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Physics Letters B 586 (2004) 191–197

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Study of hadronic five-body decays ofcharmed mesons involvingK0

S

FOCUS Collaboration

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, J. Jacobsd,

B. O’Reilly d, I. Segonid, M. Wahld, 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, M. Giammarchil, 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, M.M. Merlo n, D. Pantean,

D. Lopes Pegnan, S.P. Rattin, C. Riccardin, P. Vitulon, H. Hernandezo, A.M. Lopezo,E. Luiggio, H. Mendezo, A. Pariso, J.E. Ramirezo, Y. Zhango, J.R. Wilsonp,T. Handlerq, R. Mitchellq, D. Enghr, M. Hosackr, W.E. Johnsr, M. Nehringr,

P.D. Sheldonr, K. Stensonr, 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, I-00044 Frascati, 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 reserveddoi:10.1016/j.physletb.2003.11.078

.

http://www.elsevier.com/locate/physletb

192 FOCUS Collaboration / Physics Letters B 586 (2004) 191–197

ay

r

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 29 October 2003; accepted 28 November 2003

Editor: M. Doser

Abstract

We study the decay ofD0 andD+s mesons into five-body final states including aK0

Sand report the discovery of the dec

modeD+s → K0

SK0Sπ+π+π−. The branching ratio for the new mode is

Γ (D+s →K0

SK0Sπ+π−π+)

Γ (D+s →K0

SK−π+π+)= 0.102± 0.029± 0.029.

We also determine the branching ratio ofΓ (D0→K0

Sπ+π+π−π−)

Γ (D0→K0Sπ+π−)

= 0.095± 0.005± 0.007 as well as an upper limit fo

Γ (D0→K0SK−π+π+π−)

Γ (D0→K0Sπ+π+π−π−)

< 0.054 (90% CL). An analysis of the resonant substructure forD0 → K0Sπ+π+π−π− is also

performed. 2004 Elsevier B.V. All rights reserved.

PACS: 13.25.Ft; 14.40.Lb

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More information on multibody final states in thcharm sector is an essential ingredient for our abto model decay rates and to further increase our unstanding of the decay process in heavy quark systeThis is particularly important for theD+

s decays wherea substantial part of its hadronic decay rate is snot identified. In this Letter we extend our work [on four-body decays involving aK0

S to five-body de-cays involving aK0

S . We have already published rsults on all charged five-body modes [2]. The FOCCollaboration presents the first evidence of the demodeD+

s → K0SK0

Sπ+π+π−, measures an inclusivbranching ratio for the modeD0 → K0

Sπ+π+π−π−relative toD0 → K0

Sπ+π− and places an upper limon the modeD0 → K0

SK−π+π+π−. Finally wepresent the first resonant substructure analysis odecay modeD0 → K0

Sπ+π+π−π−.The data were collected during the 1996–19

fixed target run at Fermilab. Bremsstrahlung of eltrons and photons with an endpoint energy ofproximately 300 GeV produces photons which

E-mail address: [email protected] (J.P. CumalaURL: http://www-focus.fnal.gov/authors.html.

.

teract in a segmented beryllium-oxide target to pduce charmed particles. The average photon enfor events which satisfy our trigger is≈ 180 GeV.Charged decay particles with a momentum of 1 GeV/c

and above are analyzed by two oppositely polaridipole magnets. Tracking is performed by a systof silicon vertex detectors [3] in the target region aby multi-wire proportional chambers downstreamthe interaction. Particle identification is performedthree thresholdCerenkov counters, two electromanetic calorimeters, a hadronic calorimeter, and tmuon systems.

Five-body D0 and D+s decays are reconstructe

using a candidate driven vertex algorithm [4]. A dcay vertex is formed from the reconstructed chartracks. TheK0

S is also reconstructed using techniqudescribed elsewhere [5]. The momentum informatfrom theK0

S and the charged tracks is used to foa candidateD momentum vector, which is intersectwith other tracks to find the production vertex. Eveare selected based on several criteria. The confidlevel for the production vertex and for the charm dcay vertex must be greater than 1%. The reconstrumass of theK0

S must be within four standard deviations of the nominalK0

S mass. The typicalK0S mass

http://www-focus.fnal.gov/authors.html

FOCUS Collaboration / Physics Letters B 586 (2004) 191–197 193

Fig. 1. Invariant mass distributions for (a)K0Sπ+π+π−π−, (b) K0

Sπ+π+π−π− for D∗ tagged events, (c)K0

SK0

Sπ+π−π±, and (d)

K0SK−π+π−π+. The fits are described in the text.

ion,niontiveorehod

dedinrac-e-the

ly-nd

a-

ingevi-(a)

rtted

reehei-

pi-evelthere-

n

theian

resolution is approximately 6 MeV/c2. The likelihoodfor each charged particle to be a proton, kaon, por electron based onCerenkov particle identificatiois used to make additional requirements [6]. For pcandidates we require a loose cut that no alternahypothesis is favored over the pion hypothesis by mthan 6 units of log-likelihood. In addition, for eackaon candidate we require the negative log-likelihokaon hypothesis,WK = −2 ln(kaon likelihood), to befavored over the corresponding pion hypothesisWπ byWπ −WK > 2. We also require the distance (≈ 5 mm)between the primary and secondary vertices diviby its error (≈ 500 µm) to be at least 10. Finally,order to reduce background due to secondary intetions of particles from the production vertex, we rquire the secondary vertex to be located outsidetarget material.

For individual modes we apply additional anasis cuts. Due to the large combinatoric backgroufor D0 → K0

Sπ+π+π−π−, we increase the separ

tion requirement of the secondary vertex from bejust outside the target material to two standard dations from the edge of the target material. Fig. 1shows theK0

Sπ+π+π−π− invariant mass plot foevents that satisfy these cuts. The distribution is fiwith a Gaussian for theD0 signal (1283± 57 events)with the width and mass floated and a first degpolynomial for the background. Fig. 1(b) shows tK0

Sπ+π+π−π− invariant mass plot for events orignating from aD∗+ → D0π+ decay.

The D+s → K0

SK0Sπ+π+π− mode is difficult to

detect due to the relative inefficiency ofK0S recon-

struction and that most of the time only the threeons define the secondary vertex. The confidence lthat a pion track from the decay vertex intersectsproduction vertex must be less than 2%. We alsoquire a reconstructedD+

s momentum of greater tha25 GeV/c. Fig. 1(c) shows theK0

SK0Sπ+π+π− mass

plot for events which satisfy these cuts. This isfirst observation of this mode. We fit with a Gauss


Table 1Branching ratios, event yields, and efficiency ratios for modes involving aK0

S. All branching ratios are inclusive of subresonant modes

Decay mode Ratio of events Efficiency ratio Branching ratio



1283±5723408±405 0.58 0.095± 0.005± 0.007

Γ (D+s →K0

SK0

Sπ+π+π−)

Γ (D+s →K0

SK−π+π+)

37±10962±57 0.38 0.102± 0.029± 0.029

Γ (D0→K0SK−π+π+π−)


<5.64197±16 0.53 < 0.054 (90% CL)

atd.

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Table 2Comparison of this measurement ofD0 → K0

Sπ+π+π−π− modeto previous measurements

Experiment EventsΓ (D0→K0

Sπ+π+π−π−)


E831 (this measurement) 1283 0.095± 0.005± 0.007PDG average [7] 0.107± 0.029ARGUS [8] 11 0.07± 0.02± 0.01CLEO [9] 56 0.149± 0.026E691 [10] 6 0.18± 0.07± 0.04

(37± 10 events) with mass and width allowed to floand a second degree polynomial for the backgroun

The decayD0 → K0SK−π+π+π− is Cabibbo sup-

pressed, and we do not observe a signal in this mThus we choose our analysis cuts by maximizingquantityS/

√B, whereS is the fitted yield from our

Monte Carlo simulation of the mode, andB is thenumber of background events in the signal region frdata. Based on this optimization we require a recstructedD0 momentum of greater than 50 GeV/c.We also require theD0 come from aD∗+ decay, thatis 0.142 GeV/c2 < MD∗+ − MD0 < 0.149 GeV/c2.Fig. 1(d) shows the resultingK0

SK−π+π+π− invari-ant mass plot. As there is no apparent signal we rean upper limit branching ratio.

We measure the branching fraction of theD0 →K0

Sπ+π+π−π− mode relative toD0 → K0Sπ+π−.

The relative efficiency is determined by Monte Casimulation. TheK0

Sπ+π− andK0Sπ+π+π−π− chan-

nels are produced as an incoherent mixture of subonant decays based on PDG information [7] andanalysis described below, respectively. We measthe D+

s → K0SK0

Sπ+π+π− mode relative toD+s →

K0SK−π+π+. We test for dependency on cut sele

tion in both modes by individually varying each cuThe results are shown in Table 1, and we compare

measurement of theD0 → K0Sπ+π+π−π− branch-

ing ratio with previous measurements in Table 2.We studied systematic effects due to uncertain

in the reconstruction efficiency, in the unknown renant substructure, and on the fitting procedure. Totermine the systematic error due to the reconstrucefficiency we follow a procedure based on theS-factormethod used by the Particle Data Group [7]. For emode we split the data sample into four independsubsamples based onD momentum and on the period of time in which the data was collected. Thesplits provide a check on the Monte Carlo simulatof charm production, of the vertex detector (it changduring the course of the run), and on the simulationthe detector stability. We then define the split samvariance as the difference between the scaled variand the statistical variance if the former exceedslatter. The method is described in detail in Ref. [11].addition, we split the data sample into three indepdent subsamples based on the location and geomof theK0

S decay. We then calculate theK0S reconstruc-

tion variance using the same procedure describedthe split sample variance. We also vary the subrenant states in the Monte Carlo and use the variancthe branching ratios as a contribution to the systemerror. We also determine the systematic effects baon different fitting procedures. The branching ratare evaluated under various fit conditions, and the vance of the results is used as an additional systemerror. Finally, we evaluate systematic effects fromcertainty in the absolute tracking efficiency of mulbody decays using studies ofD0 → K−π+π+π− andD0 → K−π+ decays. The systematic effects are thall added in quadrature to obtain the final systemerror. Table 3 summarizes the contributions to the stematic errors for the two branching ratios.

We do not observe a signal in the decayD0 →K0

SK−π+π+π− and we calculate an upper lim


Table 3Summary of the systematic error contributions



Γ (D+s →K0

SK0

Sπ+π+π−)

Γ (D+s →K0

SK−π+π+)

D momentum and run period 0.003 0.020Fit variance 0.004 0.009Monte Carlo statistics 0.001 0.002KS reconstruction 0.002 0.013Abs. tracking efficiency 0.004 0.004Resonant substructure 0.002 0.012

Total 0.007 0.029

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for the branching ratio with the respect toD0 →K0

Sπ+π+π−π−. We evaluate the upper limit usinthe method of Rolke and Lopez [12]. We define tsignal region as being within±2σ of the nominalD0

mass, and the two sideband regions as (4–8)σ aboveand below theD0 mass. We observe 3 events in tsignal region and 6 events in the sidebands, cosponding to an upper limit of 5.02 events (@90% C

We study systematic effects for this channel frocut variation and resonant substructure, and inclthese in our determination of the upper limit usingmethod of Cousins and Highland [13]. We determthe systematic error from cut variation by individuavarying each cut, fitting the resulting distributioand taking the variance between each branching rmeasurement as our systematic error. We also ssystematic effects from our uncertainty in the resonsubstructure of the mode by varying the subresonstates included in the Monte Carlo simulation, aused the variance in the resulting branching raas our systematic error. These two systematic effare then added in quadrature to give a final relasystematic error of 26%.

We then determine the increase in our upper limievents,∆U , taking into account the systematic errThe increase in the upper limit is based on the equaof Cousins and Highland:

∆U = 1

2U2σ 2

sysU + b − s

U + b,

whereU is the original upper limit of events,σsys isthe percent systematic error determined above,b is thenumber of events observed in the sideband region,s is the number of signal events. We calculate an uplimit of 5.64 events, corresponding to an upper lim

for the branching ratio of:

Γ (D0 → K0SK−π+π+π−)

Γ (D0 → K0Sπ+π+π−π−)

< 0.054 (@90% CL).

We have studied the resonance substructure in thecay D0 → K0

Sπ+π+π−π−. We use an incoherenbinned fit method [14] developed by the E687 Claboration which assumes the final state is an incoent superposition of subresonant decay modes coning vector resonances. A coherent analysis woulddifficult given our limited statistics. For subresonadecay modes we consider the lowest mass (K0

Sπ−)and (π+π−) resonances, as well as a nonresonchannel:K∗−π+π+π−, K0

Sρ0π+π−, K∗−ρ0π+ and(K0

Sπ+π+π−π−)NR. All states not explicitly considered are assumed to be included in the nonresochannel.

For the resonant substructure analysis ofD0 →K0

Sπ+π+π−π− we place additional cuts to enhanthe signal to background ratio. We require the cfidence level that a track from the decay vertextersects the production vertex be less than 8%.also require theD0 to come from aD∗+ decay, thatis 0.144 GeV/c2 < MD∗+ − MD0 < 0.148 GeV/c2,in order to reduce background and distinguishtweenD0 and D0. Requiring the pion tag to distinguish betweenD0 and D0 is crucial in reducing thenumber of combinations per event. Without thisquirement theKS would need to be paired with eacpion when searching for aK∗− and the real combination could not be identified given our statisticFig. 1(b) shows theK0

Sπ+π+π−π− invariant massplot for events which satisfy these cuts. We thentermine the acceptance corrected yield into eachresonant mode using a weighting technique whereach event is weighted by its kinematic values in th


Fig. 2. K0Sπ+π+π−π− weighted invariant mass for (a)(K0

Sπ+π+π−π−)NR, (b) K∗−π+π+π−, (c) K0

Sρ0π+π−, (d) K∗−ρ0π+,

(e) inclusive sum of all four modes.

e

onthe

nte

-

e

toheds.

truc-re

urventub-

achthensUs-b-to

our

submasses: (K0Sπ−), (π+π−), and (π+π+). No reso-

nance in the (π+π+) submass exists, but we includit in order to compute a meaningfulχ2 estimate of thefit. Eight population bins are constructed dependingwhether each of the three submasses falls withinexpected resonance (in the case ofπ+π+, the bin issplit into high and low mass regions). For each MoCarlo simulation the bin population,ni , in the eightbins is determined and a matrix,Tiα , is calculated between the generated states,α, Monte Carlo yields,Yα ,and the eight binsi:

ni =∑

α

TiαYα.

The elements of the matrix,T , can be summed to givthe efficiency for each mode,εα :

εα =∑

i

Tiα.

The Monte Carlo determined matrix is invertedcreate a new weighting matrix which multiplies tbin populations to produce efficiency corrected yiel

Table 4Fractions relative to the inclusive mode for the resonance substure of theD0 → K0

Sπ+π+π−π− decay mode. These values anot corrected for unseen decay modes

Subresonant mode Fraction ofK0Sπ+π−π+π−

(K0Sπ+π+π−π−)NR < 0.46 @90% CL

K∗−π+π+π− 0.17± 0.28± 0.02K0

Sρ0π+π− 0.40± 0.24± 0.07

K∗−ρ0π+ 0.60± 0.21± 0.09

The weight includes the contributions from the focombinations we have for each event. Each data ecan then be weighted according to its values in the smass bins. Once the weighted distributions for eof the four modes are generated, we determineacceptance corrected yield by fitting the distributiowith a Gaussian signal and a linear background.ing incoherent Monte Carlo mixtures of the four suresonant modes we verify our procedure is ablecorrectly recover the generated mixtures of the fmodes.


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The results forK0Sπ+π+π−π− are summarized

in Table 4. The four weighted histograms with fiare shown in Fig. 2, where Fig. 2(e) is the weighdistribution for the sum of all subresonant modThe goodness of fit is evaluated by calculating aχ2

for the hypothesis of consistency between the mopredictions and observed data yields in each of thsubmass bins. The calculatedχ2 is 9.7 (4 degrees ofreedom), with most of theχ2 contribution resultingfrom a poor Monte Carlo simulation of theπ+π+spectrum in the nonresonant channel.

We observe results similar to previous studiesfive-body charm decays, with a small nonresoncomponent and the dominant mode of the form vecvector–pseudoscalar. Such a result has been predby theoretical discussion of a vector-dominance mofor heavy flavor decays [15], which suggests tcharm decays are dominated by quasi-two-bodycays in which theW± immediately hadronizes inta charged pseudoscalar, vector or axial vectorson. Results consistent with the vector-dominamodel have already been seen by FOCUS in fibody decays [2]. Such theoretical discussion rathe possibility that the resonant substructure fordecayD0 → K0

Sπ+π+π−π− is dominated by thequasi-two-body decayK∗−a+

1 . (Although the centravalue of thea+

1 mass lies outside of phase space,broad width of thea+

1 makes the decay possible.) Ttest this hypothesis we generate Monte Carlo simlations of this decay, assuming thea+

1 has a widthof 400 MeV/c2 and decays entirely as anS-wave toρ0π+, and use our subresonant analysis procedureplained above. We observe yield fractions in eachthe subresonant modes similar to the reported ftions from the data, suggesting our results are content with the decay being dominated by theK∗−a+

1subresonant state.

In conclusion we have measured relative branchratios of many-body hadronic modes ofD0 andD+

s

involving a K0S decay and have presented the fi

evidence of the decay modeD+s → K0

SK0Sπ+π+π−.

We have also performed an analysis of the resonsubstructure of the decayD0 → K0

Sπ+π+π−π−.

d

Finally we have placed an upper limit on the relatbranching fraction of the Cabibbo suppressed deD0 → K0

SK−π+π+π−.

Acknowledgements

We acknowledge the assistance of the staffsFermi National Accelerator Laboratory, the INFNItaly, and the physics departments of the collaboing institutions. This research was supported in parthe US National Science Foundation, the US Depment of Energy, the Italian Istituto Nazionale di FisiNucleare and Ministero della Istruzione, Universe Ricerca, the Brazilian Conselho Nacional de Dsenvolvimento Científico e Tecnológico, CONACyMéxico, and the Korea Research Foundation ofKorean Ministry of Education.

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