� 1032 yearsKS ! �+�� (3-ring) 2.8% 0.2 0 2.3 2:5� 1032 yearsKS ! �+�� (2-ring) 5.3% 1.3 0 2.3 4:7� 1032 years ombined 14% - - 2.3 12� 1032 yearsTable 9.9: Summary of three methods used to sear h for p! �+K0 .The motivation for these sele tion riteria is the same as those in previous se tions.Plots of j~ptotj vs. Mtot for p! e+K0 ; KS ! �0�0 and atmospheri neutrino MonteCarlo events passing riteria H1-H2 are shown in �gure 9.26. Other uts beyondH1-H4 were studied, but they did not signi� antly improve the signal to noise ratio.By applying sele tion riteria H1-H4 to the p! e+K0 ; KS ! �0�0 and 40-yearatmospheri neutrino Monte Carlo samples the dete tion eÆ ien y and ba kgroundwere estimated to be 11:8% and 1.2, respe tively. The breakdown of the types ofneutrino intera tions whi h aused the ba kground is in table 9.10. When the uts

139

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0 200 400 600 800 1000 1200Figure 9.26: Momentum vs. mass for events passing riteria H1-H2 for p ! e+K0 ;KS ! �0�0 Monte Carlo and 40-year atmospheri neutrino Monte Carlo.were applied to the 61-kton�year data sample, one event passed (�gure 9.27). Thisis onsistent with the expe tation from atmospheri neutrino indu ed ba kground,therefore a lower limit on the lifetime into p! e+K0 of 7:5� 1032 years at the 90% on�den e level was set.9.4.2 KS ! �+��A sample p! e+K0 ; KS ! �+�� event is shown in �gure 9.28. Like the sear h forp ! �+K0 ; KS ! �+�� , the sear h for p ! e+K0 ; KS ! �+�� was divided intotwo sear h methods for the ases where both pions are above Cherenkov thresholdand where one pion is below Cherenkov threshold. The sele tion riteria for eventswhere both pions are above Cherenkov threshold were sele ted to be:I1. three rings, at least one of whi h is e-likeI2. zero or one de ay ele tron

140

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0 200 400 600 800 1000 1200Figure 9.27: Momentum vs. mass for events passing riteria H1-H2 the 61-kton�yearSuper{Kamiokande data sample.Ba kground for p! e+K0 ; KS ! �0�0intera tion �e + ��e �� + ���Nnorm % Nnorm %quasi-elasti 1.2 6.9% 0.7 4.0%single-� 3.5 20.2% - -CC multiple-� 4.7 26.9% 0.7 4.0%K prod. - - - -� prod. - - 0.7 4.0%quasi-elasti - - - -single-� - - 1.2 6.9%NC multiple-� 1.2 6.9% 3.5 20.2%K prod. - - - -� prod. - - - -TOTALS 10.6 60.9% 6.8 39.1%Table 9.10: Breakdown of ba kground ontributions to the de ay p! e+K0 ; KS !�0�0 (see table 9.1 for an explanation of Nnorm and %.)

141Super-KamiokandeRun 999999 Event 1299-03-01:20:35:57

Inner: 2445 hits, 3829 pE

Outer: 2 hits, 1 pE (in-time)

Trigger ID: 0x03

D wall: 757.0 cm

FC e-like, p = 371.5 MeV/c

Resid(ns) > 22 20- 22 17- 20 14- 17 11- 14 8- 11 5- 8 2- 5 0- 2 -2- 0 -5- -2 -8- -5 -11- -8 -14- -11 -17- -14 < -17

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Times (ns)Figure 9.28: p ! e+K0 ; KS ! �+�� Monte Carlo event. The two lower energy ollapsed Cherenkov rings are from the �+ and �� from the KS de ay.I3. 750 MeV= 2 < Mtot < 1000 MeV= 2I4. j~ptotj < 300 MeV= I5. 450 MeV= 2 < M�� < 550 MeV= 2Sin e multiple e-like rings are allowed, the ring orresponding to the e+ in p! e+K0must be hosen. This was done by sele ting the most energeti ring. The other tworings were taken to be the �+ and ��. From this,Mtot, ~ptot, andM�� were al ulated.The distributions of j~ptotj vs. Mtot for p ! e+K0 ; KS ! �+�� and atmospheri neutrino Monte Carlo samples are shown in �gure 9.29. The invariant mass of the twopion rings were then re onstru ted for events passing sele tion riteria I1-I4 (�gure9.30).

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0 200 400 600 800 1000 1200Figure 9.29: Momentum vs. mass for events passing riteria I1-I2 for p ! e+K0 ;KS ! �+�� Monte Carlo and 40-year atmospheri neutrino Monte Carlo.p→e+K0 ; K0

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143Based on the Monte Carlo samples for signal and ba kground, the dete tioneÆ ien y and ba kground for p ! e+K0 ; KS ! �+�� re onstru ting three ringswere estimated to be 1:4% and < 0:2, respe tively. Passing the 61-kton�year datasample through sele tion riteria I1-I5 yielded no events (�gure 9.31). A lower limiton the partial lifetime into p! e+K0 of 1:2� 1032 years at the 90% on�den e levelwas set.

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300 350 400 450 500 550 600 650 700Figure 9.31: a) Total momentum vs. total mass for the 61-kton�year data sample forevents passing sele tion riteria I1-I2. b) M�� for the data event in the 61-kton�yeardata sample whi h passed sele tion riteria I1-I4.For those p ! e+K0 ; KS ! �+�� events where one pion is either belowCherenkov threshold or not found by the ring-�nder, sele tion riteria were generatedbased on the two-ring s enario:J1. one e-like ringJ2. one �-like ringJ3. one de ay ele tron

144J4. 250 MeV= < j~pej < 400 MeV= J5. j~ptotj < 300 MeV= Plots of j~ptotj vs. j~pej are shown for p! e+K0 ; KS ! �+�� and 40-year atmospheri neutrino Monte Carlo in �gure 9.32. Based on these samples, the dete tion eÆ ien yand expe ted ba kground were estimated to be 6:2% and 0.9 events, respe tively.The ba kground is summarized in table 9.11. The majority of the events ome from harged urrent single pion produ tion. Applying uts J1-J5 to the 61-kton�year datasample yielded six events (�gure 9.33), signi� antly above the ba kground. The limitset for p! e+K0 was 1:3� 1032 years at the 90% on�den e level.Some dis ussion of the ex ess in the number of signal events is needed. If thiswere nu leon de ay into p! e+K0 , events would also be expe ted in the other twomethods for the p ! e+K0 sear h. The number of events that ould be expe tedin the KS ! �0�0 sear h is 10 and the number for KS ! �+�� 3-ring s enario is1. Observation of no events in the KS ! �+�� 3-ring s enario is onsistent withthis hypothesis, but the observation of only one event in the KS ! �0�0 sear h( onsistent with ba kground) is not. Therefore, the anomaly is most likely not dueto nu leon de ay via p! e+K0 .The statisti al error of ba kground estimation is only �0.2, so is not enough toa ount for the ex ess in the data. However, the systemati error is important. All ofthe ba kground is due to single-� produ tion whi h has an un ertainty of about 20%.An illustration of this un ertainty is in the expe ted number of single-�0 events fromneutral urrent intera tions ompared with the number from data (see �gure 5.16)The data have about 10% more �0s than the Monte Carlo. Also, the un ertaintyof pion-nu leon s attering in the nu leus is estimated to be about 20%. In ludingthese un ertainties, one gets a maximum expe ted ba kground of 1.5 events. The

145probability to observe 6 events given an expe tation of 1.5 is about 0.35%.

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0 100 200 300 400 500 600Figure 9.32: Distribution of j~ptotj vs. j~pej for events passing sele tion riteria J1-J3for p ! e+K0 ; KS ! �+�� Monte Carlo and 40-year atmospheri neutrino MonteCarlo.9.4.3 Final Limit of p! e+K0Table 9.12 summarizes the sear h for p! e+K0 . Based on the three sear h methodsdes ribed above there was no eviden e for proton de ay into p ! e+K0 , thereforethe limits derived from the three methods were ombined yielding a limit of 4:4�1032years at the 90% C.L. This an be ompared to previous limits of 0:32� 1032 yearsset by IMB [12℄ and 1:5 � 1032 years set by Kamiokande [58℄. The reason that the ombined limit is smaller than the limit drawn only from p! e+K0 ;KS ! �0�0 isthe relatively large number of events in the data whi h fell within the signal regionfor the p! e+K0 ;KS ! �+�� s enario with two rings.

146

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0 100 200 300 400 500 600Figure 9.33: Data sear h for p ! e+K0 ; KS ! �+�� with sele tion riteria J1-J5.Total momentum vs. total mass for the 61-kton�year data sample.Ba kground for p! e+K0 ; KS ! �+��2-ring s enariointera tion �e + ��e �� + ���Nnorm % Nnorm %quasi-elasti - - - -single-� 7.0 55.6% 4.4 34.8%CC multiple-� - - - -K prod. - - - -� prod. - - - -quasi-elasti - - - -single-� - - 1.2 9.6%NC multiple-� - - - -K prod. - - - -� prod. - - - -TOTALS 7.0 55.6% 5.6 44.4%Table 9.11: Breakdown of ba kground ontributions to the de ay p! e+K0 ; KS !�+�� for the two-ring s enario (see table 9.1 for an explanation of Nnorm and %.)

147Method eÆ ien y N expBG Nobs s90 �=B (90% CL)KS ! �0�0 12% 1.2 1 3.2 7:5� 1032 yearsKS ! �+�� (3-ring) 1.4% < 0:2 0 2.3 1:2� 1032 yearsKS ! �+�� (2-ring) 6.2% 0.9 6 9.6 1:4� 1032 years ombined 20% - - 9.1 4:4� 1032 yearsTable 9.12: Summary of three methods used to sear h for p! e+K0 .Parti le lifetime � � mass De ay Mode Bran hingRatioK+ 12.9 ns 3.7 m 493.7 MeV/ 2 �+�� 63.5%�+�0 21.2%K0S .089 ns 2.7 m 497.7 MeV/ 2 �+�� 68.6%�0�0 31.4%K0L 52 ns 15.5 m 497.7 MeV/ 2 ��e��e 38.8%������ 27.2%3�0 21.1%�+���0 12.6%Table 9.13: Summary of K mesons. Values taken from the Parti le Data Book.9.5 SummaryThis se tion is a summary of the nu leon de ay analyses in this hapter. Table 9.13is a summary of the properties of the K mesons, table 9.14 summarizes the sear hesfor the various modes, and tables 9.15, 9.16, 9.17,and 9.18 summarize the sele tion riteria used to sear h for the various modes.

148Mode Method eÆ ien y N expBG Nobs s90 �=B (1032 years)(90% CL)K+ ! �+�0 6.8% 1.7 0 2.3 6.0p! ��K+ K+ ! �+�� prompt 9.3% 1.0 0 2.3 8.2K+ ! �+�� spe trum �t 33% 137 128 15.6 4.3 ombined 49% - - 6.2 17KS ! �0�0 6.1% 11 5 3.5 2.8n! ��K0 KS ! �+�� 2.0% 2.0 4 6.1 0.5 ombined 8.1% - - 5.4 2.5KS ! �0�0 6.1% 1.0 0 2.3 5.4p! �+K0 KS ! �+�� (3-ring) 2.8% 0.2 0 2.3 2.5KS ! �+�� (2-ring) 5.3% 1.3 0 2.3 4.7 ombined 14% - - 2.3 12KS ! �0�0 12% 1.2 1 3.2 7.5p! e+K0 KS ! �+�� (3-ring) 1.4% < 0:2 0 2.3 1.2KS ! �+�� (2-ring) 6.2% 0.9 6 9.6 1.4 ombined 20% - - 9.1 4.4Table 9.14: Summary of �nal results for sear hes for p ! ��K+ , n ! ��K0 , p !�+K0 , and p! e+K0 .Method Sele tion CriteriaA1) two e-like ringsA2) one de ayK+ ! �+�0 A3) 85 MeV/ 2 < M < 185 MeV/ 2A4) 175 MeV/ < p < 250 MeV/ A5) 40 PE < Qba k < 100 PEB1) one �-like ringK+ ! �+�� B2) one de ayprompt B3) 215 MeV/ < p� < 260 MeV/ -ray B4) proton reje tionB5) N12 nshit > 7B1) one �-like ringK+ ! �+�� B2) one de ayspe trum �t B3) 215 MeV/ < p� < 260 MeV/ B6) N12 nshit � 7Table 9.15: Summary of the sele tion riteria used to sear h for p! ��K+ .

149Method Sele tion CriteriaC1) three or four e-like ringsC2) no de aysKS ! �0�0 C3) 400 MeV/ 2 < M s < 600 MeV/ 2C4) 200 MeV/ < p s < 400 MeV/ C5) �0 onstraintD1) two �-like ringsKS ! �+�� D2) one de ayD3) 450 MeV/ 2 < M�� < 550 MeV/ 2D4) 200 MeV/ < p�� < 400 MeV/ Table 9.16: Summary of the sele tion riteria used to sear h for n! ��K0 .Method Sele tion CriteriaE1) one �-like ringE2) two to four e-like ringsE3) zero or one de ayKS ! �0�0 E4) 750 MeV/ 2 < Mtot < 1000 MeV/ 2E5) ptot < 300 MeV/ E6) 400 MeV/ 2 < M s < 600 MeV/ 2E7) 150 MeV/ < p� < 400 MeV/ F1) three ringsKS ! �+�� F2) one or two de aysthree-ring F3) 750 MeV/ 2 < Mtot < 1000 MeV/ 2F4) ptot < 300 MeV/ F5) 450 MeV/ 2 < M�� < 550 MeV/ 2G1) two �-like ringsKS ! �+�� G2) two de aystwo-ring G3) ptot < 300 MeV/ G4) 250 MeV/ < p� < 400 MeV/ Table 9.17: Summary of the sele tion riteria used to sear h for p! �+K0 .

150

Method Sele tion CriteriaH1) three to �ve e-like ringsKS ! �0�0 H2) no de aysH3) 750 MeV/ 2 < Mtot < 1000 MeV/ 2H4) ptot < 300 MeV/ I1) three rings, at least one e-likeKS ! �+�� I2) zero or one de aythree-ring I3) 750 MeV/ 2 < Mtot < 1000 MeV/ 2I4) ptot < 300 MeV/ I5) 450 MeV/ 2 < M�� < 550 MeV/ 2J1) one e-like ringKS ! �+�� J2) one �-like ringtwo-ring J3) one de ayJ4) 250 MeV/ < pe < 400 MeV/ J5) ptot < 300 MeV/ Table 9.18: Summary of the sele tion riteria used to sear h for p! e+K0 .

Chapter 10Con lusion10.1 SummaryAfter a 991-day (61-kton�year) exposure, 7940 ontained events were re orded in the�du ial volume of the Super{Kamiokande dete tor. This data sample was sear hedfor nu leon de ay via p ! ��K+ , n ! ��K0 , p ! �+K0 , and p ! e+K0 . Noeviden e for nu leon de ay into any of the modes was found, therefore lower limitson the partial lifetimes into these modes of (17, 2.5, 12, and 4.4) �1032 at the90% on�den e level were set. These limits ex eed limits set by previous dete torssigni� antly. A summary of the results for IMB, Kamiokande, Soudan II, and Super{Kamiokande is shown in table 10.1 and in �gure 10.1.Limit summary (1032 years, 90% CL)Mode Super{Kamiokande IMB[12℄ Kamiokande [58℄ Soudan II [97, 54℄p! ��K+ 17 1.8 1.0 0.46n! ��K0 2.5 0.86 0.27 0.26p! �+K0 12 1.3 1.2 1.2p! e+K0 4.4 0.32 1.5 0.85Table 10.1: Summary of limits studied in this dissertation for Super{Kamiokande,IMB, Kamiokande, and Soudan II. 151

152Super-KamiokandeIMBKamiokandeSoudan II

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3010

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35Figure 10.1: Summary of limits set in this dissertation and previous limits.10.2 FutureUnfortunately, the sensitivity to the nu leon de ay modes studied in this dissertationis now limited by the ba kground from atmospheri neutrinos. Therefore an in reasein the exposure by a fa tor of x will result in a sensitivity of only px. For instan e,assuming that the dete tion eÆ ien y does not hange and that the number of ob-served events be omes omparable to the number of estimated ba kground, the limitfor p ! ��K+ after an exposure of 610 kton�years (10 times the urrent exposureof Super{Kamiokande) is estimated to be about 7 � 1033 years (90% C.L.). This

153impa ts the potential \next dete tor" in that new ways must be found to eliminatethe ba kground. Some of this an be done by developing better event re onstru tionalgorithms or imposing more stringent sele tion riteria.However, before thinking of new ways to reje t the ba kground, the ba kgroundmust be better understood. As of now, the various ontributions to the ba kgroundestimation are not well understood. Un ertainties in the overall atmospheri neutrino ux, the loss of muon neutrinos in neutrino os illations, the pion produ tion ross-se tions, and the hadroni intera tions of pions all ontribute to the reasonably largeun ertainty in the ba kground estimation [98℄. Sin e the ba kground a�e ts thesensitivity of a dete tor to spe i� nu leon de ay modes, these ontributions to theba kground estimation must be better understood in order to optimize the potentialperforman e of the next dete tor.10.3 Dis ussionThe result for p! ��K+ presented in this dissertation essentially ex ludes the min-imal SUSY SU(5) model. However, in the past several years interest has grown inmodels based on the SO(10) symmetry group. The SO(10) group is desirable sin eit allows for a right-handed neutrino and puts all fermions into a single multiplet.The SO(10) model by Lu as and Raby [23℄ predi ts proton lifetimes into p !��K+ varying from 1 � 1033 to 2 � 1034 years and bound neutron lifetimes inton ! ��K0 varying from 2 � 1032 to 1 � 1033 years. The results for p ! ��K+and n! ��K0 presented in this dissertation are beginning to test these predi tions,however more exposure and sensitivity is needed to signi� antly onstrain them.There has been re ent ex itement about an SO(10) model in orporating neutrinomass proposed by Babu, Pati, and Wil zek [24℄ whi h suggests that the proton

154lifetime into p ! ��K+ should be less than 5 � 1033 years [32℄. In addition, itpredi ts that the bran hing ratio for p! �+K0 is omparable to that for p! ��K+ .Simultaneous observation of these de ays would support this theory. No eviden efor nu leon de ay into either of these modes was found with the analysis presentedin this dissertation. Furthermore, the limits set on these modes are omparable tothe predi tion for the lifetimes. If this model is indeed orre t, Super{Kamiokandeshould begin to see events within the next ouple of years. If not, the results will onstrain the model signi� antly.

Appendix ASetting a LimitThe de ay rate � of a proton (and subsequently the lifetime �) is given by the simpleformula � = nobsN0 1�t � B = 1� (A.1)where nobs is the number of observed proton de ays, N0 is the number of protons att = 0, �t is the exposure time, � is the dete tion eÆ ien y, and B is the bran hingratio of the proton into a parti ular mode. The partial lifetime removes the unknownbran hing ratio and is de�ned as �B = N0�t � Bnobs (A.2)The probability to observe n events is governed Poisson statisti sP (n; �) = �nn! e�� (A.3)where � is the mean of the distribution. For ases where ba kground exists themean � is �s + �b where �s is the mean number of signal events and �b is the mean155

156number of ba kground events. When the observed number of events is either zeroor onsistent with the expe ted ba kground, an upper limit on the number of eventsfrom that parti ular nu leon de ay mode is set. This upper limit sP l is de�ned asthe value of �s for whi h any repeat of the experiment would yield more than thenumber observed in the urrent experiment with a probability P l. In general, limitsare quoted with P l = 90%, or in other words, at the 90% on�den e level. Thegeneral formula for al ulating s90 is0:90 = R s900 P (nobs; x) dxR10 P (nobs; x) dx (A.4)this is the ba kground unsubtra ted limit. To get the ba kground subtra ted limit, xis substituted with x+�b where �b is the mean expe ted ba kground. This method ofsetting limits is the Poisson pro esses with ba kground method outlined in referen e[96℄. All limits quoted in this dissertation were based on this pro edure. The lowerlimit on the partial lifetime is then given by�B > Np(n) � �Bms90 (A.5)where Np(n) is the number of protons (neutrons) per kiloton in water, � is the dete torexposure in kiloton�years, � is the dete tion eÆ ien y, and Bm is the meson bran hingratio.Finally, when using di�erent methods to set limits on a single nu leon de aymodes (i.e. di�erent meson de ay modes), the limits are ombined to make a �nallimit for that parti ular de ay mode. The ombined s90 for n experiments is similarto equation A.4 0:90 = R s900 Qni=1 [P (nobs; ni(x))℄ dxR10 Qni=1 [P (nobs; ni(x))℄ dx (A.6)

157where i denotes the ith method, nobs is the number of observed events, and ni(x) isgiven by ni(x) = �b;i + �iBi�tPni=1 �iBi�tx (A.7)

Bibliography[1℄ Murray Gell-Mann. A s hemati model of baryons and mesons. Physi s Letters,8:214, 1964.[2℄ M. Breidenba h et al. Observed behavior of highly inelasti ele tron protons attering. Physi al Review Letters, 23:935, 1969.[3℄ H. Weyl. Zeits hrift f�ur Physik, 56:330, 1929.[4℄ E.C.G. St�u kelberg. Helveti a Physi a A ta, 11:229, 1939.[5℄ E.P. Wigner. Pro eedings of the Ameri an Philosophy So iety, 93:521, 1949.[6℄ S.L. Glashow. Nu lear Physi s, 22:579, 1961.[7℄ A. Salam. Pro eedings Of The Nobel Symposium Held 1968 At Lerum, Sweden,page 367, 1968.[8℄ S. Weinberg. Physi al Review Letters, 19:1264, 1967.[9℄ N. Cabibbo. Physi al Review Letters, 10:531, 1963.[10℄ M. Kobayashi and T. Maskawa. Progress in Theoreti al Physi s, 49:652, 1973.[11℄ H. Georgi and S. Glashow. Physi al Review Letters, 32:438, 1974.[12℄ C. M Grew et al. Physi al Review, D59:052004, 1999.158

159[13℄ M. Shiozawa et al. Physi al Review Letters, 81:3319{3323, 1998.[14℄ E. Witten. Nu lear Physi s, B188:513, 1981.[15℄ S. Dimopoulos and S. Raby. Nu lear Physi s, B192:353, 1981.[16℄ J. Ellis, D.V. Nanopoulos, and Serge Rudaz. Nu lear Physi s, B202:43, 1982.[17℄ S. Weinberg. Physi al Review, D26:287, 1982.[18℄ N. Sakai and T. Yanagida. Nu lear Physi s, B197:83, 1982.[19℄ S. Dimopoulos, S. Raby, and F. Wil zek. Physi s Letters, 112B:133, 1982.[20℄ S. Dimopoulos and H. Georgi. Nu lear Physi s, B193:150, 1981.[21℄ N. Sakai. Zeits hrift f�ur Physik, C11:153, 1981.[22℄ J. Hisano, H. Murayama, and T. Yanagida. Nu lear Physi s, 402B:46, 1993.[23℄ V. Lu as and S. Raby. Physi al Review, D55:6986, 1997.[24℄ K.S. Babu J.C. Pati and F. Wil zek. Nu lear Physi s, B566:33, 2000.[25℄ Q. Sha� and Z. Tavartkiladze. Physi s Letters, B473:272, 2000.[26℄ H.V. Klapdor-Kleingrothaus and A. Staudt. Parti le Astrophysi s. Institute ofPhysi s Publishing, London, 1995.[27℄ K.S. Babu, J.C. Pati, and F. Wil zek. Physi s Letters, B423:337, 1998.[28℄ Y. Fukuda et al. Physi al Review Letters, 81:1562{1567, 1998.[29℄ Mark D. Messier. Eviden e for Neutrino Mass from Observations of Atmospheri Neutrinos with Super-Kamiokande. PhD thesis, Boston University, 1999.

160[30℄ J.C. Pati and A. Salam. Physi al Review Letters, 32:661, 1973.[31℄ J.C. Pati and A. Salam. Physi al Review, D10:275, 1974.[32℄ Jogesh C. Pati. Talk presented at NNN 2000 Workshop in Irvine,CA, Feb. 2000.[33℄ P. Nath, A.H. Chamesddine, and R. Arnowitt. Physi al Review, D32:2348,1985.[34℄ P. Nath and R. Arnowitt. Invited talk at the International Symposium on Leptonand Baryon Number Conservation, 1998.[35℄ S.P. Rosen. Physi al Review Letters, 34:774, 1975.[36℄ M. Goldhaber, P. Langa ker, and R. Slansky. S ien e, 210:851, 1980.[37℄ F. Reines, C.L. Cowan, and M. Goldhaber. Physi al Review, 96:1157, 1954.[38℄ C.C. Giamati and F. Reines. Physi al Review, 126:2178, 1962.[39℄ W.R. Kropp and F. Reines. Physi al Review, 137B:740, 1965.[40℄ H.S. Gurr, W.R. Kropp, F. Reines, and B. Meyer. Physi al Review, 158:1321,1967.[41℄ F. Reines and M.F. Crou h. Physi al Review Letters, 32:493, 1974.[42℄ J. Learned, F. Reines, and A. Soni. Physi al Review Letters, 43:907, 1979.[43℄ G. Flerov, D. Klo hkov, V. Skobkin, and V. Terent'ev. Soviet Physi s Doklady,3:79, 1958.[44℄ J.C. Evans Jr. and R.I. Steinberg. S ien e, 197:989, 1977.

161[45℄ R.I. Steinberg and Jr. J.C. Evans. Pro eedings from Neutrino '77, page 321,1977.[46℄ J. Bartelt et al. Physi al Review, D36:1990, 1987.[47℄ M.R. Krishnaswamy et al. Physi s Letters, 106B:339, 1981.[48℄ M.R. Krishnaswamy et al. Physi s Letters, 115B:349, 1982.[49℄ G. Battistoni et al. Nu lear Instruments and Methods in Physi s Resear h,A245:277, 1986.[50℄ C. Berger et al. Nu lear Instruments and Methods in Physi s Resear h,A262:463, 1987.[51℄ W.W.M. Allison et al. Physi s Letters, B391:491, 1997.[52℄ G. Battistoni et al. Physi s Letters, 133B:454, 1983.[53℄ C. Berger et al. Physi s Letters, B269:227, 1991.[54℄ D. Wall et al. Physi al Review, D61:72004, 2000.[55℄ R. Be ker-Szendy et al. Nu lear Instruments and Methods in Physi s Resear h,A324:363, 1993.[56℄ R. Claus et al. Nu lear Instruments and Methods in Physi s Resear h,A261:540, 1987.[57℄ T.J. Phillips et al. Physi s Letters, B224:348, 1989.[58℄ Hirata et al. Physi s Letters, B220:308, 1989.[59℄ J.D. Ja kson. Classi al Ele trodynami s. John Wiley and Sons, New York, 1975.

162[60℄ H. Kume et. al. Nu lear Instruments and Methods in Physi s Resear h, 205:443{449, 1983.[61℄ A. Suzuki et. al. Nu lear Instruments and Methods in Physi s Resear h,A329:299{313, 1993.[62℄ H. Ikeda et. al. Nu lear Instruments and Methods in Physi s Resear h,A320:310{316, 1992.[63℄ Je�rey S. George. Experimental Study of the Atmospheri ��=�e Ratio in theMulti-GeV Energy Range. PhD thesis, University of Washington, June 1998.[64℄ M. Nakahata et al. Nu lear Instrumemtatopm and Methods in Physi s Resear h,A421:113, 1999.[65℄ S. Hiramatsu et al. Pro eedings for the International Conferen e on Nu learStru ture Studies Using Ele tron S attering and Photorea tion, Sendai, Japan,page 429, 1972.[66℄ R.D. Woods and D.S. Saxon. Physi al Review, 95:577, 1954.[67℄ H. Ejiri. Physi al Review, C48:1442, 1993.[68℄ Parti le Data Group. The European Physi al Journal, C3:1{794, 1998.[69℄ J.S. Hyslop et al. Physi al Review, D46:961, 1992.[70℄ R.G. Glasser et al. Physi al Review, D15:1200, 1977.[71℄ M. Honda et al. Physi s Letters, B248:193, 1990.[72℄ M. Honda et al. Physi al Review, D52:4985, 1995.[73℄ G. Barr, T.K.Gaisser, and T. Stanev. Physi al Review, D39:3532, 1989.

163[74℄ T. Futagami et al. Physi al Review Letters, 82:5194, 1999.[75℄ C.H. Llewellyn Smith. Physi s Reports, 3:261, 1972.[76℄ D. Rein and L.M. Sehgal. Annals of Physi s, 133:79, 1981.[77℄ D. Rein and L.M. Sehgal. Nu lear Physi s, B223:29, 1983.[78℄ P. Marage et al. Zeits hrift f�ur Physik, C31:191, 1986.[79℄ M. Glu k E. Reya and A. Vogt. Zeits hrift f�ur Physik, C67:433, 1995.[80℄ S.J. Barish et al. Physi al Review, D17:1, 1978.[81℄ S. Barlag et al. Zeits hrift f�ur Physik, C11:283, 1982.[82℄ P. Musset and J. Vialle. Physi s Reports, C39:1, 1978.[83℄ J.E. Kim et al. Review of Modern Physi s, 53:211, 1981.[84℄ D. Rein. Zeits hrift f�ur Physik, 35:43, 1987.[85℄ E. Oset et al. Nu lear Physi s, A484:557, 1988.[86℄ M. Nakahata et al. Journal of the Physi al So iety of Japan, 55:3786, 1986.[87℄ C.H.Q. Ingram et al. Physi al Review, C27:1578, 1983.[88℄ D. Ashery et al. Physi al Review, C23:2173, 1981.[89℄ D. Casper et al. Physi al Review Letters, 66:2561, 1991.[90℄ Hirata et al. Physi s Letters, B280:146, 1992.[91℄ Y. Fukuda et al. Physi s Letters, B433:9{18, 1998.

164[92℄ GEANT Dete tor Des ription and Simulation Tool. CERN Geneva, Switzerland,1993.[93℄ T.A. Gabriel et al. IEEE Transa tions on Nu lear S ien e, 36,1:14, 1989.[94℄ Davies. Ma hine Vision : Theory, Algorithms, Pra ti alities. A ademi Press,San Diego, 1997.[95℄ Yoshinari Hayato. Sear h for proton de ay into K+��. PhD thesis, Tokyo Insti-tute of Te hnology, February 1998.[96℄ Parti le Data Group. Physi al Review, D54:85, 1996.[97℄ W. W. M. Allison et al. Physi s Letters, B427:217, 1998.[98℄ Dave Casper. Talk presented at NNN 2000 Workshop in Irvine,CA, Feb. 2000.