The purely leptonic decays Ds -> mu nu and Ds -> tau nu are studied in a sample of four million hadronic Z decays collected in 1991--1995 with the ALEPH detector at LEP. The tau nu channel is analyzed in the tau -> e nu nubar and mu nu nubar final states. The branching fraction measurements are used to extract the pseudoscalar decay constant f_Ds

Pütz, J

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ALEPH 98{063CONF 98{0338 July 1998Abstract Registration Number 937Parallel session: 9Plenary session: 11P R E L I M I N A R YLeptonic decays of the DsmesonThe ALEPH CollaborationAbstractThe purely leptonic decays Ds!  and Ds!  are studied in a sample offour million hadronic Z decays collected in 1991{1995 with the ALEPH detectorat LEP. A linear discriminant analysis is used to measure the branching fractionB(Ds! ) = [0:64  0:08(stat)  0:21(syst)  0:15(BR)]%. Within theStandard Model, this result corresponds to fDs= [284 18(stat) 49(syst)34(BR)]MeV.ALEPH contribution to 1998 summer conferencesContact person: John Putz (John.Putz@cern.ch)OPEN-99-30808/07/981 IntroductionThe branching fraction of the Dsto a lepton and a neutrino is interesting because in thequark model it represents the annihilation of the Dsmeson's constituent quark and anti-quark. The rate of these decays is governed partly by the quark{anti-quark wavefunctionat the origin. This quantity is parametrized by the Dsdecay constant fDs. Besides itsown intrinsic interest this measurement is useful because it sheds light on the theoreticalunderstanding of the decay constants of other heavy mesons. The B and Bsmesondecay constants inuence the B-B mixing rates. At present these decay constants cannotbe measured experimentally, so the interpretation of mixing measurements depends ontheoretical calculations. Better experimental determination of fDswill serve as a valuablecheck on these calculational techniques. Knowing the values of fBand fBswill allow for theextraction of the third generation CKM matrix elements from the B mixing measurementsand further constrain the three-generation mixing unitarity triangle.The branching fraction for the leptonic decay Ds! ` is given byB(Ds! `) = DsG2F8f2DsjVcsj2MDsM2` 1 M2`M2Ds!2; (1)where Dsis the lifetime of the Dsmeson, GFis the Fermi coupling constant, Vcsis aCKM matrix element, and M`and MDsare the lepton and Dsmasses.2 Data sample and event selectionThe selection is optimized to select e+e ! cc events containing the decay Ds! . Thepreselection of hadronic Z decays is performed according to the standard ALEPH selectionbased on charged tracks. The cut on the minimum number of reconstructed charged trackscoming from the area of the interaction point is tightened to reduce the background frome+e ! + events. The event thrust axis is required to satisfy jcos thrustj < 0:8 toselect events within the acceptance of the vertex detector. A loose muon identicationalgorithm based on muon chamber hits and the digital pattern information from thehadron calorimeter is used to select muon candidates.A kinematic t is then performed in order to improve the resolution on the missingmomentum, assumed to arise from the undetected neutrino from Ds! . In this t,the missing mass is constrained to be zero and the Dsdisplacement direction (from theprimary event vertex to some point on the muon track) is constrained to be parallelto the Dsmomentum direction. The energies of the reconstructed charged and neutralparticles are varied in the t, while their directions are held constant. The event primaryvertex and the Dsdecay vertex are also allowed to vary within their uncertainties. Theenergy resolutions for charged, neutral electromagnetic, and neutral hadronic objects areparametrized from simulated events. The tted energy of the Dscandidate (the muonand the neutrino) is required to be greater than 15GeV.To reduce background from bb events, selections are made based on a set of rapid-ity and impact parameter dependent hemisphere variables. An existing ALEPH lifetimetag [3] was modied to include a dependence on the rapidity of the charged tracks in theevent. Events from cc are expected to have higher rapidity tracks relative to the jet axes1than bb events because of the lower mass of c hadrons compared to b hadrons. Addition-ally, if one excludes the identied muon, signal events will only have fragmentation tracksin the muon hemisphere, and can be distinguished from other cc events. The tracks ineach hemisphere are divided according to whether their rapidity is greater or less thana certain value. The probabilities that the sets of high and low rapidity tracks in eachhemisphere originate from the Z production point are then calculated. Cuts are made onthe probabilites for the low rapidity tracks in each hemisphere, and on the high rapiditytracks' probability in the muon hemisphere.Finally, to distinguish signal from the remaining primarily cc and bb backgroundevents a hard cut is made on the energy of the tted Dscandidate (> 25GeV). The lep-tonic branching fractions are extracted by means of a tting procedure which is designed todistinguish between the two principal background components separately. Two linear dis-criminant variables are created. One is constructed specically to separate cc ! Ds! events from bb background events (mainly containing semileptonic b and c decays), andanother to separate them from cc background events (mainly containing semileptonic cdecays). The linear discriminant variables Uband Ucare linear combinations of vari-ables which optimally distinguish between two distributions. Each linear discriminantvariable is a linear combination of fteen variables. Plots of the distributions for thecc ! Ds!  events and the respective background events are shown in Fig. 1.The procedure to t for the Ds!  (plus Ds! ) component in the data consistsof tting slices of the invariant mass distribution of the  and  combination in 36 bins(66) in the (Ub; Uc) plane simultaneously. Fitting functions are generated by separatelytting the mass distributions for each event type in each slice. One to three Gaussiansare used depending on the number of events in the slice. The ts for each event typeare normalized to one another according to the Monte Carlo predictions. In the t tothe data the backgrounds are divided into two categories, bb events and all other events(including udsc events and the few remaining e+e ! + events). The normalizationof each background component is allowed to vary separately, while the shapes are xed.The signal distribution combines the purely leptonic Dsdecays from cc and bb events; itincludes a small fraction from D+!  and D+!  which are nearly indistinguishablefrom Dsleptonic decays. The constraint B(Ds! )=B(Ds! ) = 9:75 (from Eq. 1)is imposed.3 ResultsThe t to the data, summed over all 36 slices, is shown in Fig. 2. Figure 3 shows the dataplus the tted composition of Monte Carlo events for each of four regions in the (Ub; Uc)plane.The tted branching fraction is B(Ds! ) = (0:670 0:083)%. The tted numberof signal events is 747  93, while the total number of background events is 5496. Theindividual contributions are shown in Table 1.2-0.5-0.2500.250.50.7511.251.50 1 2 3 4 5UbMC bb– bkg-0.5-0.2500.250.50.7511.251.50 1 2 3 4 5cc–→Ds→µν-1-0.75-0.5-0.2500.250.50.7511.251.50 1 2 3 4 5Mass(µν) GeVUcMC cc– bkg-1-0.75-0.5-0.2500.250.50.7511.251.50 1 2 3 4 5cc–→Ds→µνMass(µν) GeVFigure 1: Unnormalized Ubvs M() (top) and Ucvs M() (bottom) distributions forbb background (left) and cc ! Ds!  (right), and cc background and cc ! Ds! ,respectively. The same cuts used in the tting procedure are applied here.30200400600800100012000 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5ALLCHAN   5876.0501001502002500 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5ALLCHAN   697.9Mass(µν) GeVNo. Entries / 0.5 GeVFigure 2: The t to the mass distribution in the data summed over all 36 slices. The dataare the crosses. The top plot shows the data and the tted contributions. The dashedcurve is the sum of all contributions. The dot-dash curve shows the bb background events.The dotted curve is the udsc background. The solid curve is the signal. The bottom plotshows the data minus the background, and the curve is the tted signal contribution.4Table 1: Fitted numbers of events in the individual signal and background components.Source No. EventsSignal:cc ! Ds!  185cc ! Ds!  386bb! Ds!  108bb! Ds!  23D+! ` 46Total 747Background:uds 593cc 2864bb 2024+ 15Total 54964 Systematic uncertaintiesThere is a small bias in the tting procedure when run on Monte Carlo events. The ttedsignal amplitude is overestimated by a factor of 1.048. The fractional uncertainty due tothe limited Monte Carlo statistics is 0.087.The production fractions of charmed mesons in bb and cc events are renormalizedaccording to the most recent ALEPH measurements. Applying the corrections to theMonte Carlo distributions produces a shift in the tted leptonic branching fraction. Theproduction fractions are also varied according to their experimental uncertainties. Thesum in quadrature of the variations in the resulting branching fraction measurement plushalf the shift is taken as the uncertainty on the branching fraction measurement.The uncertainty in the signal eciency due to the muon identication eciency andthe uncertainty on the fragmentation parameter for the signal events is estimated. Themuon eciency is reduced by 20% in the Monte Carlo for muons with P < 3GeV andthe data is retted. The uncertainty due to fragmentation is estimated by lowering theenergy cut on the Dscandidate by 2%. The resulting change in the fraction of signalevents predicted by Monte Carlo is taken as the uncertainty.A check on the assumed = signal ratio is done by allowing the  and  branchingfractions to vary independently. The results of this t are B(Ds! ) = (0:5960:246)%and B(Ds! )=B(Ds! ) = 11:8 7:0, consistent with the branching fraction ttedabove and with the expected = ratio of 9.75.There remain other signicant systematic errors to estimate. The fragmentationparametrization needs to be varied. The composition and properties of the principalbackground components need to be understood. A check on the t can also be performedby running the analysis to look for Ds! e, which is expected to be extremely smalldue to helicity suppression. The signal eciency can be better estimated by analyzingDs!  decays. The reason for the bias in the tting routine needs to be understood.5Table 2: Summary of systematic errors.Source Fractional uncertaintyFit bias  MC statistics +0:048 0:087Hadron production fractions:=2 0:032 0:056Physics parameters:f(c ! Ds) 0:133 0:195 (BR)f(c ! D+) 0:005f(b! Ds) 0:019 0:041 (BR)f(b! D+) 0:001B(D+! )=B(Ds! ) 0:003B(D+! )=B(Ds! ) 0:002Signal eciency: identication 0:01Fragmentation 0:04Background shape:( 5 hadron prod unc) 0:30Total bias and uncertainty +0:05 0:34 0:24 (BR)The eect of detector resolution on the results must be examined.Table 2 summarizes the systematic uncertainties which have been estimated. Theuncertainties under the heading physics parameters refer to uncertainties on the signal.The largest component comes from f(c ! Ds) which almost corresponds to the overallnormalization of the signal, since the contributions from the bb! Ds!  and D+! `channels are small. The errors labelled (BR) refer to the uncertainty in the measurementof Ds! . The background shape uncertainty is a conservative estimate which includesas yet unaccounted for eects relating to the shape of the background distributions.5 ConclusionsA preliminary measurement of B(Ds! ) has been made. The result is B(Ds! ) =[0:64 0:08 0:21 0:15(BR)]%. This value corresponds to B(Ds! ) = 6:2%, underthe assumption B(Ds! )=B(Ds! ) = 9:75 which is assumed in the t to the data.The decay constant fDsis calculated to be [284 18 49 34(BR)]MeV.6References[1] L3 Collaboration, Phys. Lett. B 396 (1997) 327.[2] DELPHI Collaboration, International Europhysics Conference on High EnergyPhysics, Jerusalem, 19{26 August 1997, contributed paper 455.[3] ALEPH Collaboration, D. Buskulic et al., Phys. Lett. B313 (1993) 535.701002003004005006000 1 2 3 4 5ALLCHAN   3153.Uc<0.1 & Ub<0.450204060801001201400 1 2 3 4 5ALLCHAN   943.0Uc>0.1 & Ub<0.450501001502002503003500 1 2 3 4 5ALLCHAN   1223.Uc<0.1 & Ub>0.45bkg+sigudscbb–sig0204060801001200 1 2 3 4 5ALLCHAN   557.0Uc>0.1 & Ub>0.45Figure 3: Data divided into four regions in the (Ub; Uc) plane. The histograms are thetted contributions from udsc background, bb background, and signal events.8

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