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Belle Prerpint 2006-36 KEK Preprint 2006-53 hep-ex/0611045 A Search for the Rare Leptonic Decays B+ → µ+ ν and B+ → e+ ν µ e 7 0 0 Belle Collaboration 2 n N. Satoyamaan, K. Abei, I. Adachii, H. Aiharaau, D. Anipkoa, a J A. M. Bakichap, E. Barberiov, I. Bednya, K. Belousℓ, 2 U. Bitenco, I. Bizjako, A. Bondara, A. Bozekab, M. Braˇckoi,u,o, 2 T. E. Browderh, M.-C. Changf, P. Changaa, A. Cheny, 2 v W. T. Cheny, B. G. Cheonc, R. Chistovn, Y. Choiao, 5 4 Y. K. Choiao, S. Coleap, J. Dalsenov, M. Dashaz, 0 A. Drutskoyd, S. Eidelmana, S. Fratinao, N. Gabysheva, 1 1 T. Gershoni, A. Goy, G. Gokhrooaq, H. Haq, J. Habai, 6 0 Y. Hasegawaan, K. Hayasakaw, D. Heffernanag, T. Hokuuew, / x Y. Hoshias, S. Houy, W.-S. Houaa, T. Iijimaw, K. Ikadow, e p- K. Inamiw, A. Ishikawaau, R. Itohi, M. Iwasakiau, Y. Iwasakii, e J. H. Kangba, S. U. Kataokax, N. Katayamai, H. Kawaib, h v: T. Kawasakiad, H. R. Khanav, H. Kichimii, H. J. Kimr, i X S. K. Kimam, Y. J. Kimg, K. Kinoshitad, S. Korparu,o, ar P. Kriˇzant,o, P. Krokovnyi, R. Kumarah, C. C. Kuoy, A. Kuzmina, Y.-J. Kwonba, J. S. Langee, G. Lederm, M. J. Leeam, T. Lesiakab, A. Limosanii, S.-W. Linaa, D. Liventsevn, G. Majumderaq, T. Matsumotoaw, S. McOnieap, H. Miyakeag, H. Miyataad, Y. Miyazakiw, R. Mizukn, T. Moriw, T. Nagamineat, I. Nakamurai, E. Nakanoaf, M. Nakaoi, H. Nakazaway, Z. Natkaniecab, S. Nishidai, O. Nitohay, S. Noguchix, T. Nozakii, S. Ogawaar, T. Ohshimaw, S. Okunop, Y. Onukiaj, H. Ozakii, P. Pakhlovn, G. Pakhlovan, H. Parkr, R. Pestotniko, L. E. Piilonenaz, H. Sahooh, Y. Sakaii, T. Schietingers, O. Schneiders, J. Schu¨mannz, C. Schwandam, R. Seidlj,aj, K. Senyow, Preprint submitted to Elsevier Science 7 February 2008 M. E. Seviorv, M. Shapkinℓ, H. Shibuyaar, B. Shwartza, J. B. Singhah, A. Sokolovℓ, A. Somovd, N. Soniah, S. Staniˇcae, M. Stariˇco, H. Stoeckap, K. Sumisawai, T. Sumiyoshiaw, S. Suzukiak, F. Takasakii, K. Tamaii, N. Tamuraad, M. Tanakai, G. N. Taylorv, Y. Teramotoaf, X. C. Tianai, I. Tikhomirovn, T. Tsuboyamai, T. Tsukamotoi, S. Ueharai, T. Uglovn, S. Unoi, P. Urquijov, G. Varnerh, S. Villas, C. C. Wangaa, C. H. Wangz, M.-Z. Wangaa, Y. Watanabeav, R. Weddv, E. Wonq, Q. L. Xiek, B. D. Yabsleyap, A. Yamaguchiat, Y. Yamashitaac, M. Yamauchii, Z. P. Zhangaℓ, V. Zhilicha, and A. Zupanco, aBudker Institute of Nuclear Physics, Novosibirsk, Russia bChiba University, Chiba, Japan cChonnam National University, Kwangju, South Korea dUniversity of Cincinnati, Cincinnati, OH, USA eUniversity of Frankfurt, Frankfurt, Germany fDepartment of Physics, Fu Jen Catholic University, Taipei, Taiwan gThe Graduate University for Advanced Studies, Hayama, Japan hUniversity of Hawaii, Honolulu, HI, USA iHigh Energy Accelerator Research Organization (KEK), Tsukuba, Japan jUniversity of Illinois at Urbana-Champaign, Urbana, IL, USA kInstitute of High Energy Physics, Chinese Academy of Sciences, Beijing, PR China ℓInstitute for High Energy Physics, Protvino, Russia mInstitute of High Energy Physics, Vienna, Austria nInstitute for Theoretical and Experimental Physics, Moscow, Russia oJ. Stefan Institute, Ljubljana, Slovenia pKanagawa University, Yokohama, Japan qKorea University, Seoul, South Korea rKyungpook National University, Taegu, South Korea sSwiss Federal Institute of Technology of Lausanne, EPFL, Lausanne, Switzerland tUniversity of Ljubljana, Ljubljana, Slovenia uUniversity of Maribor, Maribor, Slovenia vUniversity of Melbourne, Victoria, Australia wNagoya University, Nagoya, Japan xNara Women’s University, Nara, Japan 2 yNational Central University, Chung-li, Taiwan zNational United University, Miao Li, Taiwan aaDepartment of Physics, National Taiwan University, Taipei, Taiwan abH. Niewodniczanski Institute of Nuclear Physics, Krakow, Poland acNippon Dental University, Niigata, Japan adNiigata University, Niigata, Japan aeUniversity of Nova Gorica, Nova Gorica, Slovenia afOsaka City University, Osaka, Japan agOsaka University, Osaka, Japan ahPanjab University, Chandigarh, India aiPeking University, Beijing, PR China ajRIKEN BNL Research Center, Brookhaven, NY, USA akSaga University, Saga, Japan aℓUniversity of Science and Technology of China, Hefei, PR China amSeoul National University, Seoul, South Korea anShinshu University, Nagano, Japan aoSungkyunkwan University, Suwon, South Korea apUniversity of Sydney, Sydney, NSW, Australia aqTata Institute of Fundamental Research, Bombay, India arToho University, Funabashi, Japan asTohoku Gakuin University, Tagajo, Japan atTohoku University, Sendai, Japan auDepartment of Physics, University of Tokyo, Tokyo, Japan avTokyo Institute of Technology, Tokyo, Japan awTokyo Metropolitan University, Tokyo, Japan ayTokyo University of Agriculture and Technology, Tokyo, Japan azVirginia Polytechnic Institute and State University, Blacksburg, VA, USA baYonsei University, Seoul, South Korea Abstract We present a search for the decays B+ µ+ν and B+ e+ν in a 253fb−1 µ e → → data sample collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy B factory. We find no significant evidence for a signal and set 90% confidence level upper limits of (B+ µ+ν ) < 1.7 10−6 and (B+ µ e+ν ) < 9.8 10−7. B → × B → e × 3 Key words: Leptonic, B decay PACS: 13.25.Hw, 14.20.Lq, 14.40.Nd 1 Introduction The purely leptonic decay B+ ℓ+ν (charge conjugate states are implied ℓ → throughout the paper) is of particular interest since it provides a direct mea- surement oftheproduct ofthemagnitude oftheCabibbo-Kobayashi-Maskawa matrixelement, V [1],andtheB mesondecay constant,f .IntheStandard ub B | | Model (SM) the branching fraction of the decay B+ ℓ+ν is given as ℓ → G2m m2 m2 2 (B+ ℓ+ν ) = F B ℓ 1 ℓ f2 V 2τ , (1) B → ℓ 8π − m2B! B| ub| B where G is the Fermi coupling constant, m and m are the charged lepton F ℓ B and B meson masses, and τ is the B+ lifetime. The expected branching B fractions are (4.7 0.7) 10−7 for B+ µ+ν and (1.1 0.2) 10−11 for µ B+ e+ν assum±ing V× = (4.39 0.3→3) 10−3 determin±ed fro×m inclusive e ub → | | ± × charmless semileptonic B decay data [2], τ = 1.643 0.010 ps [2], and f = B B ± 0.216 0.022GeV obtained from lattice QCD calculations [3]. However, non- ± SM physics could yield larger branching fractions [4]. The Belle experiment has recently found the first evidence for the purely leptonic decay B+ τ+ν [5]. The other purely leptonic B decays, B+ τ → → µ+ν and B+ e+ν , have not yet been observed. The most stringent current µ e upper limits fo→r these modes are (B+ µ+ν ) < 6.6 10−6 [6] and (B+ µ e+ν ) < 1.5 10−5 [7]. PreliminaBry lim→its of (B+ ×µ+ν ) < 2.0 B10−6 [→8] e µ and (B+ × e+ν ) < 7.9 10−6 [9] are alsBo avai→lable from the×Belle and e B → × BaBar collaborations, respectively. In this paper, we present a search for the decays B+ µ+ν and B+ e+ν . µ e → → 2 Data Set and Experiment The data used in this analysis were collected with the Belle detector at the KEKB asymmetric-energy e+e− collider [10]. The sample has an integrated luminosity of 253fb−1 accumulated at the Υ(4S) resonance, at a center-of- mass (CM) energy of 10.58GeV (on-resonance), and 28.1fb−1 accumulated at a CM energy 60MeV below the Υ(4S) resonance (off-resonance). 4 The Belle detector is a large solid-angle spectrometer based on a 1.5T super- conducting solenoid magnet. Charged particle tracking and momentum measurements are made with a three-layer, double-sided silicon vertex detector (SVD) and a central drift chamber (CDC). Identification of charged hadrons is provided by a combination of three measurements: specific ionization loss (dE/dx)intheCDC,photonyieldintheaerogelthresholdCherenkovcounters (ACC), and time-of-flight information from a cylindrical array of 128 scintilla- tion counters (TOF). Photons are detected in an electromagnetic calorimeter (ECL) system made of an array of 8736 CsI(Tl) crystals surrounding the TOF system. The ECL is also used for electron identification. Muons are identified by a resistive plate chamber system (KLM) located within the solenoid’s ex- ternal return yoke. ± ± Particle identification for e and µ is important for this analysis. Electron identification isbasedontheratioofthecluster energyintheECL tothetrack momentum from the CDC and the SVD (E/p), the dE/dx in the CDC, the position and shower shape of the cluster in the ECL and the response from the ACC. Muon identification is based on the hit positions and the depth of pen- etration into the KLM. The efficiency of electron identification is over 90% in the momentum range of this analysis while the misidentification rate is below 0.5%. The muon identification efficiency is approximately 85% in the momentum range of this analysis with a misidentification rate of approximately 1%. The Belle detector is described in detail elsewhere [11]. A detailed Monte Carlo (MC) simulation, which fully describes the detector geometry and response based on GEANT [12], is used to estimate the signal detection efficiency and to study the background. The MC samples are produced with the EvtGen event generator [13]. 3 Signal Selection We search for events in which there is one well-identified lepton. The signal candidate muon or electron is required to pass tight particle identification requirements; lepton candidates that can be associated to other tracks in the event to reconstruct K0 mesons or photon conversions are explicitly vetoed. S Signal lepton candidates are required to originate from the interaction point (IP) and to have their polar angle, θ , formed by the lepton momentum with ℓ the detector axis (opposite to the direction of the positron beam), in the range 0.5 < cosθ < 0.8 for muons and 0.50 < cosθ < 0.85 for electrons. ℓ ℓ − − As B+ ℓ+ν is a two-body decay, the lepton has a fixed momentum in the ℓ → signal B meson (Bsig) rest frame, with pB equal to approximately half of the ℓ B meson mass, pB m /2. The lepton momentum in the CM frame, p∗, is ℓ ∼ B ℓ 5 related to pB by ℓ ∗ p~ pBℓ ≃ p∗ℓ 1− |mBBsig| cosθℓ−Bsig! (2) where ~p∗ is the momentum of the Bsig in the CM frame and cosθ Bsig ℓ−Bsig represents the cosine of the angle between the directions of the signal lepton and Bsig in the CM frame. Since the neutrino is not detected in the Bsig decay, we obtain p~∗ by inclu- Bsig sive reconstruction of the companion B meson (Bcomp) recoiling against Bsig. For the Bcomp reconstruction, we use all detected photons and charged tracks, except for the signal lepton candidate. K0 π+π− and γ e+e− decays S → → are fully reconstructed, in order to correctly account for the momentum of tracks originating from vertices displaced from the IP. The missing momentum in the laboratory frame that is calculated by using all photons, charged ∗ tracks, and the signal lepton, is assigned to the neutrino. The quantity p~ | Bsig| is approximately given by E2 m2 0.32GeV/c using the beam energy beam − B ≃ in the CM frame (Ebeam)q, while cosθℓ−Bsig is related to the angle between the direction of the signal lepton and the momentum of Bcomp(θℓ−Bcomp) by cosθℓ−Bsig = cosθℓ−Bcomp. Thus, equation 2 can be expressed in terms of two − ∗ measurable quantities, pℓ and cosθℓ−Bcomp: pBℓ ≃ p∗ℓ(1+0.06cosθℓ−Bcomp). (3) SignalcandidatesareselectedusingthekinematicvariablesM = E2 p~∗ 2 ∗ ∗ ∗ bc beam −| B| and ∆E = EB −Ebeam, where p~B and EB are the momentum anqd energy of Bcomp, all variables being evaluated in the CM frame. Events in the fit region that satisfy 5.10GeV/c2 < M < 5.29GeV/c2 and 0.8 ( 1.0)GeV < ∆E < bc − − 0.4GeV for the muon (electron) mode are kept for further analysis. A more restricted signal region is also defined by the same requirements on ∆E and by M > 5.26GeV/c2. bc The dominant background arises from the continuum process e+e− qq¯(q = → u,d,s,c) and semileptonic B meson decays, mostly into charm final states (B X ℓν) with contributions from rare b u modes (B X ℓν). The c u → → → missing momentum of continuum events is often due to undetected particles that are outside the detector acceptance. In order to reduce such backgrounds, we require the transverse component of the missing momentum to be greater than 1.75GeV/c, and the cosine of the polar angle to be less than 0.84 (0.82) for the muon (electron) mode, respectively. Figure 1 shows the measured pB distributions after reconstruction of the com- ℓ panion B meson. We require 2.6GeV/c < pB < 2.84GeV/c and 2.6GeV/c < µ 6 V/c B fi m n 253fb-1 V/c35000 B fi e n 253fb-1 Ge35000 On resonance Ge On resonance 0.05 30000 Off resonance 0.05 30000 Off resonance ntries/25000 BSXiBug ln nal x 3000 ntries/2205000000 XBSiBug ln nal(arbitrary) E20000 E 15000 15000 10000 10000 5000 5000 20.3 2.4 2.5 2.6 2.7 2.8 2.9 20.3 2.4 2.5 2.6 2.7 2.8 2.9 pB [GeV/c] pB [GeV/c] l l Fig. 1. Lepton momentum distributions in the rest frame of the signal B meson for the muon (left) and electron (right) mode after reconstruction of the companion B meson. Points show the on-resonance data, and solid histograms show the expected background due to rare B X ℓν decays (hatched, from MC); other BB¯ u → events, principallyB X ℓν decays (cross-hatched,also fromMC);andcontinuum c → events (light shaded, taken from scaled off-resonance data). The dashed histograms represent the signal as predicted by the MC with arbitrary normalization. pB < 2.8GeV/c for the signal candidates. This requirement removes most of e the B X ℓν background. c → In order to further suppress the continuum background we exploit the event shape difference between continuum events, which are jet-like, and BB¯ events, which tend to have a more spherical topology. Modified Fox-Wolfram mo- ments [14,15] are combined into a Fisher discriminant (F). Figure 2 shows the Fisher discriminant distributions for events that passed the cosθ selection. ℓ We require F > 0.3 for the muon mode and F > 0 for the electron mode, which retain approximately 51% (60%) of the signal in the signal region and remove approximately 99% (95%) of the continuum background in the signal region for the muon (electron) mode. Wedetermine allselection criteria bymaximizing N /√N +N ,where N is S S B S the number of signal events expected in the signal region computed assuming the SM branching fractions and N is the number of expected background B events in the signal region from MC. After all selection criteria have been applied, the signal selection efficiency in the signal region is estimated to be ǫ = 2.18 0.06% for the muon mode µ ± and ǫ = 2.39 0.06% for the electron mode. The efficiencies in the fit region e ± are 3.15 0.07% for the muon mode and 3.86 0.08% for the electron mode. ± ± Figure3showsthepB distributionsafterallotherselectionshavebeenapplied. ℓ The background that remains in the signal region consists of approximately 76% continuum and 24% B X ℓν according to the off-resonance data and u → MC studies. The MC study also indicates that the latter exhibits a peaking M distribution with significantly larger width than the signal distribution. bc 7 0.5 40000 B fi m n 253fb-1 0.5 B fi e n 253fb-1 es/ On resonance es/25000 On resonance ntri35000 Off resonance ntri Off resonance E30000 BB E20000 BB Xu l n Xu l n 25000 Signal x 4000 15000 Signal(arbitrary) 20000 15000 10000 10000 5000 5000 0-4 -3 -2 -1 0 1 2 3 0 -3 -2 -1 0 1 2 3 F F Fig. 2. Fisher discriminant distributions for the muon (left) and electron (right) mode after cosθ requirements have been applied. Points show the on-resonance ℓ data, and solid histograms show the expected background due to rare B X ℓν u → decays (hatched, from MC); other BB¯ events, principally B X ℓν decays c → (cross-hatched, also from MC); and continuum events (light shaded, taken from scaled off-resonance data). The dashed histograms represent the signal as predicted by the MC with arbitrary normalization. c c V/140 B fi m n 253fb-1 V/160 B fi e n 253fb-1 e e G On resonance G On resonance 05 120 Off resonance 05 140 Off resonance Entries/0.10800 BSXiBug ln nal x 10 Entries/0.110200 XBSiBug ln nal(arbitrary) 80 60 60 40 40 20 20 20.3 2.4 2.5 2.6 2.7 2.8 2.9 20.3 2.4 2.5 2.6 2.7 2.8 2.9 pB [GeV/c] pB [GeV/c] l l Fig.3.pB distributionsforthesignalcandidates.Pointsshowtheon-resonancedata, ℓ and solid histograms show the expected background due to rare B X ℓν decays u → (hatched,fromMC);otherBB¯ events,principallyB X ℓν decays(cross-hatched, c → alsofromMC);andcontinuumevents (light shaded,taken fromscaled off-resonance data). Dashed histograms are MC B ℓν signals that are obtained by multiplying → the SM expectations by a factor of 10 for the muon mode and by 5 106 for the × electron mode. The arrows show the signal regions. 4 Signal Extraction The signal yields are extracted from unbinned maximum likelihood fits to M bc distributions in the fit region. The signal M distribution is parameterized bc by a Crystal Ball function [16] modeled on the signal MC. The background is described by ARGUS functions [17], with shape parameters determined from ¯ theoff-resonancedataforthecontinuum backgroundandfromMCfortheBB background. We do not include the peaking component from B X ℓν in u → this fit since an examination of ∆E sideband data indicates that the peaking contribution is negligible. The expected number of background events in the 8 Muon Mode Electron Mode Signal Efficiency (fit region) 3.15 0.07% 3.86 0.08% ± ± Signal Efficiency (signal region) 2.18 0.06% 2.39 0.06% ± ± Observed in Signal region [events] 12 15 Expected background [events] 7.4 1.0 13.4 1.4 ± ± Signal yield [events] 4.1 3.1 1.8 3.3 ± − ± Significance 1.3 – SM Prediction [events] 2.8 0.2 (7.3 1.4) 10−5 ± ± × Table 1 Selection efficiencies, expected numbers of events for signal and background and fit results. signal region is estimated by fitting the M distribution outside the signal bc region to a background shape determined from the BB¯ MC and off-resonance data. The expected number of background events is 7.4 1.0 (13.4 1.4) ± ¯ ± for the muon (electron) mode. Use of the combination of the BB MC samples and off-resonance data instead of the on-resonance data gives similar expected number of background events. The M distributions are used as probability bc density functions (PDF) to compute an extended likelihood function defined as follows: e−(ns+nb) N (n ,n ) = (n f (i)+n f (i)) (4) s b s s b b L N! i=1 Y where n and n represent the numbers of signal and background events in s b the fit region to be determined in the fit, N is the number of observed events, f and f are the signal and background PDFs, respectively. The negative log s b likelihood function is minimized using MINUIT [18] with two free parameters n and n where n = ǫ N (B+ ℓ+ν) with ǫ being the efficiency in b s s ℓ BB¯ ℓ the fit region, and N ×the tota×lBnumbe→r of BB¯ events analysed. We assume BB¯ the number of the charged and neutral BB¯ pairs to be equal. Figure4showstheM distributionsofeventsinthe∆E signalregiontogether bc with the fit results. We observe 12 (15) events for the muon (electron) mode in the signal region. The signal yield extracted from the fit is 4.1 3.1 events for ± themuonmodeand 1.8 3.3eventsfortheelectronmodeinthesignalregion. FortheSMbranchin−gfrac±tions,weexpect2.8 0.2and(7.3 1.4) 10−5events ± ± × for the muon mode and the electron mode, respectively. The significance of the signal in the muon mode is 1.3, which is defined as 2ln( / ) where max 0 L L max is the likelihood value for the best-fit signal yield aqnd 0 is the likelihood L L value for no signal event. No excess of events is observed in the electron mode. Selection efficiencies, expected numbers of events for signal and background and fit results are summarized in Table 1. 9 2 2 V/c12 On resonance B fi m n V/c14 On resonance B fi e n e Combined function e Combined function G G Background PDF Background PDF 1 10 1 12 0 Signal PDF 0 Signal PDF(arbitrary) 0. 0. s / 8 s / 10 e e ntri ntri8 E6 E 6 4 4 2 2 0 0 5.1 5.125.145.165.18 5.2 5.225.245.265.28 5.3 5.1 5.125.145.165.18 5.2 5.225.245.265.28 5.3 M [GeV/c2] M [GeV/c2] bc bc Fig. 4. M distributions for the events in the ∆E signal region, together with the bc fit results (dotted lines). The solid curves are the background contributions. The dashed curves are the signal contributions. The signal contribution in the electron mode is multiplied by a factor of 4 to make it visible on the plot. − 5 Systematic Uncertainties The main sources of systematic uncertainty in calculating (B+ ℓ+ν) arise from the uncertainties in the number of B+B− events (N B= (2→76.6 3.1) BB¯ ± × 106), determination of the signal efficiency, and parameterization of the M bc distributionforthesignalandbackground. Theuncertainty duetothenumber of BB¯ pairs is 1.1%. The uncertainties from the signal efficiencies are: 1% due to the uncertainties in the track-finding efficiency for the signal, 4.4% due to the uncertainty in the muon ID efficiency and 1.1% due to the electron ID efficiency, 2.3% (2.1%) for the muon (electron) mode from the MC statistics. We calculate an efficiency correction factor, to account for differences between MC and data, by analyzing a control data sample of fully reconstructed B+ D¯(∗)0π+ decays, where we treat the pion as a signal lepton and the D¯(∗)0 →as the accompanying neutrino. The event topology is similar to that of the signal events as both are two-body decays. The companion B is reconstructed in the control data samples as in the signal sample. We compare the efficiencies of the control data sample and a corresponding MC sample and determine correction factors for the signal efficiencies. The correction factors obtained are 1.01 0.04 for the muon mode and 1.13 0.04 for the electron mode. ± ± We apply a correction only to the electron mode, while uncertainties on the correction factors contribute to the systematic uncertainties of both modes at the level of 3.6%. The uncertainties related to the signal M shapes are estimated by repeating bc the fits while varying the Crystal Ball function parameters by their uncertainties; their contribution is 6.5% for the muon mode and 3.2% for the electron 10