A study of decay channels

b

Physics Letters B 607 (2005) 59–66

www.elsevier.com/locate/physlet

A study ofD0 → K0SK0

SX decay channels

FOCUS Collaboration1

J.M. Linka, P.M. Yagera, J.C. Anjosb, I. Bediagab, C. Göbelb, A.A. Machadob,J. Magninb, A. Massafferrib, J.M. de Mirandab, I.M. Pepeb, E. Polycarpob,

A.C. dos Reisb, S. Carrilloc, E. Casimiroc, E. Cuautlec, A. Sánchez-Hernándezc,C. Uribec, F. Vázquezc, L. Agostinod, L. Cinquinid, J.P. Cumalatd, B. O’Reilly d,I. Segonid, K. Stensond, J.N. Butlere, H.W.K. Cheunge, G. Chiodinie, I. Gainese,

P.H. Garbinciuse, L.A. Garrene, E. Gottschalke, P.H. Kaspere, A.E. Kreymere,R. Kutschkee, M. Wange, L. Benussif, M. Bertanif, S. Biancof, F.L. Fabbrif, A. Zallo f,

M. Reyesg, C. Cawlfieldh, D.Y. Kim h, A. Rahimih, J. Wissh, R. Gardneri,A. Kryemadhii, Y.S. Chungj, J.S. Kangj, B.R. Koj, J.W. Kwakj, K.B. Leej, K. Chok,

H. Parkk, G. Alimonti l, S. Barberisl, M. Boschinil, A. Ceruttil , P. D’Angelol,M. DiCoratol, P. Dinil, L. Ederal, S. Erbal, P. Inzanil, F. Leverarol, S. Malvezzil,

D. Menascel, M. Mezzadril, L. Moroni l, D. Pedrinil, C. Pontogliol, F. Prelzl,M. Roverel, S. Salal, T.F. Davenport IIIm, V. Arenan, G. Bocan, G. Bonomin,

G. Gianinin, G. Liguorin, D. Lopes Pegnan, M.M. Merlo n, D. Pantean, S.P. Rattin,C. Riccardin, P. Vitulon, H. Hernandezo, A.M. Lopezo, H. Mendezo, A. Pariso,

J. Quinoneso, J.E. Ramirezo, Y. Zhango, J.R. Wilsonp, T. Handlerq, R. Mitchellq,D. Enghr, M. Hosackr, W.E. Johnsr, E. Luiggir, J.E. Moorer, M. Nehringr,

P.D. Sheldonr, E.W. Vaanderingr, M. Websterr, M. Sheaffs

a University of California, Davis, CA 95616, USAb Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ, Brazil

c CINVESTAV, 07000 México City, DF, Mexicod University of Colorado, Boulder, CO 80309, USA

e Fermi National Accelerator Laboratory, Batavia, IL 60510, USAf Laboratori Nazionali di Frascati dell’INFN, Frascati I-00044, Italy

g University of Guanajuato, 37150 Leon, Guanajuato, Mexicoh University of Illinois, Urbana-Champaign, IL 61801, USA

i Indiana University, Bloomington, IN 47405, USAj Korea University, Seoul 136-701, South Korea

k Kyungpook National University, Taegu 702-701, South Koreal INFN and University of Milano, Milano, Italy

m University of North Carolina, Asheville, NC 28804, USAn Dipartimento di Fisica Nucleare e Teorica and INFN, Pavia, Italy

0370-2693/$ – see front matter 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2004.12.063

60 FOCUS Collaboration / Physics Letters B 607 (2005) 59–66

re

tic.

o University of Puerto Rico, Mayaguez, PR 00681, USAp University of South Carolina, Columbia, SC 29208, USA

q University of Tennessee, Knoxville, TN 37996, USAr Vanderbilt University, Nashville, TN 37235, USA

s University of Wisconsin, Madison, WI 53706, USA

Received 27 October 2004; accepted 17 December 2004

Available online 24 December 2004

Editor: M. Doser

Abstract

Using data from the FOCUS experiment (FNAL-E831), we report on the decay ofD0 mesons into final states containing mothan oneK0

S . We present evidence for two Cabibbo favored decay modes,D0 → K0SK0

SK−π+ andD0 → K0SK0

SK+π−, and

measure their combined branching fraction relative toD0 → K0π+π− to beΓ (D0→K0

SK0SK±π∓)

Γ (D0→K0π+π−)= 0.0106±0.0019±0.0010.

Further, we report new measurements ofΓ (D0→K0

SK0SK0

S)

Γ (D0→K0π+π−)= 0.0179±0.0027±0.0026, Γ (D0→K0K0)

Γ (D0→K0π+π−)= 0.0144±0.0032±

0.0016, andΓ (D0→K0

SK0Sπ+π−)

Γ (D0→K0π+π−)= 0.0208± 0.0035± 0.0021 where the first error is statistical and the second is systema

2004 Elsevier B.V. All rights reserved.

cayto

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1. Introduction

Detailed measurements of rare exclusive demodes of charm mesons provide a powerful wayprobe the details of charm decay such as the cobutions ofW exchange diagrams and final stateteractions. These measurements aid our understanof the interplay between the weak and strong intertions, mainly for multibodydecays where theoreticpredictions are poorer than for two body decays.report the first observation ofD0 → K0

SK0Sπ±K∓,

and new measurements ofD0 → K0SK0

SK0S , D0 →

K0SK0

S , andD0 → K0SK0

Sπ+π−.The fixed-target charm photoproduction expe

ment FOCUS, an upgraded version of E687[1], col-lected data during the 1996–1997 fixed-targetat Fermilab. A photon beam is derived from tbremsstrahlung of secondary electrons and positproduced from the 800 GeV/c Tevatron proton beamThe photon beam interacts with a segmented belium-oxide target. The average photon energy forconstructed charm events is 180 GeV.

E-mail address: david.lopes@pv.infn.it(D. Lopes Pegna).1 Seehttp://www-focus.fnal.gov/authors.htmlfor additional au-

thor information.

Two silicon microvertex systems provide excelleseparation between the production and charm devertices. One silicon strip detector called targeticon (TS) is embedded in the BeO target segme[2]. The other silicon strip detector (SSD) is locatdownstream of the target region. Charged particlestracked and momentum analyzed with five statioof multiwire proportional chambers in a two manet forward spectrometer. Three multicell threshCerenkov detectors are implemented to identify etrons, pions, kaons, and protons[3].

2. Reconstruction of individual particles: K0S , K ,

and π

A detailed description of individualK0S reconstruc-

tion in the FOCUS spectrometer can be found ewhere[4]. Briefly, K0

S ’s are identified in several different regions depending on theK0

S decay length; upstream of the magnet with silicon strip informatioupstream of the magnet without silicon strip informtion, and inside of the magnet. Depending on whetthe daughter pions from theK0

S pass through the second magnet, and hence have a well defined momtum, a series of different techniques are employ

FOCUS Collaboration / Physics Letters B 607 (2005) 59–66 61

e

and-d

bedon-rlog

y

de-

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-ed

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Roughly 15% of theK0S are found upstream of th

silicon system and can be used in locating theD0 de-cay vertex. When there are two or moreK0

S in a decaychannel, the daughter tracks must all be distinctcannot be shared betweenK0

S candidates. The reconstructed mass of theK0

S must be within three standardeviations of the nominalK0

S mass.All charged tracks from the charm decay must

singly linked to the silicon microstrip, be of gooquality, and inconsistent with zero degree photon cversion. Cerenkov particle identification (PID) focharged particles is performed by constructing alikelihood valueWi for the particle hypotheses (i =e,π,K,p). Theπ consistency of a track is defined b�Wπ =Wmin −Wπ , whereWmin is the minimumWvalue of the other three hypotheses. Similarly, wefine �WK,π = Wπ −WK and�WK,p = Wp −WK

for kaon identification and we require�WK,π > 1and�WK,p > −2 for kaons and�Wπ > −5 for pi-ons.

3. Reconstruction of D0 candidates

TheD0 candidates are formed by making a verhypothesis for the daughter particles whenever poble. We use theK0

S candidates and two charged tracof the correct charge combination to form aD0 can-didate. The confidence level of the decay vertex othe D0 candidate is required to be greater than 1The combined momentum vector located at thecay vertex forms theD0 track. Using theD0 track asa seed track for the candidate driven vertexing alrithm [1], we search for a production vertex in whicthe confidence level is greater than 1% and themary multiplicity including the seed track must haat least 3 tracks. The production vertex must beside the target. The significance of separation betwthe production and the decay vertices (L/σL) mustbe greater than 4 forD0 → K0

SK0Sπ∓K± and greater

than 6 forD0 → K0SK0

Sπ+π−. Different values arechosen for theL/σL cut due to the level of background for the two channels, but scans are performin L/σL as part of the systematic uncertainty stuies.

A stand-alone vertex algorithm is used to recostruct the primary vertex of the event for decay mo

without charged tracks[1]. All the silicon microvertextracks in the event, excluding those already assigto pions used to reconstructK0

S , are used to form alpossible vertices of the event with a confidence legreater than 1%: we then choose the primary veto be the highest multiplicity vertex. Ties are resolvchoosing the most upstream vertex.

The signal channels are normalized toD0 →K0π+π− which is the most abundantD0 decay modecontaining aK0

S . We use only the most basic cuin this analysis. The invariant mass distributionD0 → K0

Sπ+π− at an L/σL > 4 is presented inFig. 1(a). To determine the reconstruction efficienof this channel we use a Monte Carlo simulationing our best determined decay distribution to genateD0 → K0π+π−. The reconstructed Monte Carsample was six times larger than the data samplefit our signals from both data and Monte Carlo withGaussian for the signal and a 2nd degree polynofor the background using a maximum likelihood fiAs our most copiousK0

S decay channel, we use th

D0 → K0Sπ+π− mode to search for variations vers

reconstructedK0S categories. We identify a systema

uncertainty onK0S reconstruction of 7.1%.

The systematic uncertaintyfor each branching fraction is independently determined. Several tests areformed. To check the stability of the branching frations we fix the cuts to their standard values and vone cut at a time. Cuts which are scanned include pcle identification, significance of separation, isolatof the secondary vertex from any other track, and cfidence level of the secondary vertex. We also perfosplit sample systematics by dividing our samples itwo sub-samples based on momentum and data-taperiod. We study fit variant systematics by calculatthe branching fraction when the signals are fit with 12nd, or 3rd degree polynomials.

We look for Monte Carlo resonance systematicssearching for a difference in reconstruction efficienbetween non-resonant generation and a specificonance channel. We also include a systematic untainty for the absolute tracking efficiency (0.2% pdifference in numbers of tracks) and forK0

S recon-

struction efficiency (7.1% perK0S ). Finally, we include

a small contribution to the systematic uncertainty dto Monte Carlo statistics. All systematic uncertaintare added in quadrature.

62 FOCUS Collaboration / Physics Letters B 607 (2005) 59–66

Fig. 1. Invariant mass distribution for variousD0 final states: (a) Reconstructed mass ofD0 → K0Sπ+π−. There are 22835± 248 events

with a sigma of 11.4 MeV/c2. (b) Reconstructed mass ofD0 → K0SK0

SK±π∓. There are 57± 10 events with a sigma of 5.0 MeV/c2.

(c) Reconstructed mass ofD0 → K0SK0

SK0S . There are 170± 26 events with a sigma of 5.6 MeV/c2.

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4. The D0 → K0SK0

SK±π∓ decay mode

The D0 final stateK0SK0

SK±π∓ has not been observed by previous experiments. While theD0 de-cay modesD0 → K0K0K+π−, D0 → K0K0K−π+,and D0 → K0K0K+π− can result in a final statK0

SK0SK±π∓, the decay modeD0 → K0K0K+π− is

doubly Cabibbo suppressed and we assume thatmode is small compared to the other two Cabibbovored modes. To distinguish the two Cabibbo favodecays we use the charge of the soft pion in thecay sequenceD∗+ → D0π+. First, we demonstrata signal for the two channels combined withouting a soft pion tag and then we argue that we hevidence for independent observations in both chnels. InFig. 1(b) we show the invariant mass plot fD0 → K0

SK0SK±π∓ at L/σ > 4. We fit the plot with

a Gaussian for the signal and a 2nd degree polymial for the background using a maximum likelihofit and we find 57± 10 events.

We find no evidence for resonant substructureD0 → K0

SK0SK±π∓ and use a non-resonant Mon

Carlo simulation to obtain the efficiency. As a systeatic check we find a 2.6% difference in efficiency froa D0 → a0(980)+K∗(892)− Monte Carlo simulation

Correcting for efficiency, we find:

Γ (D0 → K0SK0

SK±π∓)

Γ (D0 → K0π+π−)

(1)= 0.0106± 0.0019± 0.0010.

We have included systematic uncertainty contributifrom split samples(0), fit variations(0.0007), pos-sible resonant decay(0.0001), Monte Carlo statis-tics (0.0001), absolute tracking efficiency(0.0001),and variation betweenK0

S reconstruction categorie(0.00075).

While we have established that we see a new dechannel, in order to separateD0 → K0

SK0SK+π− and

D0 → K0SK0

SK−π+ we need to tag aD0 by using thesoft pion from theD∗+ → D0π+ decay. InFig. 2(c)we present the mass differenceM(K0

SK0SK±π∓πs)−

M(K0SK0

SK±π∓) in which we find 14.1 ± 4.4 signalevents when we cut around theD0 mass.Fig. 2(a), (b)shows the mass difference histogram for the evenwhich the soft pion has the opposite (same) chargthat of the kaon. The two histograms show a signa7.2±3.4 and 6.8±2.9 events, respectively. The fitsall three histograms are performed by fixing the mand width to the values returned from the Monte Ca

FOCUS Collaboration / Physics Letters B 607 (2005) 59–66 63

),cut of

Fig. 2. Mass difference betweenM(K0SK0

SK±π∓πs) and M(K0SK0

SK±π∓) where πs is a pion from the primary vertex. Plots (a(b), and (c) are for cases where theπs charge relative to the kaon charge is opposite, same, or either, respectively. A mass1.85< M(K0

SK0SK±π∓πs) < 1.88 GeV/c2 to selectD0 events is applied.

es.en-

ved

In

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(thera-

ons

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thethe

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n,s,or-dind

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5. The D0 → K0SK0

SK0S decay mode

Although this mode is Cabibbo allowed, it requireither final state interactions orW -exchange to occurDue to the limited phase space and the need to idtify three K0

S candidates, the signal can be obserwithout the need for aD∗+ tag or aL/σL cut. Thissignificantly improves the reconstruction efficiency.Fig. 1(c) we find a signal of 170± 26 events.

We find no evidence for resonant substructureuse a non-resonant Monte Carlo simulation totain the efficiency. AD0 → a0(980)0K0

S simulationis used as a measure of the systematic variationdifference in efficiency is 5.6%). For the branchingtio of this mode with respect to theD0 → K0π+π−mode we find:

(2)

Γ (D0 → K0SK0

SK0S)

Γ (D0 → K0π+π−)= 0.0179± 0.0027± 0.0026.

We have included systematic uncertainty contributifrom split samples(0), fit variations(0.0007), possi-ble resonant decay(0.0005), Monte Carlo statistics(0.0001), absolute tracking efficiency(0.0001), andthe variation betweenK0

S reconstruction categorie(0.0025). Several groups[5–8] have reported measurements ofD0 → K0

SK0SK0

S .

6. The D0 → K0SK0

S decay mode

The D0 → K0K0 decay is expected to occur prmarily via two W -exchange diagrams, which are epected to cancel out in a four-quark model. Instandard six-quark model the difference betweentwo amplitudes is tiny, proportional toSU(3) flavourbreaking effects, and we thus might expect the braning fraction for the decay to be very small (< 3 ×10−4). However, a Standard Model based calculat[9] predicts a relatively large branching fraction duto final-state interaction effects, leading to a braning ratio ofB(D0 → K0K0) = 1

2B(D0 → K+K−) =0.3%. A recent investigation[10] has focused on ths-channel and thet-channel one particle exchang(OPE) contributions. While thes-channel contribu-tion, taken into account through the poorly knowscalar mesonf0(1710), gives a small contributionthe one particlet-exchange gives higher contributionwith pion exchange being the highest. In the factization limit [11], the branching fraction is expecteto be equal to zero. Non-factorizable contributionsfactorization-type models have been recently studie[12] and predict a branching fraction of about 10−4.Several experiments[13–16] have reported measurments ofD0 → K0

SK0S .

64 FOCUS Collaboration / Physics Letters B 607 (2005) 59–66

.

S with a D∗+ − D0 mass difference cut

There are 79± 17 events with a sigma of 12.5 MeV/c2. (b) Reconstructed mass difference ofD∗+ − D0; D0 → K0SK0

S. There are 77± 17

events in the mass difference plot demonstrating consistency with (a). (c) Reconstructed mass ofD0 → K0SK0

Sπ+π−. There are 113± 21

events.

an

ffer-

m

a-

theaus-

nd and.

ob-

ethenal

aondn-

om

on-

s-

This channel is similar toD0 → K0SK0

SK0S in that

no L/σL cut is possible, but the channel requiresadditionalD∗ tag requirement. We selectD∗+ candi-dates by requiring that the reconstructed mass dience�M = MD∗+ −MD0 lies within 2 MeV/c2 of thenominal mass difference[17] of 145.42 MeV/c2.

The dominant background sources forD0 →K0

SK0S decays are from non-resonantK0

Sπ+π− andπ+π−π+π− decays. To reduce feedthrough froD0 → K0

Sπ+π− where theπ+π− invariant mass fallsin K0

S mass region or fromD0 → π+π−π+π− whereboth π+π− pairs can be misidentified asK0

S candi-dates, we make the additional requirement that theK0

S

candidates reconstructed with silicon strip informtions have a decay length significance (L/σL) greaterthan 12. We also apply a|cosθK0

S| < 0.8 cut, where

θK0S

is the angle between theK0S momentum in theD0

rest frame and theD0 laboratory momentum.In Fig. 3(a) theK0

SK0S invariant mass distribution

is shown for the events satisfying these cuts. Forsignal shape we use a double Gaussian (two Gsians with the same mean) for theD0 signal (79± 17events), as suggested by Monte Carlo studies, afirst order Chebyshev polynomial for the backgrou

The double Gaussian shape is fixed to the onetained from Monte Carlo simulation. InFig. 3(b) the�M = D∗+ − D0 mass difference distribution in thD0 mass region is plotted. A Gaussian is used to fitsignal while for the background we use the functioform

(3)a(�M − mπ)1/2 + b(�M − mπ)3/2,

wheremπ is the pion mass, the first term is fromnon-relativistic model of phase space and the secterm is the first-order relativistic correction to the norelativistic model. Consistent yields are obtained frthe two fits.

The events of the normalization modeD0 →K0

Sπ+π− have been selected using the same recstruction and fitting techniques as forD0 → K0

SK0S

mode and similar selection criteria to minimize sytematic uncertainties.

We measure

Γ (D0 → K0SK0

S)

Γ (D0 → K0Sπ+π−)

= Γ (D0 → K0K0)

Γ (D0 → K0π+π−)

(4)= 0.0144± 0.0032± 0.0016.

FOCUS Collaboration / Physics Letters B 607 (2005) 59–66 65

Table 1D0 → K0

SK0

SX branching fractions

Decay mode This experiment PDG 2004[17]

Γ (D0→K0SK0

SK±π∓)

Γ (D0→K0π+π−)0.0106± 0.0019± 0.0010 –

Γ (D0→K0SK0

SK0

S)

Γ (D0→K0π+π−)0.0179± 0.0027± 0.0026 0.0154± 0.0025

Γ (D0→K0K0)

Γ (D0→K0π+π−)0.0144± 0.0032± 0.0016 0.0119± 0.0033

Γ (D0→K0SK0

Sπ+π−)

Γ (D0→K0π+π−)0.0208± 0.0035± 0.0021 0.031± 0.010± 0.008

eenibu-

first

ddi-

g-

sr

notla-

nceng

ons

s

arer-

hing

o

affs

bo-arte-dier-De-T-the

This accounts for the unseenK0Lπ+π− and K0

LK0L

decays (note thatD0 → K0SK0

L is forbidden by CPconservation). Different systematic sources have binvestigated and the value reported includes contrtions from fit variations(0.0013) andK0

S reconstruc-tion (0.0010).

7. The D0 → K0SK0

Sπ+π− decay mode

This channel is Cabibbo-suppressed and wasobserved by the ARGUS Collaboration[18]. It has alarger background than theD0 → K0

SK0SK+π− chan-

nel due to more phase space and two pions. In ation one must eliminateπ+π− combinations whichare consistent with theK0

S mass. To increase the sinal to noise, aL/σ > 6 cut is applied. InFig. 3(c) wepresent theK0

SK0Sπ+π− invariant mass. The figure i

fit with a Gaussian for theD0 signal plus a 2nd ordepolynomial.

As the resonant structure for this channel isknown, we use a non-resonant Monte Carlo simution to compute the branching fraction.

A D0 → K∗(892)−K∗(892)+ simulation is usedas a measure of the systematic variation (the differein efficiency is 7%). Again, we calculate the branchiratio of this mode with respect to theD0 → K0π+π−mode.

Γ (D0 → K0SK0

Sπ+π−)

Γ (D0 → K0π+π−)

(5)= 0.0208± 0.0035± 0.0021.

We have included systematic uncertainty contributifrom split samples(0), fit variations(0.0013), possi-

ble resonant decay(0.0005), Monte Carlo statistics(0.0002), absolute tracking efficiency(0.0001), andthe variation betweenK0

S reconstruction categorie(0.0015).

8. Conclusions

We summarize our branching ratios and compthem inTable 1to the Particle Data Group world aveages where available[17].

We have investigated and measured the brancratios of several decay modes of the charm mesonD0

into final states containing at least twoK0S relative

to D0 → K0π+π− mode. We have evidence for twnew Cabibbo favoredD0 decay modes, namelyD0 →K0

SK0SK+π− and D0 → K0

SK0SK−π+ and we have

reported new measurements forD0 → K0SK0

SK0S ,

D0 → K0SK0

S , andD0 → K0SK0

Sπ+π−.

Acknowledgements

We wish to acknowledge the assistance of the stof Fermi National Accelerator Laboratory, the INFNof Italy, and the physics departments of the collarating institutions. This research was supported in pby the US National Science Foundation, the US Dpartment of Energy, the Italian Istituto NazionaleFisica Nucleare and Ministero della Istruzione Univsità e Ricerca, the Brazilian Conselho Nacional desenvolvimento Científico e Tecnológico, CONACyMéxico, and the Korea Research Foundation ofKorean Ministry of Education.

66 FOCUS Collaboration / Physics Letters B 607 (2005) 59–66

th-

6

1)

40

54

54

40

5

210

92

64

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