4
Physics Letters B 665 (2008) 16–19 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Direct measurements of absolute branching fractions for D 0 and D + inclusive semimuonic decays BES Collaboration M. Ablikim a , J.Z. Bai a , Y. Bai a , Y. Ban k , X. Cai a , H.F. Chen o , H.S. Chen a , H.X. Chen a , J.C. Chen a,, Jin Chen a , X.D. Chen e , Y.B. Chen a , Y.P. Chu a , Y.S. Dai q , Z.Y. Deng a , S.X. Du a , J. Fang a , C.D. Fu n , C.S. Gao a , Y.N. Gao n , S.D. Gu a , Y.T. Gu d , Y.N. Guo a , K.L. He a , M. He l , Y.K. Heng a , J. Hou j , H.M. Hu a , T. Hu a , G.S. Huang a,1 , X.T. Huang l , Y.P. Huang a , X.B. Ji a , X.S. Jiang a , J.B. Jiao l , D.P. Jin a , S. Jin a , Y.F. Lai a , H.B. Li a , J. Li a , R.Y. Li a , W.D. Li a , W.G. Li a , X.L. Li a , X.N. Li a , X.Q. Li j , Y.F. Liang m , H.B. Liao a,2 , B.J. Liu a , C.X. Liu a , Fang Liu a , Feng Liu f , H.H. Liu a,3 , H.M. Liu a , J.B. Liu a,4 , J.P. Liu p , H.B. Liu d , J. Liu a , R.G. Liu a , S. Liu h , Z.A. Liu a , F. Lu a , G.R. Lu e , J.G. Lu a , C.L. Luo i , F.C. Ma h , H.L. Ma b , L.L. Ma a,5 , Q.M. Ma a , M.Q.A. Malik 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 , G. Rong a , X.D. Ruan d , L.Y. Shan a , L. Shang 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 , J.P. Tian n , G.L. Tong a , X. Wan a , L. Wang a , L.L. Wang a , L.S. Wang a , P. Wang a , P.L. Wang a , W.F. Wang a,6 , Y.F. Wang a , Z. Wang a , Z.Y. Wang a , C.L. Wei a , D.H. Wei c , Y. Weng a , N. Wu a , X.M. Xia a , X.X. Xie a , G.F. Xu a , X.P. Xu f , Y. Xu j , M.L. Yan o , H.X. Yang a , M. Yang a , Y.X. Yang c , M.H. Ye b , Y.X. Ye o , C.X. Yu j , G.W. Yu a , C.Z. Yuan a , Y. Yuan a , S.L. Zang a,7 , 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 , X.Y. Zhang l , Y.Y. Zhang m , Z.X. Zhang k , Z.P. Zhang o , D.X. Zhao a , J.W. Zhao a , M.G. Zhao a , P.P. Zhao a , H.Q. Zheng k , J.P. Zheng a , Z.P. Zheng a , B. Zhong i , L. Zhou a , K.J. Zhu a , Q.M. Zhu a , X.W. Zhu a , Y.C. Zhu a , Y.S. Zhu a , Z.A. Zhu a , Z.L. Zhu c , B.A. Zhuang a , B.S. Zou a a Institute of High Energy Physics, Beijing 100049, People’s Republic of China b 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 China d Guangxi University, Nanning 530004, People’s Republic of China e Henan Normal University, Xinxiang 453002, People’s Republic of China f Huazhong Normal University, Wuhan 430079, People’s Republic of China g Hunan University, Changsha 410082, People’s Republic of China h Liaoning University, Shenyang 110036, People’s Republic of China i Nanjing Normal University, Nanjing 210097, People’s Republic of China j Nankai University, Tianjin 300071, People’s Republic of China k Peking University, Beijing 100871, People’s Republic of China l Shandong University, Jinan 250100, People’s Republic of China m Sichuan University, Chengdu 610064, People’s Republic of China n Tsinghua University, Beijing 100084, People’s Republic of China o University of Science and Technology of China, Hefei 230026, People’s Republic of China p Wuhan University, Wuhan 430072, People’s Republic of China q Zhejiang University, Hangzhou 310028, People’s Republic of China * Corresponding author. E-mail address: [email protected] (J.C. Chen). 1 Current address: University of Oklahoma, Norman, OK 73019, USA. 2 Current address: DAPNIA/SPP Batiment 141, CEA Saclay, 91191, Gif-sur-Yvette Cedex, France. 3 Current address: Henan University of Science and Technology, Luoyang 471003, People’s Republic of China. 4 Current address: CERN, CH-1211 Geneva 23, Switzerland. 5 Current address: University of Toronto, Toronto M5S 1A7, Canada. 6 Current address: Laboratoire de l’Accélérateur Linéaire, Orsay F-91898, France. 7 Current address: University of Colorado, Boulder, CO 80309, USA. 0370-2693/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2008.05.054

Direct measurements of absolute branching fractions for and inclusive semimuonic decays

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Physics Letters B 665 (2008) 16–19

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Direct measurements of absolute branching fractions for D0 and D+ inclusivesemimuonic decays

BES Collaboration

M. Ablikim a, J.Z. Bai a, Y. Bai a, Y. Ban k, X. Cai a, H.F. Chen o, H.S. Chen a, H.X. Chen a, J.C. Chen a,∗, Jin Chen a,X.D. Chen e, Y.B. Chen a, Y.P. Chu a, Y.S. Dai q, Z.Y. Deng a, S.X. Du a, J. Fang a, C.D. Fu n, C.S. Gao a, Y.N. Gao n, S.D. Gu a,Y.T. Gu d, Y.N. Guo a, K.L. He a, M. He l, Y.K. Heng a, J. Hou j, H.M. Hu a, T. Hu a, G.S. Huang a,1, X.T. Huang l,Y.P. Huang a, X.B. Ji a, X.S. Jiang a, J.B. Jiao l, D.P. Jin a, S. Jin a, Y.F. Lai a, H.B. Li a, J. Li a, R.Y. Li a, W.D. Li a, W.G. Li a,X.L. Li a, X.N. Li a, X.Q. Li j, Y.F. Liang m, H.B. Liao a,2, B.J. Liu a, C.X. Liu a, Fang Liu a, Feng Liu f, H.H. Liu a,3, H.M. Liu a,J.B. Liu a,4, J.P. Liu p, H.B. Liu d, J. Liu a, R.G. Liu a, S. Liu h, Z.A. Liu a, F. Lu a, G.R. Lu e, J.G. Lu a, C.L. Luo i, F.C. Ma h,H.L. Ma b, L.L. Ma a,5, Q.M. Ma a, M.Q.A. Malik 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,G. Rong a, X.D. Ruan d, L.Y. Shan a, L. Shang 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, J.P. Tian n, G.L. Tong a, X. Wan a, L. Wang a, L.L. Wang a, L.S. Wang a, P. Wang a, P.L. Wang a,W.F. Wang a,6, Y.F. Wang a, Z. Wang a, Z.Y. Wang a, C.L. Wei a, D.H. Wei c, Y. Weng a, N. Wu a, X.M. Xia a, X.X. Xie a,G.F. Xu a, X.P. Xu f, Y. Xu j, M.L. Yan o, H.X. Yang a, M. Yang a, Y.X. Yang c, M.H. Ye b, Y.X. Ye o, C.X. Yu j, G.W. Yu a,C.Z. Yuan a, Y. Yuan a, S.L. Zang a,7, 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, X.Y. Zhang l, Y.Y. Zhang m, Z.X. Zhang k, Z.P. Zhang o, D.X. Zhao a, J.W. Zhao a,M.G. Zhao a, P.P. Zhao a, H.Q. Zheng k, J.P. Zheng a, Z.P. Zheng a, B. Zhong i, L. Zhou a, K.J. Zhu a, Q.M. Zhu a, X.W. Zhu a,Y.C. Zhu a, Y.S. Zhu a, Z.A. Zhu a, Z.L. Zhu c, B.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 Chinac Guangxi Normal University, Guilin 541004, People’s Republic of Chinad Guangxi University, Nanning 530004, People’s Republic of Chinae Henan Normal University, Xinxiang 453002, People’s Republic of Chinaf Huazhong Normal University, Wuhan 430079, People’s Republic of Chinag Hunan University, Changsha 410082, People’s Republic of Chinah Liaoning University, Shenyang 110036, People’s Republic of Chinai Nanjing Normal University, Nanjing 210097, People’s Republic of Chinaj Nankai University, Tianjin 300071, People’s Republic of Chinak Peking University, Beijing 100871, People’s Republic of Chinal Shandong University, Jinan 250100, People’s Republic of Chinam Sichuan University, Chengdu 610064, People’s Republic of Chinan Tsinghua University, Beijing 100084, People’s Republic of Chinao University of Science and Technology of China, Hefei 230026, People’s Republic of Chinap Wuhan University, Wuhan 430072, People’s Republic of Chinaq Zhejiang University, Hangzhou 310028, People’s Republic of China

* Corresponding author.E-mail address: [email protected] (J.C. Chen).

1 Current address: University of Oklahoma, Norman, OK 73019, USA.2 Current address: DAPNIA/SPP Batiment 141, CEA Saclay, 91191, Gif-sur-Yvette Cedex, France.3 Current address: Henan University of Science and Technology, Luoyang 471003, People’s Republic of China.4 Current address: CERN, CH-1211 Geneva 23, Switzerland.5 Current address: University of Toronto, Toronto M5S 1A7, Canada.6 Current address: Laboratoire de l’Accélérateur Linéaire, Orsay F-91898, France.7 Current address: University of Colorado, Boulder, CO 80309, USA.

0370-2693/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2008.05.054

BES Collaboration / Physics Letters B 665 (2008) 16–19 17

a r t i c l e i n f o a b s t r a c t

Article history:Received 13 December 2007Received in revised form 19 May 2008Accepted 24 May 2008Available online 29 May 2008Editor: L. Rolandi

By analyzing approximately 33 pb−1 of sample data collected at and around 3.773 GeV with the BES-IIdetector at the BEPC collider, we directly measured the branching fractions for the neutral and chargedD inclusive semimuonic decays to be BF(D0 → μ+ X) = (6.8 ± 1.5 ± 0.8)% and BF(D+ → μ+ X) = (17.6 ±2.7 ± 1.8)%, and determined the ratio of the two branching fractions to be BF(D+→μ+ X)

BF(D0→μ+ X)= 2.59 ± 0.70 ±

0.25.© 2008 Elsevier B.V. All rights reserved.

1. Introduction

The neutral and charged D are both charmed mesons. Surpris-ingly however, the lifetime of the D+ meson is longer than thatof the D0 meson [1]. Isospin symmetry predicts that the partialwidths of Cabibbo-favored semileptonic decays of the D0 and D+mesons are equal. It is expected that the ratio of the branchingfractions for the D0 and D+ inclusive semileptonic decays is ap-proximately equal to the ratio of D0 and D+ lifetimes up to theorder of O (θ2

c ) [2]. Measurements of the branching fractions forthe D0 and D+ semileptonic decays can provide valuable infor-mation about the difference in their lifetimes, which is importantin understanding charmed meson decays. Moreover, by comparingthe branching fractions for the D0 and D+ inclusive decays withthe sum of the branching fractions for the exclusive decays, it canbe estimated whether there are decay modes yet to be observed.The inclusive D semielectronic decays have been studied by severalexperiments [1,3,4], but the experimental studies for the inclusiveD semimuonic decays are very limited, for example, there is nomeasurement available for the decay D+ → μ+ X (X = any parti-cles) in the PDG [1].

In this Letter, we report direct measurements of the abso-lute branching fractions for the inclusive decays D0 → μ+ X andD+ → μ+ X , based upon analysis of a data sample of approxi-mately 33 pb−1 collected at and around the center-of-mass energy(√

s) 3.773 GeV with the BES-II detector.

2. The Beijing spectrometer

BESII is the upgraded version of the BES detector [5] oper-ating at the Beijing Electron Positron Collider (BEPC) [6]. A 12-layer vertex chamber (VC) surrounding the beam pipe providestrigger information. A forty-layer main drift chamber (MDC) lo-cated outside the VC performs trajectory and ionization energy loss(dE/dx) measurement with a solid angle coverage of 85% of 4π

for charged tracks. Momentum resolution of σp/p = 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 surrounds the MDC and mea-sures the time of flight (TOF) of charged tracks with a resolutionof about 200 ps for the electrons. Surrounding the TOF is a 12-radiation-length, lead-gas barrel shower counter (BSC) operatedin limited streamer mode, which measures the energies of elec-trons and photons over 80% of the total solid angle, and has anenergy resolution of σE/E = 0.22/

√E (E in GeV), spatial resolu-

tions of σφ = 7.9 mrad and σZ = 2.3 cm for the electrons. Outsideof the BSC is a solenoidal magnet that provides a 0.4 T magneticfield in the central tracking region of the detector. Three double-layer muon counters instrument the magnetic flux return, andserve to identify muons with momentum greater than 0.5 GeV/c.The muon counters cover 68% of the total solid angle with lon-gitudinal (transverse) spatial resolution of 5 cm (3 cm). End-captime-of-flight and shower counters extend coverage to the forwardand backward regions. A Monte Carlo package based on GEANT3

has been developed for BESII detector simulation and comparisonswith data show that the simulation is generally satisfactory [7].

3. Data analysis

Around√

s = 3.773 GeV, electron-positron (e+e−) annihilationproduces ψ(3770) resonance that decays into D D̄ pairs with alarge branching fraction, BF(ψ(3770) → D D̄) = (85 ± 5)% [1,8–11].If we can reconstruct a D̄ (it is named as a singly tagged D̄) froma D D̄ pair, the D must exist on the recoil side of the tagged D̄ .Using this to our advantage, we can directly measure the abso-lute branching fractions for the D decays with the singly taggedD̄ samples. The singly tagged D̄ samples used in the analysis werereconstructed in the hadronic decay modes of mKnπ (m = 0,1,2;n = 0,1,2,3,4) from previous works [12,13]. These works gave thetotal numbers of 7584±198(stat.)±341(sys.) singly tagged D̄0 [12]and 5321 ± 149(stat.) ± 160(sys.) singly tagged D− [13]. Through-out this Letter, charge conjugation is implied.

3.1. Candidates for D → μ+ X

The candidates for D → μ+ X are selected in the system re-coiling against the singly tagged D̄ mesons. It is required that thecandidate tracks should be well reconstructed in the MDC withgood helix fits, and satisfy | cos θ | < 0.67, where θ is the polar an-gle. Each track must originate from the interaction region, whichrequires that the closest approach to the interaction point in thexy-plane is less than 2.0 cm and in the z direction is less than20.0 cm. To reject muons from kaon and pion decays, the selectedcandidate tracks are required to originate from the same vertex asthe tracks from the singly tagged D̄ meson decays. This is ensuredby the requirement that δz < 2σz (2.0 cm), where δz is the mini-mum distance in the z direction between the candidate track andthe tracks from the tagged D̄ decay, and σz is the standard devia-tion of the δz distribution. To ensure that the track can be detectedby the muon counter, the transverse momentum of each track isrequired to be greater than 0.52 GeV/c. Since the hit depth ofmuons in the muon counter vary with their transverse momenta,muons are selected by the requirement that tracks with a trans-verse momentum of 0.52 to 0.75 GeV/c, 0.75 to 0.95 GeV/c andgreater than 0.95 GeV/c must hit at least 1, 2 or 3 layers respec-tively. Because there is no charge symmetric background as there isin the measurements of the semielectronic decay [3,4], the muoncandidates are only required to have the “right-sign” (their chargeopposite to the flavor of the single tag).

Fig. 1 shows the resulting invariant mass spectra of the mKnπcombinations for the events in which the candidates for muon areobserved on the recoil side of the mKnπ combinations for thesingly tagged D̄0 (left column) and D− (right column) mesons. Fit-ting each invariant mass spectrum with a Gaussian function forD̄ signal and a special function [12] to describe the backgroundshape, we obtain the number of the observed muon candidates,Nμ

obs. The total numbers of observed candidates for D0 → μ+ Xand D+ → μ+ X are 79.3 ± 10.3 and 99.6 ± 11.7, respectively.

18 BES Collaboration / Physics Letters B 665 (2008) 16–19

Fig. 1. Invariant mass spectra of the mKnπ combinations for the events in whichthe muon candidates are observed on the recoil side against the mKnπ combi-nations for the singly tagged D̄0 (left column) and D− (right column) mesons,where the tracks are with the transverse momenta in the regions: (a) and (f) (0.52–0.62) GeV/c; (b) and (g) (0.62–0.72) GeV/c; (c) and (h) (0.72–0.82) GeV/c; (d) and(i) (0.82–0.92) GeV/c and (e) and (j) (0.92–1.02) GeV/c intervals.

3.2. Unfolding procedure

Since muons, electrons, kaons and pions may be misidenti-fied for one and other, the observed muon candidates consist oftrue muons as well as electrons, kaons and pions that have beenmisidentified. The true yield, Nμ

true of muons can be extractedthrough an unfolding procedure. A detailed description of the un-folding procedure can be found in Ref. [4]. The right-sign candi-dates are unfolded using the matrix Eq. (1),⎛⎜⎜⎝

Nμobs

Neobs

N Kobs

Nπobs

⎞⎟⎟⎠ =

⎛⎜⎜⎝

ημ→μ ηe→μ ηK→μ ηπ→μ

ημ→e ηe→e ηK→e ηπ→e

ημ→K ηe→K ηK→K ηπ→K

ημ→π ηe→π ηK→π ηπ→π

⎞⎟⎟⎠

⎛⎜⎜⎝

Nμtrue

Netrue

N Ktrue

Nπtrue

⎞⎟⎟⎠ , (1)

where Naobs and Nb

true (a and b denote muon, electron, kaon orpion) are the number of the observed candidates for a and thenumber of the true b particles, respectively, and ηb→a is the rateof misidentifying the particle b as a (a �= b) or the efficiency ofidentifying the particle a (a = b).

To remove the background of misidentified particles from theobserved muon candidate sample, in addition to Nμ

obs (the numberof muons), it is also necessary to know Ne

obs, N Kobs and Nπ

obs (thenumbers of electrons, kaons and pions) that have also been se-lected in the system recoiling against the singly tagged D̄ mesons.Electrons, kaons and pions are identified by using the dE/dx, TOFand BSC measurements, with which the combined confidence lev-els for the electron, kaon and pion hypotheses (C Le , C LK andC Lπ ) are calculated. An electron candidate is required to satisfyC Le > 0.1% and C Le/(C Le + C LK + C Lπ ) > 0.8, and a kaon candi-date is required to satisfy C LK > C Lπ and C LK > 0.1%. The tracksnot satisfying the selection criteria of muon, electron or kaon aretreated as pions.

To obtain the number of the true muons, we also need to es-timate the rates ηb→a by studying pure muon, electron, kaon andpion samples selected from cosmic rays, radiative Bhabha events,J/ψ → ωπ+π− and J/ψ → φK +K − decays, respectively. Theenvironment (angular distribution and momentum spectrum) of

Fig. 2. ηb→a (a and b denote muon, electron, kaon or pion) are the rates ofmisidentifying the particle b as a (a �= b) or the efficiency of identifying the par-ticle a (a = b), where the dots, squares, triangles and stars are for the particles(mis)identified as muon, electron, kaon and pion from the selected particle sam-ples: (a) muon selected from the cosmic rays; (b) electron from Bhabha; (c) kaonfrom J/ψ → φK + K − , and (d) pion from J/ψ → ωπ+π− .

tracks in the selected particle samples in each case may be dif-ferent to that of the tagged D̄ samples. The difference in theenvironment that affects the particle identification is studied bycomparing the efficiency matrices determined using tracks fromthe D D̄ Monte Carlo samples, to those matrices determined us-ing tracks from the Monte Carlo simulation of Bhabha, cosmic ray,J/ψ → φK K and J/ψ → ωππ events. The difference in the yieldsunfolded with the different matrices are about 3.9% for D0 → μ+ Xand 2.1% for D+ → μ+ X . Since the rates ηb→a vary with momentaof the particles, we divide the transverse momentum region (0.52to 1.02 GeV/c) into five intervals in the analysis. Fig. 2 shows therates ηb→a obtained from the selected particle samples in eachtransverse momentum interval.

Inserting the numbers Na,iobs and the rates ηb→a,i (i denotes the

ith transverse momentum interval) into the matrix Eq. (1), weobtain the yield of true muons in the ith momentum interval,Nμ,i

true. Summing Nμ,itrue over the intervals, gives the total numbers

of the true yield candidates to be 87.5 ± 17.1 for D0 → μ+ X and129.3 ± 19.5 for D+ → μ+ X .

3.3. Other background

In the selected candidate events, there are still some back-ground contaminations from non-semimuonic D decays due toK + → μ+νμ and π+ → μ+νμ . These background events are es-timated using the Monte Carlo simulation. The simulated back-ground events are generated as e+e− → D D̄ events, where Dand D̄ mesons are set to decay into all possible modes exceptD0 → μ+ X for studying the D0 decay, or D+ → μ+ X for studyingthe D+ decay. In the Monte Carlo simulation, the decay modes ofD mesons and their branching fractions are quoted from PDG [1],and the particle trajectories are simulated with the GEANT3 basedMonte Carlo simulation package of the BES-II detector [7]. Thenumbers of these background events are estimated to be 8.4 ± 1.8and 3.0 ± 1.6 for D0 → μ+ X and D+ → μ+ X , respectively. Aftersubtracting these background events, we obtain 79.1 ± 17.2 and126.3 ± 19.6 signal events for D0 → μ+ X and D+ → μ+ X , re-spectively.

BES Collaboration / Physics Letters B 665 (2008) 16–19 19

4. Results

The branching fractions for D → μ+ X are determined by:

BF(D → μ+ X) = ND→μ+ X

ND̄ × εD→μ+ X, (2)

where ND→μ+ X is the number of events for D → μ+ X , ND̄ is thenumber of singly tagged D̄ mesons, and εD→μ+ X is the detectionefficiency for D → μ+ X .

The detection efficiencies εD0→μ+ X and εD+→μ+ X are esti-mated with the Monte Carlo simulation. The Monte Carlo eventsare generated as e+e− → D D̄ , where D̄ decay into the singlytagged D̄ modes and D decay into semimuonic modes. Thesemileptonic decays are generated with the q2 dependence of formfactors given by the pole model [14]. This generator has been ap-plied in previous measurements [15–19]. In order to study themodel dependence of the efficiency, the semileptonic decays arealso simulated with the ISGW2 form factor model [20]. The dif-ference in efficiencies determined with the different form factormodels is about 5.8%. The averaged efficiencies are determined byweighting the branching fractions of the D semimuonic decays [1]and the numbers of the singly tagged D̄ events. The efficiencies are(15.4 ± 0.2)% for D0 → μ+ X and (13.5 ± 0.2)% for D+ → μ+ X .

Inserting ND→μ+ X the number of the signal events for D →μ+ X , ND̄ the number of the singly tagged D̄ mesons and the de-tection efficiency εD→μ+ X into Eq. (2), we calculate the branchingfractions for D → μ+ X to be

BF(

D0 → μ+ X) = (6.8 ± 1.5 ± 0.8)%

and

BF(D+ → μ+ X) = (17.6 ± 2.7 ± 1.8)%,

where the first errors stated are statistical and the second system-atic.

The systematic errors arise mainly from the uncertainties in:particle identification (∼ 5% for muon [21]); tracking (∼ 2.0% pertrack); the numbers of the singly tagged D̄ mesons (∼ 4.5% for D̄0

[12] and ∼ 3.0% for D− [13]); the δz selection criterion (∼ 3.5%);the input form factor model (∼ 5.8%); the selected samples en-vironment (∼ 3.9% for D0 and 2.1% for D+); the Monte Carlosample statistics (∼ 1.5%) and the selected control sample statistics(∼ 2.1% for D0 and ∼ 1.0% for D+). The systematic errors arisingfrom the uncertainties in the matrix elements ηb→a are evalu-ated by performing iterations of the unfolding procedure and vary-ing the matrix elements within error. The systematic errors fromthe poorly measured exclusive semileptonic decay modes are esti-mated using D D̄ Monte Carlo samples generated with or withoutthese modes, and they are about 3.3% and 4.7% for D0 → μ+νμ

and D+ → μ+νμ , respectively. Adding all these uncertainties inquadrature yields the total systematic errors to be 11.0% and 10.3%for D0 → μ+ X and D+ → μ+ X , respectively.

Using the measured branching fractions for D0 → μ+ X andD+ → μ+ X , the ratio of the two branching fractions is determinedto be:

BF(D+ → μ+ X)

BF(D0 → μ+ X)= 2.59 ± 0.70 ± 0.25,

where the first error stated is statistical. The second error is sys-tematic and arises from the uncertainties in: the numbers of singlytagged D̄ mesons; the ηb→a; the Monte Carlo sample statistics;the selected sample’s environment and the poorly measured decaymodes.

Table 1 shows the comparisons of the measured branching frac-tions for D → μ+ X by the BES Collaboration with those measured

Table 1Comparisons of the measured branching fractions for the inclusive semimuonic de-cays of D mesons with those measured by ARGUS [22], CHORUS [23] Collaborationsand the PDG values [1]

BES ARGUS CHORUS PDG06

BF(D0 → μ+ X)[%] 6.8 ± 1.5 ± 0.8 6.0 ± 0.7 ± 1.2 6.5 ± 1.2 ± 0.3 6.5 ± 0.7BF(D+ → μ+ X)[%] 17.6 ± 2.7 ± 1.8 – – –BF(D+→μ+ X)

BF(D0→μ+ X)2.59 ± 0.70 ± 0.25 – – –

τD+τD0

– – – 2.54 ± 0.02

by the ARGUS [22], CHORUS [23] Collaborations and the averagedvalue from PDG [1]. The measured BF(D0 → μ+ X) is in goodagreement with the measurements from other Collaborations.

5. Summary

Using the data sample of approximately 33 pb−1 collectedat and around

√s = 3.773 GeV with the BES-II detector at the

BEPC collider, we have studied the inclusive semimuonic decaysof D mesons. The absolute branching fractions for D0 → μ+ X andD+ → μ+ X have been measured as BF(D0 → μ+ X) = (6.8 ± 1.5 ±0.8)% and BF(D+ → μ+ X) = (17.6 ± 2.7 ± 1.8)%. To the best ofour knowledge, this is the first reported measurement of D+ →μ+ X . Using the measured branching fractions for D0 → μ+ X andD+ → μ+ X , the ratio of the two branching fractions is determinedto be BF(D+ → μ+ X)/BF(D0 → μ+ X) = 2.59 ± 0.70 ± 0.25, whichis consistent with the ratio of the lifetimes of D+ and D0 mesons,τD+/τD0 = 2.54 ± 0.02 [1].

Acknowledgements

The BES Collaboration thanks the staff of BEPC and the com-puting center for their hard efforts. This work is supported in partby the National Natural Science Foundation of China under con-tracts Nos. 10491300, 10225524, 10225525, 10425523, 10625524,10521003, the Chinese Academy of Sciences under contract No. KJ95T-03, the 100 Talents Program of CAS under Contract Nos. U-11,U-24, U-25, and the Knowledge Innovation Project of CAS underContract Nos. U-602, U-34 (IHEP), and the National Natural Sci-ence Foundation of China under Contract No. 10225522 (TsinghuaUniversity).

References

[1] W.M. Yao, et al., Particle Data Group, J. Phys. G 33 (2006) 1, and 2007 partialupdate for edition 2008 (URL: http://pdg.lbl.gov).

[2] A. Pais, S.B. Treiman, Phys. Rev. D 15 (1977) 2529.[3] N.E. Adam, et al., Phys. Rev. Lett. 97 (2006) 251801.[4] M. Ablikim, et al., Phys. Lett. B 658 (2007) 1.[5] J.Z. Bai, et al., Nucl. Instrum. Methods A 458 (2001) 627.[6] M.H. Ye, Z.P. Zheng, in: Proceeding of the XIV International Symposium on

Lepton and Photon Interaction, Stanford, California, 1989, World Scientific, Sin-gapore, 1990.

[7] M. Ablikim, et al., Nucl. Instrum. Methods A 552 (2005) 344.[8] M. Ablikim, et al., Phys. Rev. Lett. 97 (2006) 121801.[9] M. Ablikim, et al., Phys. Lett. B 641 (2006) 145.

[10] M. Ablikim, et al., Phys. Lett. B 659 (2008) 74.[11] M. Ablikim, et al., Phys. Rev. D 76 (2007) 12202.[12] M. Ablikim, et al., Phys. Lett. B 597 (2004) 39.[13] M. Ablikim, et al., Phys. Lett. B 608 (2005) 24.[14] A. Ali, T.C. Yang, Phys. Lett. B 65 (1976) 275.[15] M. Ablikim, et al., hep-ex/0610019.[16] M. Ablikim, et al., Phys. Lett. B 644 (2007) 20.[17] M. Ablikim, et al., Phys. Lett. B 597 (2004) 39.[18] M. Ablikim, et al., Phys. Lett. B 608 (2005) 24.[19] M. Ablikim, et al., Eur. Phys. J. C 47 (2006) 31.[20] D. Scora, N. Isgur, Phys. Rev. D 52 (1995) 2783.[21] M. Ablikim, et al., Phys. Lett. B 610 (2005) 183.[22] H. Albrecht, et al., Phys. Lett. B 374 (1996) 249.[23] A. Kayis-Topaksu, et al., Phys. Lett. B 626 (2005) 24.