6
Search for rare and forbidden decays of charm and charmed-strange mesons to final states h e e þ P. Rubin, 1 N. Lowrey, 2 S. Mehrabyan, 2 M. Selen, 2 J. Wiss, 2 J. Libby, 3 M. Kornicer, 4 R. E. Mitchell, 4 M. R. Shepherd, 4 C. M. Tarbert, 4 D. Besson, 5 T. K. Pedlar, 6 J. Xavier, 6 D. Cronin-Hennessy, 7 J. Hietala, 7 P. Zweber, 7 S. Dobbs, 8 Z. Metreveli, 8 K. K. Seth, 8 A. Tomaradze, 8 T. Xiao, 8 S. Brisbane, 9 L. Martin, 9 A. Powell, 9 P. Spradlin, 9 G. Wilkinson, 9 H. Mendez, 10 J. Y. Ge, 11 D. H. Miller, 11 I. P. J. Shipsey, 11 B. Xin, 11 G. S. Adams, 12 D. Hu, 12 B. Moziak, 12 J. Napolitano, 12 K. M. Ecklund, 13 J. Insler, 14 H. Muramatsu, 14 C. S. Park, 14 L. J. Pearson, 14 E. H. Thorndike, 14 F. Yang, 14 S. Ricciardi, 15 C. Thomas, 9,15 M. Artuso, 16 S. Blusk, 16 R. Mountain, 16 T. Skwarnicki, 16 S. Stone, 16 J. C. Wang, 16 L. M. Zhang, 16 G. Bonvicini, 17 D. Cinabro, 17 A. Lincoln, 17 M. J. Smith, 17 P. Zhou, 17 J. Zhu, 17 P. Naik, 18 J. Rademacker, 18 D. M. Asner, 19, * K. W. Edwards, 19 K. Randrianarivony, 19 G. Tatishvili, 19, * R. A. Briere, 20 H. Vogel, 20 P. U. E. Onyisi, 21 J. L. Rosner, 21 J. P. Alexander, 22 D. G. Cassel, 22 S. Das, 22 R. Ehrlich, 22 L. Fields, 22 L. Gibbons, 22 S. W. Gray, 22 D. L. Hartill, 22 B. K. Heltsley, 22 D. L. Kreinick, 22 V. E. Kuznetsov, 22 J. R. Patterson, 22 D. Peterson, 22 D. Riley, 22 A. Ryd, 22 A. J. Sadoff, 22 X. Shi, 22 W. M. Sun, 22 and J. Yelton 23 (CLEO Collaboration) 1 George Mason University, Fairfax, Virginia 22030, USA 2 University of Illinois, Urbana-Champaign, Illinois 61801, USA 3 Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India 4 Indiana University, Bloomington, Indiana 47405, USA 5 University of Kansas, Lawrence, Kansas 66045, USA 6 Luther College, Decorah, Iowa 52101, USA 7 University of Minnesota, Minneapolis, Minnesota 55455, USA 8 Northwestern University, Evanston, Illinois 60208, USA 9 University of Oxford, Oxford OX1 3RH, United Kingdom 10 University of Puerto Rico, Mayaguez, Puerto Rico 00681 11 Purdue University, West Lafayette, Indiana 47907, USA 12 Rensselaer Polytechnic Institute, Troy, New York 12180, USA 13 Rice University, Houston, Texas 77005, USA 14 University of Rochester, Rochester, New York 14627, USA 15 STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom 16 Syracuse University, Syracuse, New York 13244, USA 17 Wayne State University, Detroit, Michigan 48202, USA 18 University of Bristol, Bristol BS8 1TL, United Kingdom 19 Carleton University, Ottawa, Ontario, Canada K1S 5B6 20 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 21 University of Chicago, Chicago, Illinois 60637, USA 22 Cornell University, Ithaca, New York 14853, USA 23 University of Florida, Gainesville, Florida 32611, USA (Received 8 September 2010; published 22 November 2010) We have searched for flavor-changing neutral current decays and lepton-number-violating decays of D þ and D þ s mesons to final states of the form h e e þ , where h is either % or K. We use the complete samples of CLEO-c open-charm data, corresponding to integrated luminosities of 818 pb 1 at the center- of-mass energy E CM ¼ 3:774 GeV containing 2:4 10 6 D þ D pairs and 602 pb 1 at E CM ¼ 4:170 GeV containing 0:6 10 6 D s D s pairs. No signal is observed in any channel, and we obtain 90% confidence level upper limits on branching fractions BðD þ ! % þ e þ e Þ < 5:9 10 6 , BðD þ ! % e þ e þ Þ < 1:1 10 6 , BðD þ ! K þ e þ e Þ < 3:0 10 6 , BðD þ ! K e þ e þ Þ < 3:5 10 6 , BðD þ s ! % þ e þ e Þ < 2:2 10 5 , BðD þ s ! % e þ e þ Þ < 1:8 10 5 , BðD þ s ! K þ e þ e Þ < 5:2 10 5 , and BðD þ s ! K e þ e þ Þ < 1:7 10 5 . DOI: 10.1103/PhysRevD.82.092007 PACS numbers: 11.30.Fs, 11.30.Hv, 12.15.Mm, 13.20.Fc * Present address: Pacific Northwest National Laboratory, Richland, WA 99352, USA. PHYSICAL REVIEW D 82, 092007 (2010) 1550-7998= 2010=82(9)=092007(6) 092007-1 Ó 2010 The American Physical Society

Search for rare and forbidden decays of charm and charmed-strange mesons to final states

  • Upload
    j

  • View
    213

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Search for rare and forbidden decays of charm and charmed-strange mesons to final states

Search for rare and forbidden decays of charm and charmed-strangemesons to final states h�e�eþ

P. Rubin,1 N. Lowrey,2 S. Mehrabyan,2 M. Selen,2 J. Wiss,2 J. Libby,3 M. Kornicer,4 R. E. Mitchell,4 M. R. Shepherd,4

C.M. Tarbert,4 D. Besson,5 T. K. Pedlar,6 J. Xavier,6 D. Cronin-Hennessy,7 J. Hietala,7 P. Zweber,7 S. Dobbs,8

Z. Metreveli,8 K.K. Seth,8 A. Tomaradze,8 T. Xiao,8 S. Brisbane,9 L. Martin,9 A. Powell,9 P. Spradlin,9 G. Wilkinson,9

H. Mendez,10 J. Y. Ge,11 D.H. Miller,11 I. P. J. Shipsey,11 B. Xin,11 G. S. Adams,12 D. Hu,12 B. Moziak,12 J. Napolitano,12

K.M. Ecklund,13 J. Insler,14 H. Muramatsu,14 C. S. Park,14 L. J. Pearson,14 E. H. Thorndike,14 F. Yang,14 S. Ricciardi,15

C. Thomas,9,15 M. Artuso,16 S. Blusk,16 R. Mountain,16 T. Skwarnicki,16 S. Stone,16 J. C. Wang,16 L.M. Zhang,16

G. Bonvicini,17 D. Cinabro,17 A. Lincoln,17 M. J. Smith,17 P. Zhou,17 J. Zhu,17 P. Naik,18 J. Rademacker,18 D.M. Asner,19,*

K.W. Edwards,19 K. Randrianarivony,19 G. Tatishvili,19,* R. A. Briere,20 H. Vogel,20 P. U. E. Onyisi,21 J. L. Rosner,21

J. P. Alexander,22 D. G. Cassel,22 S. Das,22 R. Ehrlich,22 L. Fields,22 L. Gibbons,22 S.W. Gray,22 D. L. Hartill,22

B. K. Heltsley,22 D. L. Kreinick,22 V. E. Kuznetsov,22 J. R. Patterson,22 D. Peterson,22 D. Riley,22 A. Ryd,22 A. J. Sadoff,22

X. Shi,22 W.M. Sun,22 and J. Yelton23

(CLEO Collaboration)

1George Mason University, Fairfax, Virginia 22030, USA2University of Illinois, Urbana-Champaign, Illinois 61801, USA

3Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India4Indiana University, Bloomington, Indiana 47405, USA5University of Kansas, Lawrence, Kansas 66045, USA

6Luther College, Decorah, Iowa 52101, USA7University of Minnesota, Minneapolis, Minnesota 55455, USA

8Northwestern University, Evanston, Illinois 60208, USA9University of Oxford, Oxford OX1 3RH, United Kingdom10University of Puerto Rico, Mayaguez, Puerto Rico 0068111Purdue University, West Lafayette, Indiana 47907, USA

12Rensselaer Polytechnic Institute, Troy, New York 12180, USA13Rice University, Houston, Texas 77005, USA

14University of Rochester, Rochester, New York 14627, USA15STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, United Kingdom

16Syracuse University, Syracuse, New York 13244, USA17Wayne State University, Detroit, Michigan 48202, USA18University of Bristol, Bristol BS8 1TL, United Kingdom19Carleton University, Ottawa, Ontario, Canada K1S 5B6

20Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA21University of Chicago, Chicago, Illinois 60637, USA22Cornell University, Ithaca, New York 14853, USA

23University of Florida, Gainesville, Florida 32611, USA(Received 8 September 2010; published 22 November 2010)

We have searched for flavor-changing neutral current decays and lepton-number-violating decays of

Dþ and Dþs mesons to final states of the form h�e�eþ, where h is either � or K. We use the complete

samples of CLEO-c open-charm data, corresponding to integrated luminosities of 818 pb�1 at the center-

of-mass energy ECM ¼ 3:774 GeV containing 2:4� 106 DþD� pairs and 602 pb�1 at ECM ¼ 4:170 GeV

containing 0:6� 106 D��s D�

s pairs. No signal is observed in any channel, and we obtain 90% confidence

level upper limits on branching fractionsBðDþ ! �þeþe�Þ< 5:9� 10�6, BðDþ ! ��eþeþÞ< 1:1�10�6, BðDþ ! Kþeþe�Þ< 3:0� 10�6, BðDþ ! K�eþeþÞ< 3:5� 10�6, BðDþ

s ! �þeþe�Þ<2:2� 10�5, BðDþ

s ! ��eþeþÞ< 1:8� 10�5, BðDþs ! Kþeþe�Þ< 5:2� 10�5, and BðDþ

s !K�eþeþÞ< 1:7� 10�5.

DOI: 10.1103/PhysRevD.82.092007 PACS numbers: 11.30.Fs, 11.30.Hv, 12.15.Mm, 13.20.Fc

*Present address: Pacific Northwest National Laboratory, Richland, WA 99352, USA.

PHYSICAL REVIEW D 82, 092007 (2010)

1550-7998=2010=82(9)=092007(6) 092007-1 � 2010 The American Physical Society

Page 2: Search for rare and forbidden decays of charm and charmed-strange mesons to final states

I. INTRODUCTION

As an extension of our previously reported [1] search forrare and forbidden decays of the Dþ charm meson, Dþ !h�e�eþ, we report an analysis using CLEO-c’s full open-charm data sample for Dþ, and also a search for Dþ

s !h�e�eþ with CLEO-c’s full Dþ

s data sample. Here, h iseither � or K, and charge-conjugate modes are implicitthroughout this article. These decays probe flavor-changing neutral currents (FCNC), in Dþ ! �þeþe�and Dþ

s ! Kþeþe�, and lepton number violations(LNV), in Dþ ! h�eþeþ and Dþ

s ! h�eþeþ. Thesedecays are either highly suppressed or forbidden in thestandard model (SM), but can be significantly enhanced bysome non-SM physics scenarios [2–7]. Standard modelshort-distance FCNC decays are expected to be of order10�10 to 10�9 [3,5], but long-distance vector-pole induceddecays of Dþ or Dþ

s ! hþV0 ! hþeþe� (where V0 is anintermediate vector meson �0, !, or �) are expected to beof order 10�6 to 10�5 [3,5]. To observe an enhancement inFCNC due to non-SM physics, we need to search fordielectron mass regions away from the vector poles.Measuring long-distance induced decay itself might behelpful to understand the long-distance dynamics in theb sector, such as inclusive b ! s� decay or exclusiveB ! �� and B ! K�� decays related to extractingCabibbo-Kobayashi-Maskawa matrix elements jVtðd;sÞj. Onthe other hand, observation of LNV (�L ¼ 2) decays couldbe an indication of a Majorana nature of neutrinos [6,7].

We have used two sets of open-charm data samplescollected by the CLEO-c detector in eþe� collisions pro-vided by the Cornell Electron Storage Ring (CESR). Theintegrated luminosities are 818 pb�1 at the center-of-massenergy ECM ¼ 3:774 GeV near the peak of the c ð3770Þresonance which decays to D �D pairs, and 602 pb�1 atECM ¼ 4:170 GeV near the peak of D��

s D�s pair produc-

tion. The 3.774 GeV data set contains 2:4� 106 DþD�pairs, and is used to study Dþ ! h�e�eþ decays. The4.170 GeV data set contains 0:6� 106 D��

s D�s pairs and is

used to study Dþs ! h�e�eþ decays.

The remainder of this article is organized as follows. TheCLEO-c detector is described in Sec. II. Event selectioncriteria are described in Sec. III. Features of backgroundprocesses, our suppression strategy, and signal sensitivityare discussed in Sec. IV. Results are presented as plots andtables in Sec. V. Systematic uncertainties associated withthe branching fractions and their upper limits are discussedin Sec. VI. Finally, a summary of our results with system-atic uncertainties is provided in Sec. VII.

II. THE CLEO-C DETECTOR

The CLEO-c detector [8–11] is a general-purpose sole-noidal detector equipped with four concentric components:a six-layer vertex drift chamber, a 47-layer main driftchamber, a ring-imaging Cherenkov (RICH) detector, and

a cesium iodide electromagnetic calorimeter, all operatinginside a 1 Tesla magnetic field provided by a superconduct-ing solenoidal magnet. The detector provides acceptanceof 93% of the full 4� solid angle for both charged particlesand photons. The main drift chamber provides specific-ionization (dE=dx) measurements that discriminate be-tween charged pions and kaons. The RICH detector coversapproximately 80% of 4� and provides additional separa-tion of pions and kaons at momentum above 700 MeV.Hadron identification efficiencies are approximately 95%with misidentification rates of a few percent [12]. Electronidentification is based on a likelihood variable that com-bines the information from the RICH detector, dE=dx, andthe ratio of electromagnetic shower energy to track mo-mentum (E=p). Typical electron identification efficiency iswell over 90% on average with the pion fake rate less than0.1% and the kaon fake rate less than a percent [13,14].A GEANT-based [15] Monte Carlo (MC) simulation is

used to study efficiencies of signal and background events.Physics events are generated by EVTGEN [16], tuned withimproved knowledge of charm decays, and final-stateradiation (FSR) is modeled by PHOTOS [17]. NonresonantFCNC and LNV signal events are generated according tophase space.

III. EVENT SELECTION

Signal candidates are formed from sets of well-measured drift chamber tracks consistent with comingfrom the nominal interaction point. Charged pions andkaons are identified from the tracks with momentumgreater than 50 MeV and with j cos�j< 0:93, where � isthe angle between the track and the beam axis. Electroncandidates are required to be above 200 MeV withj cos�j< 0:90 to ensure that E=p is well measured.At ECM ¼ 3:774 GeV, for each signal candidate of the

form Dþ ! h�e�eþ (where h is either � or K), twokinematic variables are computed to define a signal region:the energy difference �E ¼ EDþ � Ebeam and the beam-

constrained mass difference �Mbc ¼ ½E2beam � p2

Dþ�1=2 �mDþ , where ðEDþ ;pDþÞ is the four-momentum of the signalDþ candidate, Ebeam is the beam energy, and mDþ is thenominal [18] mass of the Dþ meson. To improve theresolution of the kinematic variables, we recover brems-strahlung photon showers within 100 mrad of the directionof the electron candidates. We define a signal box forfurther analysis as ð�E;�MbcÞ ¼ ð�20 MeV;�5 MeVÞ,which corresponds to about 3 standard deviations of thekinematic variables. Because the expected contributionfrom the resonant decay BðDþ ! ��þ ! �þeþe�Þ �Oð10�6Þ is within our sensitivity, we further subdivideDþ ! �þeþe� candidates into two channels: resonantDþ ! �ðeþe�Þ�þ and nonresonant Dþ ! �þeþe� forthe FCNC search. If the dielectron invariant mass Mee

of the signal candidate is within �20 MeV of the nominal[18] mass of the � meson, we treat it as a resonant

P. RUBIN et al. PHYSICAL REVIEW D 82, 092007 (2010)

092007-2

Page 3: Search for rare and forbidden decays of charm and charmed-strange mesons to final states

Dþ ! �ðeþe�Þ�þ candidate and exclude it from theDþ ! �þeþe� candidates.

Similarly, at ECM ¼ 4:170 GeV, for each signal candi-date of the form Dþ

s ! h�e�eþ, the following twovariables are computed to define a signal region: themass difference �M ¼ MDþ

s�mDþ

sand the recoil mass

(against the signal candidate) difference �MrecoilðDþs Þ ¼

½ðE0 � EDþsÞ2 � ðp0 � pDþ

sÞ2�1=2 �mD�þ

s, where MDþ

sis

the invariant mass of the signal candidate, mDþs

is the

nominal [18] mass of the Dþs , ðE0;p0Þ is the total four-

momentum of the eþe� beam taking the finite beam cross-ing angle into account, ðEDþ

s;pDþ

sÞ is the four-momentum

of the signal candidate with EDþs¼ ½m2

Dþsþ p2

Dþs�1=2, and

mD�þs

is the nominal [18] mass of the D�þs . The same

bremsstrahlung recovery is performed and the Dþs !

�þeþe� channel is subdivided into resonant �ðeþe�Þ�þand nonresonant channels. The signal box is definedas ð�M;�MrecoilðDþ

s ÞÞ ¼ ð�20 MeV;�55 MeVÞ for fur-ther analysis. The broad recoil mass window �55 MeV isrequired to allow both primary and secondary (fromD�þ

s !Dþ

s � or D�þs ! Dþ

s �0) Dþ

s candidates to be selected.

IV. ANALYSIS

Backgrounds are dominantly from events with real elec-trons, particularly from D semileptonic decays. Themajority of combinatorial background events are fromdouble charm semileptonic decays, typically 4 or lesscharged particles in the event with large missing energydue to the missing neutrinos. Hadronic decays involving�-conversion and �0 (�, !) Dalitz decay, or accompaniedby another charm semileptonic decay, can mimic theh�e�eþ signal as well. Because of the low probability ofhadrons being misidentified as electrons [13], backgroundfrom D �D decays to 3-body charged-particle hadronicdecays (such as K��þ�þ, ���þ�þ, K0

SKþ, KþK��þ)

are negligible after two electrons are identified, and they donot peak at the signal region due to the wrong mass assign-ments for the hadrons misidentified as electrons. That is,D �D backgrounds are predominantly associated with thesemileptonic decays and non-D �D (q �q continuum, �-pair,radiative return, or QED events) backgrounds are associ-ated with the �-conversion and Dalitz decays. All of thesebackgrounds are nonpeaking or peak away from the signalregions.

Our background suppression criteria tuning procedurefor Dþ ! h�e�eþ channels is detailed in our previousarticle [1]. We have used the same background rejectioncriteria with the four kinematic variables to reject theabove-mentioned backgrounds inDþ channels and revisedthe criteria to accommodate the Dþ

s channels. The otherside total energy Eother is the sum of energies of all particlesother than those making up the signal candidate. We usethis variable to reject events associated with semileptonicdecays, mainly for double charm semileptonic decays, in

which the visible other side energy would be small due tothe undetectable missing neutrinos. We reject candidates ifEother < 1:0 GeV for Dþ ! �þeþe�, Eother < 1:3 GeVfor Dþ ! Kþeþe�, Eother < 1:4 GeV for Dþ

s !�þeþe�, and Eother < 1:7 GeV for Dþ

s ! Kþeþe�. Forthe LNV modes, we reject candidates if the number oftracks in the event is 4 or fewer and Eother < 0:5 GeV.Semileptonic events involving K0

S ! �þ�� in the final

state can mimic the signal in �þeþe� channels. We haveused the invariant mass M�þ�� to veto these events. Weveto the candidate when the charged pion in the signalcandidate combined with any other unused oppositelycharged track satisfies jM�þ�� �mK0

Sj< 5 MeV, where

mK0Sis the nominal [18] mass of the K0

S. Real electrons

from �-conversion and Dalitz decays are suppressed byusing the dielectron invariant mass squared q2 computedfrom the signal electron positron pair, or q2other computed

using one signal side electron (positron) combined withany oppositely charged unused track. We veto candidates ifq2 < 0:01 GeV2 or q2other < 0:0025 GeV2. For Dþ

s , we

have required the solo photon from D�þs decays to Dþ

s �to be explicitly reconstructed to further suppress under-lying nonstrange-charmed meson backgrounds at ECM ¼4:170 GeV, by requiring the recoil mass of the signalcandidate plus solo photon MrecoilðDþ

s þ �Þ to be within�30 MeV of the nominal [18] Dþ

s mass. Regardless ofwhether the signal Dþ

s candidate is the primary or second-ary Dþ

s , for the decay eþe� ! D��s D�

s ! ðD�s �ÞD�

s , themass of the system recoiling against the Dþ

s plus � shouldpeak at the Dþ

s mass.The analysis was done in a blind fashion. Before we

opened the signal box, all above-mentioned criteria wereoptimized using MC events with a sensitivity variablewhich is defined as the average upper limit one wouldget from an ensemble of experiments with the expectedbackground and no signal,

S ¼P1

Nobs¼0 CðNobsjNexpÞP ðNobsjNexpÞN�

; (1)

where Nexp is the expected number of background

events, Nobs is the observed number of events, C is the90% confidence coefficient upper limit on the signal,P is the Poisson probability, N is the number of Dþor Dþ

s , and � is the signal efficiency. In addition to thesignal MC samples, four types of background MCsamples are utilized to optimize the backgroundsuppression criteria: 20 times the data sample for open-charm (D �D, D� �D, D� �D�, D� �D�, Dþ

s D�s , and D�þ

s D�s ),

5 times the data sample of noncharm uds continuum(q �q), �-pair, and radiative return to the c ð2SÞ. To nor-malize background MC events to match the expectednumber of the data events, we have used integratedluminosity and cross sections for each process. ForDþ ! h�e�eþ events at ECM ¼ 3774 MeV, we haveused DþD� ¼ 2:91 nb [12], D0 �D0 ¼ 3:66 nb [12],

SEARCH FOR RARE AND FORBIDDEN DECAYS OF CHARM . . . PHYSICAL REVIEW D 82, 092007 (2010)

092007-3

Page 4: Search for rare and forbidden decays of charm and charmed-strange mesons to final states

q �q ¼ 13:9 nb [19], �þ�� ¼ 3:0 nb,1 and radiative re-

turn to the c ð2SÞ RR ¼ 3:4 nb [20]. For Dþs !

h�e�eþ events at ECM ¼ 4170 MeV, we have usedD��

s D�s¼ 0:916 nb [21] (and used other open-charm

cross sections from the same reference), q �q ¼ 11:4 nb

[19], �þ�� ¼ 3:6 nb, and radiative return to the c ð2SÞRR ¼ 0:50 nb [20]. We have found that the agreementsbetween data and MC simulated events are excellent invarious kinematic variables used in the background sup-pression, giving us confidence in our optimization pro-cedure using our MC samples. Possible systematicuncertainties due to the data and MC differences areassessed in Sec. VI.

V. RESULTS

Scatterplots of �E vs �Mbc and �MðDþs Þ vs

�MrecoilðDþs Þ for signal candidates with all background

suppressions applied are shown in Figs. 1 and 2. Exceptfor the �ðeþe�Þ�þ channels, we find no evidence ofsignals, and we calculate 90% confidence level upper limits(UL) on the branching fractions based on Poisson processeswith background [22] (e.g. Sec. 28.6.4 Poisson processeswith background therein) as summarized in Table I:

UL ¼ CðNobsjNexpÞN�

: (2)

For Dþ and Dþs ! �ðeþe�Þ�þ channels, we find weak

evidence of signals with significance 3.5 for theDþ and 1.8for theDþ

s , so both branching fractions and upper limits areshown in Table I.

VI. SYSTEMATIC UNCERTAINTIES

Possible sources of systematic uncertainty in ourmeasurements are summarized in Table II. Uncertaintiesassociated with upper limits are classified into three cate-gories: uncertainties due to the normalization (the numbersof Dþ and Dþ

s ), the signal efficiency, and the number ofexpected background events.

FIG. 1 (color online). Scatterplots of �Mbc vs �E. The two contours for each mode enclose regions determined with signal MCsimulation to contain 50% and 85% of signal events, respectively. The signal region, defined by ð�E;�MbcÞ ¼ ð�20 MeV;�5 MeVÞ,is shown as a box.

FIG. 2 (color online). Scatterplots of �Mrecoil vs �M. The two contours for each mode enclose regions determined with signal MCsimulation to contain 40% and 85% of signal events, respectively. The signal region, defined by ð�M;�MrecoilÞ ¼ð�20 MeV;�55 MeVÞ, is shown as a box.

1With the lowest-order QED calculation, ðeþe� ! �þ��Þ ¼2�2�ð3� �2Þ=ð3sÞ, where � ¼ ð1� 4m2

�=sÞ1=2 is the �velocity.

P. RUBIN et al. PHYSICAL REVIEW D 82, 092007 (2010)

092007-4

Page 5: Search for rare and forbidden decays of charm and charmed-strange mesons to final states

Uncertainty in the number of Dþ (Dþs ) is estimated by

adding contributions from uncertainties in integrated lumi-nosity [12] 1.0% and the production cross section [12]2.0% (5.5% for Dþ

s [21]) in quadrature. We assign relativeuncertainties of 2.2% to the number of Dþ and of 5.6% tothe number of Dþ

s .There are several sources which can contribute to

uncertainty in the signal efficiency estimation, aslisted in Table II. By adding contributions from tracking[12], particle identification (PID) [12,13], FSR [13,14],background suppression, and MC statistics in quadrature,we found total uncertainties in the signal efficiency foreach channel range from 3% to 10%.

We use the number of background events estimated bythe MC simulation rather than using the sidebands in data.The MC samples, being 5–20 times larger, have higherprecision. We have evaluated possible systematic biascaused by the use of MC events rather than the data

sideband by using alternative background shapes, and bycomparing the MC predicted number to that interpolatedfrom the data sideband. We found no indication of system-atic bias; all deviations are adequately explained as statis-tical fluctuations due to the data statistics. We concludethat our MC events reproduce the features of the databackgrounds well. We took the statistical uncertainty inthe MC simulated number of backgrounds as the system-atic uncertainty in the expected number of background, assummarized in Table II.

VII. SUMMARY

With the complete samples of CLEO-c open-charm data,corresponding to integrated luminosities of 818 pb�1 atECM ¼ 3:774 GeV containing 2:4� 106 DþD� pairs and602 pb�1 at ECM ¼ 4:170 GeV containing 0:6� 106

D��s D�

s pairs, we have searched for rare (FCNC) and

TABLE I. Upper limits on branching fractions of Dþ and Dþs ! h�e�eþ at the 90% confidence level for a Poisson process [22],

where N is the number of Dþ (orDþs ) produced in our data, � is the signal efficiency, Nexp is the number of expected background, Nobs

is the number of signal candidates, CðNobsjNexpÞ is the 90% confidence coefficient upper limit on the observed events given the

expected background, andB is the branching fraction or upper limit of the branching fraction at 90% confidence level. We increase theupper limits to account for systematic uncertainties by decreasing the efficiency, the number of Dþ (or Dþ

s ), and the expected numberof background each by 1 standard deviation. For the Dþ and Dþ

s ! �ðeþe�Þ�þ channels, we have shown both branching fractionsand upper limits.

Channel N � (%) Nexp Nobs CðNobsjNexpÞ B

Dþ ! �þeþe� 4:76� 106 33.9 5.7 9 9.3 <5:9� 10�6

Dþ ! ��eþeþ 4:76� 106 43.5 1.3 0 2.3 <1:1� 10�6

Dþ ! Kþeþe� 4:76� 106 23.1 4.9 2 3.2 <3:0� 10�6

Dþ ! K�eþeþ 4:76� 106 35.3 1.2 3 5.8 <3:5� 10�6

Dþ ! �þ�ðeþe�Þ 4:76� 106 46.2 0.3 4 ð1:7þ1:4�0:9 � 0:1Þ � 10�6

7.9 <3:7� 10�6

Dþs ! �þeþe� 1:10� 106 24.3 6.7 6 5.6 <2:2� 10�5

Dþs ! ��eþeþ 1:10� 106 33.4 2.2 4 6.2 <1:8� 10�5

Dþs ! Kþeþe� 1:10� 106 17.3 3.0 7 9.3 <5:2� 10�5

Dþs ! K�eþeþ 1:10� 106 27.7 4.1 4 5.0 <1:7� 10�5

Dþs ! �þ�ðeþe�Þ 1:10� 106 33.9 0.7 3 ð0:6þ0:8

�0:4 � 0:1Þ � 10�5

6.2 <1:8� 10�5

TABLE II. Summary of systematic uncertainties in Dþ and Dþs ! h�e�eþ decays. Uncertainties associated with the branching

fraction can be classified as three categories: uncertainties due to the normalization (the numbers of Dþ or Dþs ), the signal efficiency,

and the number of background events. The columns labeled �þ� refer to candidates with � ! eþe� decays.

Dþ Dþs

Source �þeþe� �þ� ��eþeþ Kþeþe� K�eþeþ �þeþe� �þ� ��eþeþ Kþeþe� K�eþeþ

Normalization 2.2% 2.2% 2.2% 2.2% 2.2% 5.6% 5.6% 5.6% 5.6% 5.6%

Tracking 0.9% 0.9% 0.9% 1.1% 1.1% 0.9% 0.9% 0.9% 1.1% 1.1%

PID 2.0% 2.0% 2.0% 2.0% 2.0% 2.0% 2.0% 2.0% 2.0% 2.0%

FSR 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0% 1.0%

Background suppression 5.0% 4.2% 1.5% 9.4% 1.5% 5.2% 4.5% 2.1% 9.0% 2.2%

MC statistics 0.6% 0.6% 0.5% 0.8% 0.6% 0.8% 0.6% 0.6% 1.0% 0.7%

Efficiency total 5.6% 4.9% 2.9% 9.8% 3.0% 5.8% 5.1% 3.3% 9.3% 3.4%

Number of background 12% 68% 20% 12% 25% 12% 26% 16% 15% 11%

SEARCH FOR RARE AND FORBIDDEN DECAYS OF CHARM . . . PHYSICAL REVIEW D 82, 092007 (2010)

092007-5

Page 6: Search for rare and forbidden decays of charm and charmed-strange mesons to final states

forbidden (LNV) decays ofDþ andDþs mesons of the form

h�e�eþ, where h� is either a charged pion or a chargedkaon. We found no evidence of signals and set upper limitson branching fractions at the 90% confidence level assummarized in Table I. Systematic uncertainties in thesignal efficiency, the number of Dþ (or Dþ

s ) events, andthe expected number of background events are incorpo-rated by decreasing the numbers used for those quantitiesby 1 standard deviation of the systematic uncertainty onthose quantities. These results are the most stringent limitson FCNC and LNV for theDþ andDþ

s ! h�e�eþ decaysto date and the limits in the dielectron channels are com-parable to those in the dimuon channels [18], but are still afew orders of magnitude larger than the SM expectation[3,5] in FCNC decays. This leaves some room for possibleenhancement [2–5] in both FCNC and LNV decaysinduced by non-SM physics. We have separately measuredbranching fractions of the resonant decays Dþ ! �þ� !�þeþe� and Dþ

s ! �þ� ! �þeþe� due to their largeexpected contributions to �þeþe� channels. The signifi-cance of our measured branching fractions is poor at 3.5

standard deviations for Dþ and 1.8 standard deviations forDþ

s , so we have also included upper limits in Table I.Our measured branching fractions of these decays areconsistent with the products of known world average[18] branching fractions, BðDþ !��þ ! eþe��þÞ¼BðDþ !��þÞ�Bð�! eþe�Þ¼ ½ð6:2�0:7Þ�10�3��½ð2:97�0:04Þ�10�4� ¼ ð1:8�0:2Þ�10�6 andBðDþ

s ! ��þ ! eþe��þÞ ¼ BðDþs ! ��þÞ �

Bð� ! eþe�Þ ¼ ½ð4:38 � 0:35Þ � 10�2� � ½ð2:97 �0:04Þ � 10�4� ¼ ð1:3 � 0:1Þ � 10�5.

ACKNOWLEDGMENTS

We gratefully acknowledge the effort of the CESR staffin providing us with excellent luminosity and runningconditions. D. Cronin-Hennessy thanks the A. P. SloanFoundation. This work was supported by the NationalScience Foundation, the U.S. Department of Energy, theNatural Sciences and Engineering Research Council ofCanada, and the U.K. Science and Technology FacilitiesCouncil.

[1] Q. He et al. (CLEO Collaboration), Phys. Rev. Lett. 95,221802 (2005).

[2] G. Burdman, E. Golowich, J. Hewett, and S. Pakvasa,Phys. Rev. D 66, 014009 (2002).

[3] S. Fajfer, S. Prelovsek, and P. Singer, Phys. Rev. D 64,114009 (2001).

[4] S. Fajfer and S. Prelovsek, Phys. Rev. D 73, 054026(2006).

[5] S. Fajfer, N. Kosnik, and S. Prelovsek, Phys. Rev. D 76,074010 (2007).

[6] A. Ali, A.V. Borisov, and N. B. Zamorin, Eur. Phys. J. C21, 123 (2001).

[7] A. Atre, T. Han, S. Pascoli, and B. Zhang, J. High EnergyPhys. 05 (2009) 030.

[8] R. A. Briere et al. (CESR-c and CLEO-c Taskforces,CLEO-c Collaboration), Cornell University, LEPPReport No. CLNS 01/1742, 2001 (unpublished).

[9] Y. Kubota et al. (CLEO Collaboration), Nucl. Instrum.Methods Phys. Res., Sect. A 320, 66 (1992).

[10] D. Peterson et al., Nucl. Instrum. Methods Phys. Res.,Sect. A 478, 142 (2002).

[11] M. Artuso et al., Nucl. Instrum. Methods Phys. Res., Sect.A 502, 91 (2003).

[12] S. Dobbs et al. (CLEO Collaboration), Phys. Rev. D 76,112001 (2007).

[13] D.M. Asner et al. (CLEO Collaboration), Phys. Rev. D 81,052007 (2010).

[14] D. Besson et al. (CLEO Collaboration), Phys. Rev. D 80,032005 (2009).

[15] R. Brun et al., GEANT 3.21, CERN Program LibraryLong Writeup W5013, 1993 (unpublished).

[16] D. J. Lange, Nucl. Instrum. Methods Phys. Res., Sect. A462, 152 (2001).

[17] E. Barberio and Z. Wa̧s, Comput. Phys. Commun. 79, 291(1994).

[18] C. Amsler et al. (Particle Data Group), Phys. Lett. B 667, 1(2008).

[19] J. Z. Bai et al. (BES Collaboration), Phys. Rev. Lett. 88,101802 (2002).

[20] M. Benayoun, S. I. Eidelman, V.N. Ivanchenko, and Z.K.Silagadze, Mod. Phys. Lett. A 14, 2605 (1999).

[21] D. Cronin-Hennessy et al. (CLEO Collaboration), Phys.Rev. D 80, 072001 (2009).

[22] R.M. Barnett et al. (Particle Data Group), Phys. Rev. D54, 1 (1996).

P. RUBIN et al. PHYSICAL REVIEW D 82, 092007 (2010)

092007-6