application/xmlA measurement of the [formula omitted] branching ratioOPAL CollaborationG AbbiendiC AinsleyP.F ÅkessonG AlexanderJ AllisonP AmaralG AnagnostouK.J AndersonS ArcelliS AsaiD AxenG AzuelosI BaileyE BarberioR.J BarlowR.J BatleyP BechtleT BehnkeK.W BellP.J BellG BellaA BelleriveG BenelliS BethkeO BiebelI.J BloodworthO BoeriuP BockD BonacorsiM BoutemeurS BraibantL BrigliadoriR.M BrownK BuesserH.J BurckhartS CampanaR.K CarnegieB CaronA.A CarterJ.R CarterC.Y ChangD.G CharltonA CsillingM CuffianiS DadoS DallisonA De RoeckE.A De WolfK DeschB DienesM DonkersJ DubbertE DuchovniG DuckeckI.P DuerdothE ElfgrenE EtzionF FabbriL FeldP FerrariF FiedlerI FleckM FordA FreyA FürtjesP GagnonJ.W GaryG GayckenC Geich-GimbelG GiacomelliP GiacomelliM GiuntaJ GoldbergE GrossJ GrunhausM GruwéP.O GüntherA GuptaC HajduM HamannG.G HansonK HarderA HarelM Harin-DiracM HauschildJ HauschildtC.M HawkesR HawkingsR.J HemingwayC HenselG HertenR.D HeuerJ.C HillK HoffmanR.J HomerD HorváthR HowardP Igo-KemenesK IshiiH JeremieP JovanovicT.R JunkN KanayaJ KanzakiG KarapetianD KarlenV KartvelishviliK KawagoeT KawamotoR.K KeelerR.G KelloggB.W KennedyD.H KimK KleinA KlierS KluthT KobayashiM KobelS KomamiyaL KormosT KrämerT KressP KriegerJ von KroghD KropK KrugerT KuhlM KupperG.D LaffertyH LandsmanD LanskeJ.G LayterA LeinsD LellouchL LevinsonJ LillichS.L LloydF.K LoebingerJ LuJ LudwigA MacphersonW MaderS MarcelliniT.E MarchantA.J MartinJ.P MartinG MasettiT MashimoW.J McDonaldJ McKennaT.J McMahonR.A McPhersonF MeijersP Mendez-LorenzoW MengesF.S MerrittH MesA MicheliniS MiharaG MikenbergD.J MillerS MoedW MohrT MoriA MutterK NagaiI NakamuraH.A NealR NisiusS.W O'NealeA OhA OkparaM.J OregliaS OritoC PahlG PásztorJ.R PaterG.N PatrickJ.E PilcherJ PinfoldD.E PlaneB PoliJ PolokO PoothM PrzybycieńA QuadtK RabbertzC RembserP RenkelH RickJ.M RoneyS RosatiY RozenK RungeK SachsT SaekiO SahrE.K.G SarkisyanA.D SchaileO SchaileP Scharff-HansenJ SchieckT Schörner-SadeniusM SchröderM SchumacherC SchwickW.G ScottR SeusterT.G ShearsB.C ShenP SherwoodG SiroliA SkujaA.M SmithR SobieS Söldner-RemboldF SpanoA StahlK StephensD StromR StröhmerS TaremM TasevskyR.J TaylorR TeuscherM.A ThomsonE TorrenceD ToyaP TranT TrefzgerA TricoliI TriggerZ TrócsányiE TsurM.F Turner-WatsonI UedaB UjváriB VachonC.F VollmerP VanneremM VerzocchiH VossJ VossebeldD WallerC.P WardD.R WardP.M WatkinsA.T WatsonN.K WatsonP.S WellsT WenglerN WermesD WetterlingG.W WilsonJ.A WilsonG WolfT.R WyattS YamashitaD Zer-ZionL ZivkovicJ LettsP MättigPhysics Letters B 551 (2003) 35-48. doi:10.1016/S0370-2693(02)03020-4journalPhysics Letters BCopyright © 2002 Elsevier Science B.V. All rights reserved.Elsevier B.V.0370-26935511-22 January 20032003-01-0235-48354810.1016/S0370-2693(02)03020-4http://dx.doi.org/10.1016/S0370-2693(02)03020-4doi:10.1016/S0370-2693(02)03020-4http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/JournalsS300.5PLB19384S0370-2693(02)03020-410.1016/S0370-2693(02)03020-4Elsevier Science B.V.ExperimentsFig. 1(a), (b) The number of muon layers, Nmuon, activated by the passage of a charged particle in the jet, and (c), (d) the μmatch matching between a muon track reconstructed in the tracking chamber and one reconstructed in the muon chamber. The jets in each plot have passed all other selection criteria. The arrows indicate the accepted regions. The points are data, the clear histogram is the Monte Carlo τ−→μ−ν̄μντ prediction, the singly-hatched histogram is the Monte Carlo prediction for backgrounds from other τ decays, and the cross-hatched histogram is the Monte Carlo prediction for background from non-τ sources.Fig. 2(a) The momentum of the highest momentum particle in the opposite jet, p1-opp, where the candidate muon has a momentum greater than 40 GeV/c, and (b) the combined momentum of the second and third particles in those jets which have more than one track, for jets which have passed all other selection criteria. The arrows indicate the accepted regions. The points are data, the clear histogram is the Monte Carlo τ−→μ−ν̄μντ prediction, the singly-hatched histogram is the Monte Carlo prediction for backgrounds from other τ decays, and the cross-hatched histogram is the Monte Carlo prediction for background from non-τ sources.Fig. 3The momentum of the candidate muon, pμ, for jets which have passed all of the selection criteria. The points are data, the clear histogram is the Monte Carlo τ−→μ−ν̄μντ prediction, the singly-hatched histogram is the Monte Carlo prediction for backgrounds from other τ decays, and the cross-hatched histogram is the Monte Carlo prediction for background from non-τ sources.Fig. 4The distributions used to measure the background in the τ−→μ−ν̄μντ sample are shown after the normalization. The arrows indicate the region that was chosen to measure each background. (a) Ejet is the energy measured in the electromagnetic calorimeter, (b) θacol is the acollinearity angle between the two τ jets, (c) p1-opp is the momentum of the highest momentum particle in the opposite jet to the τ−→μ−ν̄μντ candidate, (d) dE/dx is the rate of energy loss of a particle traversing the tracking chamber. The points are data, the clear histogram is the Monte Carlo τ−→μ−ν̄μντ prediction, the singly-hatched histogram is the Monte Carlo prediction for the type of background being evaluated using each distribution, and the cross-hatched histogram is the Monte Carlo prediction for all other types of background.Fig. 5The lifetime of the τ vs the τ−→μ−ν̄μντ branching ratio. The band is the Standard Model expectation, and its width is determined by the uncertainty in the mass of the τ[19]. The point with error bars is the OPAL measurement of the τ lifetime [18] and the branching ratio determined in this work.Table 1Fractional backgrounds in the τ+τ− sample together with their estimated uncertaintiesBackgroundContaminatione+e−→e+e−0.00305±0.00027e+e−→μ+μ−0.00108±0.00022e+e−→qq̄0.00377±0.00015e+e−→(e+e−)μ+μ−0.00108±0.00054e+e−→(e+e−)e+e−0.00157±0.00028Total0.01055±0.00072Table 2The main sources of background in the candidate τ−→μ−ν̄μντ sample together with their estimated uncertaintiesBackgroundsContaminationτ−→h−⩾0π0ντ0.0225±0.0016e+e−→(e+e−)μ+μ−0.0052±0.0026e+e−→μ+μ−0.0029±0.0006τ−→h−h−h+⩾0π0ντ0.0014±0.0003Other0.0004±0.0001Total0.0324±0.0031Table 3Values of the quantities used in the calculation of B(τ−→μ−ν̄μντ)ParameterValueN(τ→μ)31395Nτ193796fbk0.0324±0.0031fτbk0.0106±0.0007ϵ(τ→μ)0.8836±0.0021Fb1.0339±0.0020B(τ−→μ−ν̄μντ)0.1734±0.0009(stat)±0.0006(syst)Table 4Contributions to the total branching ratio absolute systematic uncertainty. The uncertainty in fbk has been adjusted to take into account correlations between the backgrounds in the τ+τ− and τ−→μ−ν̄μντ samplesSourceAbsolute errorϵ(τ→μ)0.00040Fb0.00034fbk0.00030fτbk0.00012Total0.00062A measurement of the τ−→μ−ν̄μντ branching ratioOPAL CollaborationGAbbiendibCAinsleyeP.FÅkessoncGAlexanderuJAllisonoPAmaralhGAnagnostouaK.JAndersonhSArcellibSAsaivDAxenzGAzuelosq1IBaileyyEBarberiog16R.JBarlowoR.JBatleyePBechtlexTBehnkexK.WBellsP.JBellaGBellauABellerivefGBenellidSBethkeaeOBiebeladI.JBloodworthaOBoeriuiPBockjDBonacorsibMBoutemeuradSBraibantgLBrigliadoribR.MBrownsKBuesserxH.JBurckhartgSCampanadR.KCarnegiefBCaronaaA.ACarterlJ.RCartereC.YChangpD.GCharltona2ACsillingg7MCuffianibSDadotSDallisonoADe RoeckgE.ADe Wolfg19KDeschxBDienesacMDonkersfJDubbertadEDuchovniwGDuckeckadI.PDuerdothoEElfgrenqEEtzionuFFabbribLFeldiPFerrarigFFiedleradIFleckiMFordeAFreygAFürtjesgPGagnonkJ.WGarydGGayckenxCGeich-GimbelcGGiacomellibPGiacomellibMGiuntadJGoldbergtEGrosswJGrunhausuMGruwégP.OGünthercAGuptahCHajduabMHamannxG.GHansondKHarderxAHareltMHarin-DiracdMHauschildgJHauschildtxC.MHawkesaRHawkingsgR.JHemingwayfCHenselxGHerteniR.DHeuerxJ.CHilleKHoffmanhR.JHomeraDHorváthab3RHowardzPIgo-KemenesjKIshiivHJeremieqPJovanovicaT.RJunkfNKanayayJKanzakivGKarapetianqDKarlenfVKartvelishvilioKKawagoevTKawamotovR.KKeeleryR.GKelloggpB.WKennedysD.HKimrKKleinj20AKlierwSKluthaeTKobayashivMKobelcSKomamiyavLKormosyTKrämerxTKressdPKriegerf12Jvon KroghjDKropkKKrugergTKuhlxMKupperwG.DLaffertyoHLandsmantDLanskemJ.GLayterdALeinsadDLellouchwLLevinsonwJLillichiS.LLloydlF.KLoebingeroJLuzJLudwigiAMacphersonaa9WMadercSMarcellinibT.EMarchantoA.JMartinlJ.PMartinqGMasettibTMashimovW.JMcDonaldaaJMcKennazT.JMcMahonaR.AMcPhersonyFMeijersgPMendez-LorenzoadWMengesxF.SMerritthHMesf1AMichelinibSMiharavGMikenbergwD.JMillernSMoedtWMohriTMorivAMutteriKNagailINakamuravH.ANealafRNisiusaeS.WO'NealeaAOhgAOkparajM.JOregliahSOritovCPahlaeGPásztord7J.RPateroG.NPatricksJ.EPilcherhJPinfoldaaD.EPlanegdavid.plane@cern.chBPolibJPolokgOPoothmMPrzybycieńg14AQuadtcKRabbertzg18CRembsergPRenkelwHRickdJ.MRoneyySRosaticYRozentKRungeiKSachsfTSaekivOSahradE.K.GSarkisyang10A.DSchaileadOSchaileadPScharff-HansengJSchieckaeTSchörner-SadeniusgMSchrödergMSchumachercCSchwickgW.GScottsRSeusterm6T.GShearsg8B.CShendPSherwoodnGSirolibASkujapA.MSmithgRSobieySSöldner-Remboldi4FSpanohAStahlcKStephensoDStromrRStröhmeradSTaremtMTasevskygR.JTaylornRTeuscherhM.AThomsoneETorrencerDToyavPTrandTTrefzgeradATricolibITriggergZTrócsányiac5ETsuruM.FTurner-WatsonaIUedavBUjváriac5BVachonyC.FVollmeradPVanneremiMVerzocchipHVossg17JVossebeldg8DWallerfC.PWardeD.RWardeP.MWatkinsaA.TWatsonaN.KWatsonaP.SWellsgTWenglergNWermescDWetterlingjG.WWilsono11J.AWilsonaGWolfwT.RWyattoSYamashitavDZer-ZiondLZivkovicwaSchool of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UKbDipartimento di Fisica dell'Università di Bologna and INFN, I-40126 Bologna, ItalycPhysikalisches Institut, Universität Bonn, D-53115 Bonn, GermanydDepartment of Physics, University of California, Riverside, CA 92521, USAeCavendish Laboratory, Cambridge CB3 0HE, UKfOttawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa, Ontario K1S 5B6, CanadagCERN, European Organisation for Nuclear Research, CH-1211 Geneva 23, SwitzerlandhEnrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637, USAiFakultät für Physik, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, GermanyjPhysikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, GermanykIndiana University, Department of Physics, Bloomington, IN 47405, USAlQueen Mary and Westfield College, University of London, London E1 4NS, UKmTechnische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, GermanynUniversity College London, London WC1E 6BT, UKoDepartment of Physics, Schuster Laboratory, The University, Manchester M13 9PL, UKpDepartment of Physics, University of Maryland, College Park, MD 20742, USAqLaboratoire de Physique Nucléaire, Université de Montréal, Montréal, Québec H3C 3J7, CanadarUniversity of Oregon, Department of Physics, Eugene, OR 97403, USAsCLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UKtDepartment of Physics, Technion-Israel Institute of Technology, Haifa 32000, IsraeluDepartment of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, IsraelvInternational Centre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo 113-0033, and Kobe University, Kobe 657-8501, JapanwParticle Physics Department, Weizmann Institute of Science, Rehovot 76100, IsraelxUniversität Hamburg/DESY, Institut für Experimentalphysik, Notkestrasse 85, D-22607 Hamburg, GermanyyUniversity of Victoria, Department of Physics, PO Box 3055, Victoria, British Columbia V8W 3P6, CanadazUniversity of British Columbia, Department of Physics, Vancouver, British Columbia V6T 1Z1, CanadaaaUniversity of Alberta, Department of Physics, Edmonton, Alberta T6G 2J1, CanadaabResearch Institute for Particle and Nuclear Physics, PO Box 49, H-1525 Budapest, HungaryacInstitute of Nuclear Research, PO Box 51, H-4001 Debrecen, HungaryadLudwig-Maximilians-Universität München, Sektion Physik, Am Coulombwall 1, D-85748 Garching, GermanyaeMax-Planck-Institute für Physik, Föhringer Ring 6, D-80805 München, GermanyafYale University, Department of Physics, New Haven, CT 06520, USA1And at TRIUMF, Vancouver, Canada V6T 2A3.16Now at Physics Department of Southern Methodist University, Dallas, TX 75275, USA.2And Royal Society University Research Fellow.7And Research Institute for Particle and Nuclear Physics, Budapest, Hungary.19Now at Universitaire Instelling Antwerpen, Physics Department, B-2610 Antwerpen, Belgium.3And Institute of Nuclear Research, Debrecen, Hungary.20Now at RWTH Aachen, Germany.12Now at University of Toronto, Department of Physics, Toronto, Canada.9And CERN, EP Division, 1211 Geneva 23.14And University of Mining and Metallurgy, Cracow, Poland.18Now at IEKP Universität Karlsruhe, Germany.10Now at University of Nijmegen, HEFIN, NL-6525 ED Nijmegen, The Netherlands, on NWO/NATO Fellowship B 64-29.6And MPI München.8Now at University of Liverpool, Department of Physics, Liverpool L69 3BX, UK.4And Heisenberg Fellow.5And Department of Experimental Physics, Lajos Kossuth University, Debrecen, Hungary.17Now at IPHE Université de Lausanne, CH-1015 Lausanne, Switzerland.11Now at University of Kansas, Department of Physics and Astronomy, Lawrence, KS 66045, USA.JLetts1515Now at University of California, San Diego, CA, USA.PMättig1313Current address Bergische Universität, Wuppertal, Germany.Editor: L. MontanetAbstractThe τ−→μ−ν̄μντ branching ratio has been measured using data collected from 1990 to 1995 by the OPAL detector at the LEP collider. The resulting value of B(τ−→μ−ν̄μντ)=0.1734±0.0009(stat)±0.0006(syst) has been used in conjunction with other OPAL measurements to test lepton universality, yielding the coupling constant ratios gμ/ge=1.0005±0.0044 and gτ/ge=1.0031±0.0048, in good agreement with the Standard Model prediction of unity. A value for the Michel parameter η=0.004±0.037 has also been determined and used to find a limit for the mass of the charged Higgs boson, mH±>1.28tanβ, in the Minimal Supersymmetric Standard Model.1IntroductionPrecise measurements of the leptonic decays of τ leptons provide a means of stringently testing various aspects of the Standard Model. OPAL previously has studied the leptonic τ decay modes by measuring the branching ratios [1,2], the Michel parameters [3], and radiative decays [4]. This work presents a new OPAL measurement of the τ−→μ−ν̄μντ branching ratio,2121Charge conjugation is assumed throughout this Letter. using e+e− data taken from 1990 to 1995 at energies near the Z0 peak, corresponding to an integrated luminosity of approximately 170 pb−1. A pure sample of τ+τ− pairs is selected from the data set, and then the fraction of τ jets in which the τ has decayed to a muon is determined. This fraction is then corrected for backgrounds and inefficiencies. The selection of τ−→μ−ν̄μντ candidates relies on only a few variables, each of which provides a highly effective means of separating background events from signal events while minimising systematic uncertainty. This new measurement supersedes the previous OPAL measurement of B(τ−→μ−ν̄μντ)=0.1736±0.0027 which was obtained using data collected in 1991 and 1992, corresponding to an integrated luminosity of approximately 39 pb−1 [2].OPAL [5] is a general purpose detector covering almost the full solid angle with approximate cylindrical symmetry about the e+e− beam axis.2222In the OPAL coordinate system, the e− beam direction defines the +z axis, and the +x axis points from the detector towards the centre of the LEP ring. The polar angle θ is measured from the +z axis and the azimuthal angle φ is measured from the +x axis. The following subdetectors are of particular interest in this analysis: the tracking system, the electromagnetic calorimeter, the hadronic calorimeter, and the muon chambers. The tracking system includes two vertex detectors, z-chambers, and a large volume cylindrical tracking drift chamber surrounded by a solenoidal magnet which provides a magnetic field of 0.435 T. This system is used to determine the particle momentum and rate of energy loss. The electromagnetic calorimeter consists of lead-glass blocks backed by photomultiplier tubes or photo-triodes for the detection of Čerenkov radiation emitted by relativistic particles. The instrumented magnet return yoke serves as a hadronic calorimeter, consisting of up to nine layers of limited streamer tubes sandwiching eight layers of iron, with inductive readout of the tubes onto large pads and aluminium strips. In the central region of the detector, the calorimeters are surrounded by four layers of drift chambers for the detection of muons emerging from the hadronic calorimeter. In each of the forward regions, the muon detector consists of four layers of limited streamer tubes arranged into quadrants which are transverse to the beam direction, and two “patch” sections which provide coverage in areas otherwise left without detector capabilities due to the presence of cables and support structures.Selection efficiencies and kinematic variable distributions for the present analysis were modelled using Monte Carlo simulated τ+τ− event samples generated with the KORALZ 4.02 package [6] and the TAUOLA 2.0 library [7]. These events were then passed through a full simulation of the OPAL detector [8]. Background contributions from non-τ sources were evaluated using Monte Carlo samples based on the following generators: multihadron events (e+e−→qq̄) were simulated using JETSET 7.3 and JETSET 7.4 [9], e+e−→μ+μ− events using KORALZ [6], Bhabha events using BHWIDE [10], and two-photon events using VERMASEREN [11].2The τ+τ− selectionAt LEP1, electrons and positrons were made to collide at centre-of-mass energies close to the Z0 peak, producing Z0 bosons at rest which subsequently decayed into back-to-back pairs of leptons or quarks from which the τ+τ− pairs were selected for this analysis. These highly relativistic τ particles decay in flight close to the interaction point, resulting in two highly-collimated, back-to-back jets in the detector.This analysis uses the standard OPAL τ+τ− selection [12], with slight modifications to reduce Bhabha background in the τ+τ− sample [13]. The τ+τ− selection requires that an event have two jets as defined by the cone algorithm in reference [14], with a cone half-angle of 35°. The average |cosθ| of the two jets was required to be less than 0.91, in order to restrict the analysis to regions of the detector that are well understood. In addition, fiducial cuts were applied to restrict the events to regions of the detector with reliable particle information and with high particle identification efficiency. If a jet was determined to be within a region of the detector associated with gaps between hadronic calorimeter sectors, or dead regions in the muon chambers due to the support structures of the detector, the entire event was removed from the τ+τ− sample. In regions near the anode wire planes in the tracking chamber, high momentum particles may have their momentum incorrectly reconstructed, an effect that is not well-modelled by the Monte Carlo simulations. Therefore, events containing particles which traverse the detector near the anode planes were also removed from the sample.The main sources of background to the τ+τ− selection are Bhabha events, dimuon events, multihadron events, and two-photon events. For each type of background remaining in the τ+τ− sample, a variable was chosen in which the signal and background can be visibly distinguished. The relative proportion of background was enhanced by loosening criteria which would normally remove that particular type of background from the sample, and/or by applying criteria to reduce the contribution from signal and to remove other types of background. A comparison of the data and Monte Carlo distribution in a background-rich region was then used to assess the modelling of the background and to estimate the corresponding systematic error on the branching ratio. The Monte Carlo simulation provides the overall shape of the background distribution, while the normalization is measured from the data. In most cases, the Monte Carlo simulation was found to be consistent with the data. When the data and Monte Carlo distributions did not agree, the Monte Carlo simulation was adjusted to fit the data. Uncertainties of 4% to 20% in the background estimates were obtained from the statistical uncertainty in the normalization, including the Monte Carlo statistical error. The following paragraphs discuss the measurement of each type of background in the τ+τ− sample.Bhabha events, e+e−→e+e−, have two-particle final states and thus can mimic τ+τ− events. They are characterized by two high-momentum tracks and large energy deposition in the electromagnetic calorimeter. The criteria used to reject the Bhabha background are identical to those used in the Z0 lineshape analysis to reject Bhabha events in the τ+τ− sample [13], rather than the standard OPAL τ+τ− selection. The requirement Etot+ptot<1.4Ecm, for τ+τ− pairs with an average |cosθ| of less than 0.7, was also added in this analysis to further reduce the Bhabha background, where Etot is the sum of the energies of all the electromagnetic calorimeter clusters, ptot is the scalar sum of the momenta of all tracks, and Ecm is the centre-of-mass energy. The Bhabha background remaining in the τ+τ− sample was measured by comparing the distributions of total scalar momentum and of total energy deposition between the data and the Monte Carlo simulation, where the Bhabha background has been enhanced by relaxing the criteria on Etot and ptot. The fraction of residual Bhabha background in the τ+τ− sample was estimated to be 0.00305±0.00027.Dimuon events, e+e−→μ+μ−, also have two particle final states with high momentum tracks, but little energy deposition in the electromagnetic calorimeter. Dimuon events are removed from the τ+τ− sample by requiring Etot+ptot<0.6Ecm in cases where both jets exhibit muon characteristics. The dimuon background remaining after the τ+τ− selection was determined by measuring the dimuon contribution to the scalar momentum distribution in the data and in the Monte Carlo simulation, where the dimuon background has been enhanced by relaxing the criterion on Etot+ptot. The fractional background in the τ+τ− sample was estimated to be 0.00108±0.00022.At LEP1 energies, multihadron events, e+e−→qq̄, typically have considerably higher track and cluster multiplicities than τ+τ− events, and are removed from the τ+τ− sample by requiring low multiplicities. In addition, the τ jets are typically much more collimated than multihadron jets. The distribution of the maximum angle between any good track in the jet (see Ref. [12] for the definition of a good track) and the jet direction was used to evaluate the agreement between the data and the Monte Carlo modelling of these events, where the multihadron background has been enhanced by modifying the multiplicity criteria. This resulted in a fractional background estimate of 0.00377±0.00015.In two-photon events, e+e−→(e+e−)ff̄, the final state e+e− pair has a small scattering angle and disappears down the beam pipe, leaving a pair of low energy fermions, usually μ+μ− or e+e−, in the detector.2323Two-photon events with τ particles, e+e−→(e+e−)τ+τ−, are considered to be signal. Since these particles do not result from the decay of the Z0, they are not constrained to be emitted back-to-back. The τ+τ− selection rejects them based upon their low energy and relatively high acollinearity, θacol.2424Acollinearity is the supplement of the angle between the two jets. The acollinearity criterion was relaxed in order to enhance the two-photon background so that it could be measured. Additionally, for e+e−→(e+e−)e+e− events, each jet was required to exhibit electron characteristics, while for e+e−→(e+e−)μ+μ− events, each jet was required to exhibit muon characteristics. The acollinearity distribution in the data then was compared with that in the Monte Carlo simulation to evaluate the backgrounds in the τ+τ− sample for e+e−→(e+e−)μ+μ− and e+e−→(e+e−)e+e− events, corresponding to fractional background estimates of 0.00108±0.00054 and 0.00157±0.00028, respectively.The τ+τ− selection leaves a sample of 96898 candidate τ+τ− events, with a predicted fractional background of 0.01055±0.00072. The backgrounds in the τ+τ− sample are summarized in Table 1.3The τ−→μ−ν̄μντ selectionAfter the τ+τ− selection, each of the 193796 candidate τ jets is analysed individually to see whether it exhibits the characteristics of the required τ−→μ−ν̄μντ signature. A muon from a τ decay will result in a track in the central tracking chamber, little energy in the electromagnetic and hadronic calorimeters, and a track in the muon chambers. The τ−→μ−ν̄μντ selection is based on information from the central tracking chamber and the muon chambers. Calorimeter information is not used in the main selection, but instead is used to create an independent τ−→μ−ν̄μντ control sample that is used to estimate the systematic error in the selection efficiency. The branching ratio of the τ−→μ−ν̄μντ decay is inclusive of radiation in the initial or final state [15], and so the τ−→μ−ν̄μντ selection retains decays that are accompanied by a radiative photon or a radiative photon that has converted in the detector into an e+e− pair.The τ−→μ−ν̄μντ candidates are selected from jets with one to three tracks in the tracking chamber, where the tracks are ordered according to decreasing particle momentum. The highest momentum track is assumed to be the muon candidate.Muons are identified by selecting charged particles that produce a signal in at least three muon chamber layers. The position of each muon chamber signal must agree with that of the extrapolated track from the drift chamber in order for it to be associated with the track. Nmuon is the number of muon chamber layers activated by a passing particle, and we require Nmuon>2. Although both the barrel region2525In the muon chambers, the barrel region has |cosθ|<0.68 and the endcaps cover the region where 0.67<|cosθ|<0.98. and endcap region nominally have four layers of muon chambers, there are areas of overlap between different regions which may result in more than four layers being activated, as shown in Fig. 1(a) and (b). The value of the Nmuon cut was chosen to minimise the background while retaining signal. The logarithmic plot shows a small discrepancy between the data and the Monte Carlo simulation at low values of Nmuon; however, changing the value of the cut or removing this criterion entirely does not significantly affect the branching ratio, as is discussed in Section 5.1.Tracks in the muon chambers are reconstructed independently from those in the tracking chamber. The candidate muon track in the tracking chamber is typically well-aligned with the corresponding track in the muon chambers, whereas this is not the case for hadronic τ decays, which are the main source of background in the sample. The majority of these background jets contain a pion which interacts in the hadronic calorimeter, resulting in the production of secondary particles which emerge from the calorimeter and generate signals in the muon chambers, a process known as pion punchthrough. Therefore, a “muon matching” variable, μmatch, which compares the agreement between the direction of a track reconstructed in the tracking chamber and that of the track reconstructed in the muon chambers, is used to differentiate the signal τ−→μ−ν̄μντ decays from hadronic τ decays.2626μmatch measures the difference in φ and in θ between a track reconstructed in the tracking chamber and one reconstructed in the muon chambers. The differences are divided by an error estimate and added in quadrature to form a χ2-like comparison of the directions. It is required that μmatch have a value of less than 5 (see Fig. 1(c) and (d)). The position of the cut was chosen to minimise the background while retaining signal.In order to reduce background from dimuon events, it is required that the momentum of the highest momentum particle in at least one of the two jets in the event, i.e., p1 in the candidate jet and p1-opp in the opposite jet, must be less than 40 GeV/c (see Fig. 2(a)).Although the τ−→μ−ν̄μντ candidates in general are expected to have one track, in approximately 2% of these decays a radiated photon converts to an e+e− pair, resulting in one or two extra tracks in the tracking chamber. In order to retain these jets but eliminate background jets, it is required that the scalar sum of the momenta of the two lower-momentum particles, p2+p3, must be less than 4 GeV/c (see Fig. 2(b)). In cases where there is only one extra track, p3 is taken to be zero.The above criteria leave a sample of 31395 candidate τ−→μ−ν̄μντ jets. The quality of the data is illustrated in Fig. 3, which shows the momentum of the candidate muon for jets which satisfy the τ−→μ−ν̄μντ selection. The backgrounds remaining in this sample are discussed in the next section.4Backgrounds in the τ−→μ−ν̄μντ sampleThe background contamination in the signal τ−→μ−ν̄μντ sample stems from other τ decay modes and from residual non-τ background in the τ+τ− sample. The procedure used to evaluate the background in the τ−→μ−ν̄μντ sample is identical to the one used to evaluate the background in the τ+τ− sample, which is outlined in Section 2.The main backgrounds from other τ decay modes can be separated into τ−→h−⩾0π0ντ, and a small number of τ−→h−h−h+⩾0π0ντ jets. The τ−→h−⩾0π0ντ decays can pass the τ−→μ−ν̄μντ selection when the charged hadron punches through the calorimeters, leaving a signal in the muon chambers. The absence or presence of π0s has no impact on whether or not the jet is selected, since there are over 60 radiation lengths of material in the detector in front of the muon chambers. The modelling of this background is tested by studying τ−→μ−ν̄μντ jets with large deposits of energy in the electromagnetic calorimeter. The distribution of jet energy, Ejet, deposited in the electromagnetic calorimeter is shown in Fig. 4(a). The τ−→h−⩾0π0ντ fractional background estimate is 0.0225±0.0016, of which approximately 75% includes at least one π0.The main backgrounds resulting from contamination in the τ+τ− sample are e+e−→(e+e−)μ+μ− and e+e−→μ+μ− events. The e+e−→(e+e−)μ+μ− contribution in the τ−→μ−ν̄μντ sample was evaluated by fitting the Monte Carlo distribution of the acollinearity angle, θacol, to that of the data, where the acollinearity criterion in the τ+τ− selection which requires that θacol<15° has been relaxed, and ptot is required to be less than 20 GeV/c, as shown in Fig. 4(b). This resulted in a fractional background estimate of 0.0052±0.0026. For this particular background, the quoted uncertainty also takes into account the spread in the fitted normalization when the range of θacol is extended to 20 and to 25 degrees. This is motivated by a discrepancy between the data and the Monte Carlo simulation which can be seen in the region where θacol>20°.The contribution of dimuon events (e+e−→μ+μ−) was enhanced in the τ−→μ−ν̄μντ sample by removing the requirement that p1-opp<40 GeV/c or p1<40 GeV/c, and instead requiring that p1>40 GeV/c. The distribution of p1-opp was then used to evaluate the agreement between the data and the Monte Carlo simulation for this background. The resulting estimate of the dimuon fractional background in the τ−→μ−ν̄μντ sample is 0.0029±0.0006. The corresponding distribution is shown in Fig. 4(c).Signal events with three tracks are due to radiative τ−→μ−ν̄μντ decays where the photon converts in the tracking chamber to an e+e− pair, whereas the three-track background consists mainly of jets with three pions in the final state. Electrons and pions have different rates of energy loss in the OPAL tracking chamber, and hence the background can be isolated from the signal by using the rate of energy loss as the particle traverses the tracking chamber, dE/dx, of the second-highest-momentum particle in the jet. The Monte Carlo modelling was compared to the data as shown in Fig. 4(d), yielding a fractional background measurement of 0.0014±0.0003.The remaining background in the τ−→μ−ν̄μντ sample is almost negligible and is estimated from the Monte Carlo simulation. The total estimated fractional background in the τ−→μ−ν̄μντ sample after the selection is 0.0324±0.0031. The main background contributions are summarized in Table 2.5The branching ratioThe τ−→μ−ν̄μντ branching ratio is given by (1)B=N(τ→μ)Nτ(1−fbk)(1−fτbk)1ϵ(τ→μ)1Fb, where the first term, N(τ→μ)/Nτ, is extracted from the data and is the number of τ−→μ−ν̄μντ candidates after the τ−→μ−ν̄μντ selection, divided by the number of τ candidates selected by the τ+τ− selection. The remaining terms include the estimated fractional backgrounds in the τ−→μ−ν̄μντ and τ+τ− samples, fbk and fτbk, respectively, which must be subtracted off the numerator and denominator in the first term of Eq. (1). The evaluation of these backgrounds has been discussed in Sections 2 and 4. The efficiency of selecting the τ−→μ−ν̄μντ jets out of the sample of τ+τ− candidates is given by ϵ(τ→μ). The Monte Carlo prediction of the efficiency is cross-checked using a control sample, and will be discussed in Section 5.1. Fb is a bias factor which accounts for the fact that the τ+τ− selection does not select all τ decay modes with the same efficiency, and will also be explained in more detail in Section 5.1. The corresponding values of these parameters for the τ−→μ−ν̄μντ selection are shown in Table 3. Eq. (1) results in a branching ratio value of B(τ−→μ−ν̄μντ)=0.1734±0.0009±0.0006, where the first error is statistical and the second is systematic.5.1Systematic checksThe statistical uncertainty in the branching ratio is taken to be the binomial error in the uncorrected branching ratio, N(τ→μ)/Nτ. The systematic errors include the contributions associated with the Monte Carlo modelling of each of the main sources of background in the τ−→μ−ν̄μντ sample, the error in the efficiency, the error in the background in the τ+τ− sample, and the error in the bias factor. These errors are listed in Table 3 and their contribution to the error in the branching ratio is shown in Table 4. The errors in the backgrounds have already been discussed in Sections 2 and 4. A discussion of the error in the efficiency and in the bias factor follows.A second sample of τ−→μ−ν̄μντ data candidates was selected using information from the tracking chamber plus the electromagnetic and hadronic calorimeters. The selection looks for jets with one to three tracks satisfying p2+p3<4 GeV/c, and which leave little energy in the electromagnetic or hadronic calorimeters but still leave an observable signal in several layers of the hadronic calorimeter. This yields a sample of 28042 τ−→μ−ν̄μντ jets and results in a branching ratio of 0.1730 with a measured fractional background of 0.0396 and an efficiency of 0.7853. The candidates selected using this calorimeter selection are highly correlated with those selected for the main branching ratio analysis using the tracking selection, even though the two selection procedures are largely independent. Because of the high level of correlation, the advantage of combining the two selection methods is negligible; however, the calorimeter selection is very useful for producing a control sample of τ−→μ−ν̄μντ jets which can be used for systematic checks.A potentially important source of systematic error in the analysis is the Monte Carlo modelling of the selection efficiency. In order to estimate the error on the efficiency, both data and Monte Carlo simulated jets are required to satisfy the calorimeter selection criteria. This produces two control samples of candidate τ−→μ−ν̄μντ jets, one which is data, and one which is Monte Carlo simulation. The efficiency of the tracking selection is then evaluated as the fraction of jets in the calorimeter sample which pass the tracking selection. The ratio of the efficiency found using the data to the efficiency found using the Monte Carlo simulation is 1.0002±0.0024. The uncertainty in the ratio was taken as the systematic error in the τ−→μ−ν̄μντ selection efficiency.Further checks of the Monte Carlo modelling are made by varying each of the selection criteria and noting the resulting changes in the branching ratio. The requirement on the number of tracks was changed to allow only one track in the jet, in order to remove the radiative decays with photon conversions. This was found to change the branching ratio by 0.0003. Changing the requirement on Nmuon from two to one resulted in a branching ratio change of 0.0002. Removing this criterion entirely resulted in a change of 0.0003. Varying the μmatch value of the match between a tracking chamber track and a muon chamber track by ±1/2 resulted in changes of 0.0002. The requirement on p1-opp was changed by ±2 GeV/c and resulted in a change of 0.00001. Removing the requirement of p1-opp entirely results in a similar change. All of these changes are within the systematic uncertainty that has already been assigned due to the background and efficiency errors, which are equivalent to an uncertainty in the branching ratio of 0.0005. Thus one has confidence that the error in the modelling of the background and the signal does not exceed the error already quoted.The τ Monte Carlo simulations create events for the different τ decay modes in accordance with the measured τ decay branching ratios [15]. However, the τ+τ− selection does not select each τ decay mode with equal efficiency. This can introduce a bias in the measured value of B(τ−→μ−ν̄μντ). The τ+τ− selection bias factor, Fb, measures the degree to which the τ+τ− selection favours or suppresses the decay τ−→μ−ν̄μντ relative to other τ decay modes. It is defined as the ratio of the fraction of τ−→μ−ν̄μντ decays in a sample of τ decays after the τ+τ− selection is applied, to the fraction of τ−→μ−ν̄μντ decays before the selection. The dependence of the bias factor on B(τ−→μ−ν̄μντ) was checked by varying the branching ratio within the uncertainty of 0.0007 given in Ref. [15]. This resulted in negligible changes in the bias factor. In addition, extensive studies of systematic errors in the bias factor have been made in previous OPAL τ-decay analyses [1,16], including rescaling the centre-of-mass energy and then recalculating the bias factor, and smearing some Monte Carlo variables and then again recalculating the bias factor. These checks have indicated that the systematic effects do not contribute to the uncertainty in a significant manner compared with the statistical uncertainty, and so we have not included a systematic component in the error.6DiscussionThe value of B(τ−→μ−ν̄μντ) obtained in this analysis can be used in conjunction with the previously measured OPAL value of B(τ−→e−ν̄eντ) to test various aspects of the Standard Model. For example, the Standard Model assumption of lepton universality implies that the coupling of the W boson to all three generations of leptons is identical. The leptonic τ decays have already provided some of the most stringent tests of this hypothesis (see, for example, [1]). With the improved precision of B(τ−→μ−ν̄μντ) presented in this Letter, it is worth testing this assumption again. In addition, the leptonic τ branching ratios can be used to measure the Michel parameter η, which can be used to set a limit on the mass of the charged Higgs particle in the Minimal Supersymmetric Standard Model. These topics are discussed below.6.1Lepton universalityThe Standard Model assumption of lepton universality implies that the coupling constants ge, gμ, and gτ are identical, thus the ratio gμ/ge is expected to be unity. This can be tested experimentally by taking the ratio of the corresponding branching ratios, which yields (2)B(τ−→μ−ν̄μντ)B(τ−→e−ν̄eντ)=gμ2ge2f(m2μ/m2τ)f(m2e/m2τ), where f(m2e/m2τ)=1.0000 and f(m2μ/m2τ)=0.9726 are the corrections for the masses of the final state leptons [17]. We use Eq. (2) to compute the coupling constant ratio, which, with the value of B(τ−→μ−ν̄μντ) from this work and the OPAL measurement of B(τ−→e−ν̄eντ)=0.1781±0.0010[1], yields gμge=1.0005±0.0044, in good agreement with expectation. The OPAL measurements of the branching ratios B(τ−→e−ν̄eντ) and B(τ−→μ−ν̄μντ) are assumed to be uncorrelated.In addition, the τ−→μ−ν̄μντ branching ratio can be used in conjunction with the muon and τ masses and lifetimes to test lepton universality between the first and third lepton generations, yielding the expression (3)gτ2ge2=B(τ−→μ−ν̄μντ)mμ5mτ5τμττf(m2e/m2μ)f(m2μ/m2τ)1+δRCμ1+δRCτ. The values 1+δRCτ=0.99597 and 1+δRCμ=0.99576, which take into account photon radiative corrections and leading order W propagator corrections, and f(m2e/m2μ)=0.9998, are obtained from Ref. [17]. Using the OPAL value for the τ lifetime, ττ=289.2±1.7±1.2 fs [18], the BES Collaboration value for the τ mass, mτ=1777.0±0.3 MeV/c2[19], and the Particle Data Group [15] values for the muon mass, mμ, and muon lifetime, τμ, we obtain gτge=1.0031±0.0048, again in good agreement with the Standard Model assumption of lepton universality. If one assumes lepton universality, then Eq. (3) can be rearranged to express the τ lifetime as a function of the branching ratio B(τ−→μ−ν̄μντ). The resulting relationship is plotted in Fig. 5.6.2Michel parameter η and the charged Higgs massThe leptonic τ branching ratios can be used to probe the Lorentz structure of the matrix element through the Michel parameters [3,20], η, ρ, ξ, and δ, which parameterize the shape of the τ leptonic decay spectrum. In the Standard Model V-A framework, η takes the value zero. A non-zero value of η would contribute an extra term to the leptonic τ decay widths. This effect potentially would be measurable by taking the ratio of branching ratios, as in Eq. (4)[21], (4)B(τ−→μ−ν̄μντ)B(τ−→e−ν̄eντ)=0.97261+4ηmμmτ. The B(τ−→μ−ν̄μντ) result presented here, together with the OPAL measurement of B(τ−→e−ν̄eντ)[1] and Eq. (4), then results in a value of η=0.004±0.037. This can be compared with a previous OPAL result of η=0.027±0.055 [3] which has been obtained by fitting the τ decay spectrum.In addition, a non-zero η may imply the presence of scalar couplings, such as those predicted in the Minimal Supersymmetric Standard Model. The dependence of η upon the mass of the charged Higgs particle in this model, mH±, can be approximately written as [21,22](5)η=−mτmμ2tanβmH±2, where tanβ is the ratio of the vacuum expectation values of the two Higgs fields. Thus, η can be used to place constraints on the mass of the charged Higgs. A one-sided 95% confidence limit using the η evaluated in this work gives a value of η>−0.057, and a model-dependent limit on the charged Higgs mass of mH±>1.28tanβ.7ConclusionsOPAL data collected at energies near the Z0 peak have been used to determine the τ−→μ−ν̄μντ branching ratio, which is found to be B(τ−→μ−ν̄μντ)=0.1734±0.0009(stat)±0.0006(syst). This is the most precise measurement to date, and is consistent with the previous OPAL measurement [2] and with previous results from other experiments [15].The branching ratio measured in this analysis, in conjunction with the OPAL τ−→e−ν̄eντ branching ratio measurement, has been used to verify lepton universality at the level of 0.5%. Although lepton universality has been tested to precisions of 0.2% using pion decays, the scalar nature of pions constrains the mediating W boson to be longitudinal, whereas τ decays involve transverse W bosons, making these two universality tests potentially sensitive to different types of new physics.In addition, these branching ratios have been used to obtain a value for the Michel parameter η=0.004±0.037, which in turn has been used to place a limit on the mass of the charged Higgs boson, mH±>1.28tanβ, in the Minimal Supersymmetric Standard Model. This result is complementary to that from another recent OPAL analysis [23], where a limit of mH±>1.89tanβ has been obtained from the decay b→τ−ν̄τX.AcknowledgementsWe particularly wish to thank the SL Division for the efficient operation of the LEP accelerator at all energies and for their close cooperation with our experimental group. In addition to the support staff at our own institutions we are pleased to acknowledge the –Department of Energy, USA,–National Science Foundation, USA,–Particle Physics and Astronomy Research Council, UK,–Natural Sciences and Engineering Research Council, Canada,–Israel Science Foundation, administered by the Israel Academy of Science and Humanities,–Benoziyo Center for High Energy Physics,–Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and a grant under the MEXT International Science Research Program,–Japanese Society for the Promotion of Science (JSPS),–German–Israeli Bi-national Science Foundation(GIF),–Bundesministerium für Bildung und Forschung, Germany,–National Research Council of Canada,–Hungarian Foundation for Scientific Research,OTKA T-029328, and T-038240,–The NWO/NATO Fund for Scientific Reasearch, The Netherlands.References[1]OPAL CollaborationGAbbiendiPhys. Lett. B4471999134[2]OPAL CollaborationRAkersZ. Phys. C661995543[3]OPAL CollaborationKAckerstaffEur. Phys. J. C819993[4]OPAL CollaborationGAlexanderPhys. Lett. B3881996437[5]OPAL CollaborationKAhmetNucl. Instrum. Methods A3051991275OPAL CollaborationP.PAllportNucl. Instrum. Methods A324199334OPAL CollaborationP.PAllportNucl. Instrum. Methods A3461994476[6]SJadachB.F.LWardZWa̧sComput. Phys. Commun.791994503[7]SJadachComput. Phys. Commun.761993361[8]JAllisonNucl. Instrum. Methods A317199247[9]TSjöstrandComput. Phys. Commun.82199474[10]SJadachWPlaczekB.F.LWardPhys. Lett. B3901997298[11]RBhattacharyaJSmithGGrammerPhys. Rev. D1519773267J.A.MVermaserenGGrammerPhys. Rev. D1519773280[12]OPAL CollaborationGAlexanderPhys. Lett. B2661991201OPAL CollaborationPActonPhys. Lett. B2881992373[13]OPAL CollaborationGAbbiendiEur. Phys. J. C192001587[14]OPAL CollaborationGAlexanderZ. Phys. C521991175[15]Particle Data GroupD.EGroomEur. Phys. J. C1520001[16]OPAL CollaborationKAckerstaffEur. Phys. J. C41998193[17]W.JMarcianoASirlinPhys. Rev. Lett.6119881815[18]OPAL CollaborationGAlexanderPhys. Lett. B3741996341[19]BES CollaborationJ.ZBaiPhys. Rev. D53199620[20]LMichelProc. Phys. Soc. A631950514[21]AStahlPhys. Lett. B3241994121and references therein[22]M.TDovaJSwainLTaylorNucl. Phys. B (Proc. Suppl.)761999133[23]OPAL CollaborationGAbbiendiPhys. Lett. B52020011