Physics Letters B 644 (2007) 20–24

www.elsevier.com/locate/physletb

Direct measurement of the branching fraction for D+ → K̄0μ+νμ anddetermination of Γ (D0 → K−μ+νμ)/Γ (D+ → K̄0μ+νμ)

BES Collaboration

M. Ablikim a, J.Z. Bai a, Y. Ban l, X. Cai a, H.F. Chen p, H.S. Chen a, H.X. Chen a, J.C. Chen a,Jin Chen a, Y.B. Chen a, Y.P. Chu a, Y.S. Dai r, L.Y. Diao i, Z.Y. Deng a, Q.F. Dong o, S.X. Du a,

J. Fang a, S.S. Fang a,1, C.D. Fu o, C.S. Gao a, Y.N. Gao o, S.D. Gu a, Y.T. Gu d, Y.N. Guo a, K.L. He a,M. He m, Y.K. Heng a, J. Hou k, H.M. Hu a, J.H. Hu c, T. Hu a, X.T. Huang m, X.B. Ji a, X.S. Jiang a,X.Y. Jiang e, J.B. Jiao m, D.P. Jin a, S. Jin a, Y.F. Lai a, G. Li a,2, H.B. Li a, J. Li a, R.Y. Li a, S.M. Li a,W.D. Li a, W.G. Li a, X.L. Li a, X.N. Li a, X.Q. Li k, Y.F. Liang n, H.B. Liao a, B.J. Liu a, C.X. Liu a,

F. Liu f, Fang Liu a, H.H. Liu a, H.M. Liu a, J. Liu l,3, J.B. Liu a, J.P. Liu q, Jian Liu a, Q. Liu a,R.G. Liu a, Z.A. Liu a, Y.C. Lou e, F. Lu a, G.R. Lu e, J.G. Lu a, C.L. Luo j, F.C. Ma i, H.L. Ma b,

L.L. Ma a,4, Q.M. Ma a, Z.P. Mao a, X.H. Mo a, J. Nie a, R.G. Ping a, N.D. Qi a, H. Qin a, J.F. Qiu a,Z.Y. Ren a, G. Rong a,∗, X.D. Ruan d, L.Y. Shan a, L. Shang a, C.P. Shen a, D.L. Shen a, X.Y. Shen a,H.Y. Sheng a, H.S. Sun a, S.S. Sun a, Y.Z. Sun a, Z.J. Sun a, X. Tang a, G.L. Tong a, D.Y. Wang a,5,L. Wang a, L.L. Wang a, L.S. Wang a, M. Wang a, P. Wang a, P.L. Wang a, Y.F. Wang a, Z. Wang a,Z.Y. Wang a, Zheng Wang a, C.L. Wei a, D.H. Wei a, Y. Weng a, N. Wu a, X.M. Xia a, X.X. Xie a,

G.F. Xu a, X.P. Xu f, Y. Xu k, M.L. Yan p, H.X. Yang a, Y.X. Yang c, M.H. Ye b, Y.X. Ye p, Z.Y. Yi a,G.W. Yu a, C.Z. Yuan a, Y. Yuan a, S.L. Zang a, Y. Zeng g, B.X. Zhang a, B.Y. Zhang a, C.C. Zhang a,D.H. Zhang a, H.Q. Zhang a, H.Y. Zhang a, J.W. Zhang a, J.Y. Zhang a, S.H. Zhang a, X.Y. Zhang m,

Yiyun Zhang n, Z.X. Zhang l, Z.P. Zhang p, D.X. Zhao a, J.W. Zhao a, M.G. Zhao a, P.P. Zhao a,W.R. Zhao a, Z.G. Zhao a,6, H.Q. Zheng l, J.P. Zheng a, Z.P. Zheng a, L. Zhou a, K.J. Zhu a,Q.M. Zhu a, Y.C. Zhu a, Y.S. Zhu a, Z.A. Zhu a, B.A. Zhuang a, X.A. Zhuang a, B.S. Zou a

a Institute of High Energy Physics, Beijing 100049, People’s Republic of Chinab China Center for Advanced Science and Technology (CCAST), Beijing 100080, People’s Republic of China

c Guangxi Normal University, Guilin 541004, People’s Republic of Chinad Guangxi University, Nanning 530004, People’s Republic of China

e Henan Normal University, Xinxiang 453002, People’s Republic of Chinaf Huazhong Normal University, Wuhan 430079, People’s Republic of China

g Hunan University, Changsha 410082, People’s Republic of Chinah Jinan University, Jinan 250022, People’s Republic of China

i Liaoning University, Shenyang 110036, People’s Republic of Chinaj Nanjing Normal University, Nanjing 210097, People’s Republic of China

k Nankai University, Tianjin 300071, People’s Republic of Chinal Peking University, Beijing 100871, People’s Republic of China

m Shandong University, Jinan 250100, People’s Republic of Chinan Sichuan University, Chengdu 610064, People’s Republic of Chinao Tsinghua University, Beijing 100084, People’s Republic of China

p University of Science and Technology of China, Hefei 230026, People’s Republic of Chinaq Wuhan University, Wuhan 430072, People’s Republic of China

r Zhejiang University, Hangzhou 310028, People’s Republic of China

Received 9 October 2006; accepted 5 November 2006

Available online 27 November 2006

0370-2693/$ – see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2006.11.026

BES Collaboration / Physics Letters B 644 (2007) 20–24 21

Editor: W.-D. Schlatter

Abstract

The absolute branching fraction for the decay D+ → K̄0μ+νμ is determined using 5321 ± 149 ± 160 singly tagged D− sample from thedata collected around

√s = 3.773 GeV with the BESII detector at the BEPC collider. In the system recoiling against the singly tagged D−

mesons, 28.7 ± 6.4 events for D+ → K̄0μ+νμ are observed. These yield the absolute branching fraction to be BF(D+ → K̄0μ+νμ) =(10.3 ± 2.3 ± 0.8)%. The ratio of the two partial widths for the decays D0 → K−μ+νμ and D+ → K̄0μ+νμ is determined to be Γ (D0 →K−μ+νμ)/Γ (D+ → K̄0μ+νμ) = 0.87 ± 0.24 ± 0.15.© 2006 Elsevier B.V. All rights reserved.

1. Introduction

Measurements of the absolute branching fractions for ex-clusive semileptonic decays of charmed mesons can provideimportant information about decay mechanism of the mesons.If the isospin symmetry holds in the exclusive semileptonicdecays of the charged and neutral D mesons, the two par-tial widths for the decays D0 → K−l+νl and D+ → K̄0l+νl

are expected to be equal, which means the ratio Γ (D0 →K−l+νl)/Γ (D+ → K̄0l+νl) = 1. The measured branchingfractions for the semielectronic decays historically yielded theratio Γ (D0 → K−e+νe)/Γ (D+ → K̄0e+νe) = 1.4 ± 0.2 [1],which deviates from 1.0 by 2σ . This was historically called a“long-standing puzzle” in the D exclusive semielectronic de-cays. Recently, BES Collaboration measured the ratio Γ (D0 →K−e+νe)/Γ (D+ → K̄0e+νe) = 1.08 ± 0.22 ± 0.07 [2], indi-cating that the isospin symmetry holds in the exclusive semi-electronic decays of the charged and neutral D mesons, andthereby solving the “long-standing puzzle” [1]. This was con-firmed by the CLEO measurement [3].

In this Letter, we report a direct measurement of the ab-solute branching fraction for the decay D+ → K̄0μ+νμ anddetermination of the ratio of the two partial widths for thesemimuonic decays Γ (D0 → K−μ+νμ)/Γ (D+ → K̄0μ+νμ),which can be used to check if the isospin symmetry holds in theexclusive semimuonic decays.

2. The BESII detector

The BESII is a conventional cylindrical magnetic detectorthat is described in detail in Ref. [4]. A 12-layer vertex chamber(VC) surrounding the beryllium beam pipe provides input to theevent trigger, as well as coordinate information. A forty-layermain drift chamber (MDC) located just outside the VC yields

* Corresponding author.E-mail address: rongg@mail.ihep.ac.cn (G. Rong).

1 Current address: DESY, D-22607 Hamburg, Germany.2 Current address: Universite Paris XI, LAL-Bat. 208, BP34, 91898 Orsay

cedex, France.3 Current address: Max-Plank-Institut für Physik, Foehringer Ring 6,

D-80805 Munich, Germany.4 Current address: University of Toronto, Toronto M5S 1A7, Canada.5 Current address: CERN, CH-1211 Geneva 23, Switzerland.6 Current address: University of Michigan, Ann Arbor, MI 48109, USA.

precise measurements of charged particle trajectories with asolid angle coverage of 85% of 4π ; it also provides ionizationenergy loss (dE/dx) measurements which are used for parti-cle identification. Momentum resolution of 1.7%

√1 + p2 (p in

GeV/c) and dE/dx resolution of 8.5% for Bhabha scatteringelectrons are obtained for the data taken at

√s = 3.773 GeV.

An array of 48 scintillation counters surrounding the MDCmeasures the time of flight (TOF) of charged particles with aresolution of about 180 ps for electrons. Outside the TOF, a 12radiation length, lead-gas barrel shower counter (BSC), operat-ing in self-quenching streamer mode, measures the energies ofelectrons and photons over 80% of the total solid angle with anenergy resolution of σE/E = 0.22/

√E (E in GeV) and spatial

resolutions of σφ = 7.9 mrad and σZ = 2.3 cm for electrons.A solenoidal magnet outside the BSC provides a 0.4 T magneticfield in the central tracking region of the detector. Three double-layer muon counters instrument the magnet flux return, andserve to identify muons of momentum greater than 500 MeV/c.They cover 68% of the total solid angle.

3. Data analysis

The data used in the analysis were collected with the BESIIdetector at the BEPC collider. A total integrated luminosity ofabout 33 pb−1 was taken at and around the center-of-mass en-ergy of

√s = 3.773 GeV. Around these energies, the ψ(3770)

resonance is produced in e+e− annihilation. It decays to DD̄

pairs (D0D̄0 and D+D−) with a large branching fraction ofabout (85 ± 6)% [5]. Taking the advantage of the ψ(3770) de-cay to D+D− pairs, we can do absolute measurement of thebranching fraction for D+ → K̄0μ+νμ with a singly taggedD− sample. If a D− meson is fully reconstructed (it is calleda singly tagged D− meson) from this data sample, the D+ me-son must exist in the system recoiling against the singly taggedD− meson. In the recoil system, we can select the semileptonicdecay D+ → K̄0μ+νμ based on the kinematic signature of thesingly tagged D− event, and measure the branching fraction forthis decay directly.

3.1. Event selection

In order to ensure the well-measured 3-momentum vectorsand the reliably charged particle identification, the chargedtracks used in the single tag analysis are required to be within

22 BES Collaboration / Physics Letters B 644 (2007) 20–24

| cos θ | < 0.85, where θ is the polar angle of the charged track.All tracks, save those from K0

S decays, must originate from theinteraction region: the closest approach of the charged track inthe xy plane is less than 2.0 cm and the absolute z position ofthe track is less than 20.0 cm. Pions and kaons are identified bymeans of TOF and dE/dx measurements. Pion identificationrequires a consistency with the pion hypothesis at a confidencelevel (CLπ ) greater than 0.1%. In order to reduce misidentifi-cation, a kaon candidate is required to have a larger confidencelevel (CLK ) for a kaon hypothesis than that for a pion hypothe-sis. The π0 is reconstructed in the decay of π0 → γ γ . To selectgood photons from the decay of π0, the energy of a photondeposited in the BSC is required to be greater than 0.07 GeV[2,6,7], and the electromagnetic shower is required to start inthe first 5 readout layers of the BSC. In order to reduce back-grounds due to fake photons, the angle between the photon andthe nearest charged track is required to be greater than 22◦ [6]and the angle between the direction of the cluster developmentand the direction of the photon emission to be less than 37◦ [6].

For the single tag modes of D− → K+π+π−π−π− andD− → π+π−π−, backgrounds are further reduced by requir-ing the difference between the measured energy of the D−candidate and the beam energy to be less than 70 and 60 MeV,respectively. In addition, the cosine of the D− production anglerelative to the beam direction is required to be | cos θD−| < 0.8.

3.2. Singly tagged D− sample

The D− meson is reconstructed in the nine hadronic decaymodes of K+π−π−, K0π−, K0K−, K+K−π−, K0π−π−π+,K0π−π0, K+π−π−π0, K+π+π−π−π− and π+π−π−. Thesingly tagged D− mesons are obtained by examining the invari-ant masses of mKnπ (m = 0,1,2, n = 0,1,2,3,4) combina-tions. A total number of 5321 ± 149 ± 160 reconstructed D−mesons are accumulated from the data sample, where the firsterror is statistical and the second systematic. Ref. [2] discussedthe selection of the singly tagged D− sample in detail.

3.3. Candidates for D+ → K̄0μ+νμ

The candidates for the decay D+ → K̄0μ+νμ are selectedfrom the tracks in the recoil system. The candidates are onlyallowed to have three good charged tracks in the recoil side.One of them is identified as muon with the charge opposite tothat of the tagged D− and the other two are identified as π+and π−. The π+ and π− are identified by requiring the confi-dence level CLπ for the pion hypothesis to be greater than theconfidence level CLK for the kaon hypothesis or by requiringCLπ > 0.1%. To select the K0

S , it is required that the invariantmass of the π+π− combination should be within ±20 MeV/c2

mass window of the K0S nominal mass and the π+π− must orig-

inate from a secondary vertex which is displaced from the eventvertex at least by 4 mm.

To obtain the information about the missing neutrino fromthe semileptonic decay D+ → K̄0μ+νμ under study, a kine-matic quantity Umiss = Emiss − pmiss is defined, where Emissand pmiss are the total energy and momentum of all missing par-

ticles in the event. To select candidates for D+ → K̄0μ+νμ, itis required that each event should have its |Umiss,i | < 2σUmiss,i ,where σUmiss,i is the standard deviation of the Umiss,i distribu-tion, which is obtained by analyzing the Monte Carlo events ofD+ → K̄0μ+νμ versus the ith singly tagged D− mode.

The main sources of the backgrounds to the semileptonic de-cay are D+ → K̄0π0μ+νμ and D+ → K̄0π+π0. These back-grounds can be suppressed by rejecting the events with extraisolated photons which are not used in the reconstruction of thesingly tagged D−. The isolated photon should have its energyto be greater than 0.1 GeV and should satisfy photon selec-tion criteria as mentioned earlier. In the data analysis, we donot use the information from the muon counter to separatethe muon from pion since we want to reconstruct more sig-nal events for the semileptonic decay. Due to misidentifyinga pion (or an electron) as a muon, the events such as D+ →K̄0π+, D+ → K−π+π+, D+ → K̄0ρ+ and D+ → K̄0e+νe

could be misidentified as D+ → K̄0μ+νμ. Monte Carlo studyshows that these events are the main backgrounds to the semi-leptonic decay D+ → K̄0μ+νμ. However, these backgroundevents can be suppressed by requiring the invariant masses ofK̄0μ+ combinations to be less than 1.5 GeV/c2. Fig. 1 showsthe distribution of the invariant masses of K̄0μ+ combina-tions from the Monte Carlo events of e+e− → ψ(3770) →D+D−, where Fig. 1(a) shows the distribution for the events ofD− → K+π−π− versus D+ → K̄0μ+νμ and Fig. 1(b) showsthe distribution for the events of D− → K+π−π− versusD+ → K̄0π+. The invariant masses of K̄0μ+ combinationsare widely distributed from 0.6 to 1.8 GeV/c2 due to missingof the neutrino from the semileptonic decay D+ → K̄0μ+νμ,while the invariant masses of K̄0μ+ combinations misidenti-fied from the decay D+ → K̄0π+ are concentrated at the peakof the D+ mass. Fig. 2 shows the distribution of the invari-ant masses of K̄0μ+ combinations for the Monte Carlo events

Fig. 1. The distributions of the invariant masses of the K̄0μ+ combinationsfor the Monte Carlo events of (a) D+ → K̄0μ+νμ versus D− → K+π−π−;(b) D+ → K̄0π+ versus D− → K+π−π−, where the K̄0π+ are misidenti-fied as K̄0μ+.

BES Collaboration / Physics Letters B 644 (2007) 20–24 23

Fig. 2. The distribution of the invariant masses of K̄0μ+ combinations forthe Monte Carlo events of e+e− → DD̄ (D0D̄0 and D+D−), where the D

mesons are set to decay into all possible final states except for D+ → K̄0μ+νμ

(see text).

Fig. 3. The distribution of the fitted masses of mKnπ combinations for theevents for which the D+ → K̄0μ+νμ candidates are observed in the systemrecoiling against the mKnπ combinations.

of e+e− → DD̄ (D0D̄0 and D+D−), where the DD̄ are setto decay into all possible final states according to their decaymodes and branching fractions quoted from PDG [8]. Theseselected events are misidentified from the source of the mainbackgrounds as mentioned above and marked on the figure. TheMonte Carlo sample is fourteen times larger than the data sam-ple. The criterion MK̄0μ+ < 1.5 GeV/c2 can reject most of themain backgrounds to the selected semileptonic decay events.

Fig. 3 shows the distribution of the fitted invariant masses ofthe mKnπ combinations for the events for which the D+ →K̄0μ+νμ candidates satisfying the selection criteria mentionedabove are observed in the system recoiling against the mKnπ

combinations, where a clear signal for the singly tagged D− isobserved. In Fig. 3, there are 38 events in the ±3σmass,i signalregions, while there are 15 events in the outside of the signalregions; where the σmass,i is the standard deviation of the fit-ted mass distribution for the single tag mode(i) (i = 1 is forK+π−π−; i = 2 is for K0π−, . . . and i = 9 is for π+π−π−modes). Assuming that the background distribution is flat ex-cept the ones described in Section 3.4, 5.2 ± 1.4 backgroundevents are estimated in the signal region. In addition, there mayalso be the π+π− combinatorial background. By selecting theevents in which the invariant masses of the π+π− combinationsin the recoil side of the tags are outside of the K0

S mass win-dow, we estimate that there are 0.6 ± 0.3 background events inthe candidate events. After subtracting these numbers of back-

Fig. 4. The distribution of the muon momenta from the selected candidatesfor D+ → K̄0μ+νμ decay, where error bars are the data after subtracting thebackgrounds estimated from Monte Carlo DD̄ events, while the histogram isfrom the Monte Carlo events for D+ → K̄0μ+νμ.

grounds we obtain 32.2 ± 6.3 candidates for D+ → K̄0μ+νμ

decay.

3.4. Background subtraction

There are, however, still some background contaminationsin the selected candidate events due to some other semileptonicdecays or hadronic decays, which are not rejected by the selec-tion criteria as described above. These background events mustbe subtracted from the sample of the selected candidate events.The numbers of background events can be estimated by ana-lyzing the Monte Carlo sample of fourteen times larger thanthe data. By analyzing this Monte Carlo sample and normal-ize the number of the background events observed from thissample, totally 3.5 ± 0.7 background events are obtained in theselected semileptonic decay sample from the data. After sub-tracting the number of background events, 28.7 ± 6.4 signalevents for D+ → K̄0μ+νμ decay are retained.

Fig. 4 shows the distribution of the momenta of the μ+ fromthe selected candidate events for the decay D+ → K̄0μ+νμ.The error bars in the figure show the events from the data aftersubtracting the backgrounds estimated from the Monte CarloDD̄ events, while the histogram shows the events from theMonte Carlo for the decay D+ → K̄0μ+νμ.

4. Results

The detection efficiency for reconstruction of the semilep-tonic decay D+ → K̄0μ+νμ is obtained from Monte Carlosimulation. The efficiency is εD+→K̄0μ+νμ

= (5.24 ± 0.06)%

including the branching fraction for the decay K0S → π+π−,

where the error is statistical.The branching fraction is obtained by dividing the observed

number of the semileptonic decay events N(D+ → K̄0μ+νμ)

by the number of the singly tagged D− mesons ND−tag

and the

reconstruction efficiency εD+→K̄0μ+νμ,

(1)BF(D+ → K̄0μ+νμ

) = N(D+ → K̄0μ+νμ)

ND−tag

× εD+→K̄0μ+νμ

.

24 BES Collaboration / Physics Letters B 644 (2007) 20–24

Inserting these numbers in Eq. (1), we obtain the branchingfraction for D+ → K̄0μ+νμ decay to be

(2)BF(D+ → K̄0μ+νμ

) = (10.3 ± 2.3 ± 0.8)%,

where the first error is statistical and the second systematic.The systematic uncertainty arises from the particle identifica-tion (∼ 1.8%), tracking efficiency (∼ 2.0% per track), photonreconstruction (∼ 2.0%), Umiss selection (∼ 0.6%), the num-ber of the singly tagged D− (∼ 3.0%), background fluctua-tion (∼ 2.4%), uncertainty in background estimation due tounknown branching fractions of some background channels(∼ 2.4%), and Monte Carlo statistics (∼ 1.1%). Adding theseuncertainties in quadrature yields the total systematic error of∼ 8.1%. Our measured branching fraction for this decay isconsistent within error with the one measured by the FOCUSCollaboration [9].

With the same data sample, BES Collaboration measured theabsolute branching fraction for D0 → K−μ+νμ decay to beBF(D0 → K−μ+νμ) = (3.55 ± 0.56 ± 0.59)% [10]. Using themeasured branching fractions for the decays D0 → K−μ+νμ,D+ → K̄0μ+νμ and the lifetimes of the D0 and D+ quotedfrom PDG [8], we determine the ratio of the decay widths

(3)Γ (D0 → K−μ+νμ)

Γ (D+ → K̄0μ+νμ)= 0.87 ± 0.24 ± 0.15,

where the first error is statistical and the second systematic aris-ing from some uncanceled systematic uncertainty (∼ 16.6%) inthe measured ratio of the branching fractions for the two decaysand the uncertainty (0.8%) in the measured ratio of the D0 andD+ lifetimes.

The BES Collaboration previously measured the ratio of thedecay widths [2]

(4)Γ (D0 → K−e+νe)

Γ (D+ → K̄0e+νe)= 1.08 ± 0.22 ± 0.07.

Averaging the two ratios obtained from analyses of the semi-mounic and semielectronic decays of the D mesons by weight-ing the combined statistical and independent systematic errors,we obtain

(5)Γ (D0 → K−l+νl)

Γ (D+ → K̄0l+νl)= 1.00 ± 0.17 ± 0.06,

with l = e,μ, where the first error is combined from statisti-cal and independent systematic uncertainty, and the second iscommon systematic arising from some uncanceled systematicuncertainty (∼ 6.0%) in the measured ratio of the branchingfractions for the two decays and the uncertainty (0.8%) in themeasured ratio of the D0 and D+ lifetimes.

5. Summary

In summary, from analyzing the data sample of about33 pb−1 collected at and around 3.773 GeV with the BE-SII detector at the BEPC collider, we measured the branch-ing fraction for the decay D+ → K̄0μ+νμ to be BF(D+ →K̄0μ+νμ) = (10.3 ± 2.3 ± 0.8)%. Using the values of themeasured branching fractions for the decays D0 → K−μ+νμ

and D+ → K̄0μ+νμ, we determined the ratio of the two par-tial widths Γ (D0 → K−μ+νμ)/Γ (D+ → K̄0μ+νμ) = 0.87±0.24 ± 0.15, which is consistent within error with the spectatormodel prediction. Combining the ratios obtained from analy-ses of the semimuonic and semielectronic decays of the D

mesons yields the ratio Γ (D0→K−l+νl)

Γ (D+→K̄0l+νl)= 1.00 ± 0.17 ± 0.06,

which improves the measurements of the ratios from analysesof the exclusive semimuonic and semielectronic decays of theD mesons, and supports that the isospin conservation holds inthe exclusive semileptonic decays of the D+ → K̄0l+νl andD0 → K−l+νl .

Acknowledgements

The BES Collaboration thanks the staff of BEPC for theirhard efforts. This work is supported in part by the NationalNatural Science Foundation of China under contracts Nos.10491300, 10225524, 10225525, the Chinese Academy of Sci-ences under contract No. KJ 95T-03, the 100 Talents Pro-gram of CAS under Contract Nos. U-11, U-24, U-25, and theKnowledge Innovation Project of CAS under Contract Nos. U-602, U-34 (IHEP); and by the National Natural Science Foun-dation of China under Contract No. 10175060 (USTC), andNo. 10225522 (Tsinghua University).

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