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Nuclear Physics B (Proc. Suppl.) 27 (1992) 158-163North-Holland

THE SEMILEPTONIC DECAY RATES AND FRAGMENTATION PARAMETERS OF b AND c STATES

Gary TAYLOR, representing the ALEPH Collaboration

Imperial College, LONDON

From a fit to the p,pl distributions of single electron and muon candidates in a sample of 127 083 hadronicZ decays, collected using the ALEPH detector at LEP, measurements of the average semileptonic branchingratios B(b --+ 1) and B(c -; 1) are obtained. In the fit Standard Model values are assumed for the branchingratios Z --+ bb/Z -* qq- = 0.217 and Z -> cc/Z -+ qq- = 0.171 . In the fit the heavy quarks are assumedfragment according to the model of Peterson et al.. Within the framework of this model the mean valuesX = Ehdr~lEa~am are obtained for both b and c states .

1. INTRODUCTION

Within the framework of the spectator model theheavy masses of the b and c quarks are assumed to sup-press QCD effects, allowing the decays of heavy flavourhadrons to be treated essentially as those of free heavyquarks. This approximation should be more applica-ble to the heavier b quark and to the case of semilep-tonic decays, where the number of final state quarksis smaller. In such a model the lifetime and branchingratios of all heavy flavour hadrons are identical. In thec sector large deviations from the spectator model havebeen observed with the semileptonic branching ratio ofthe D+ meson measured to be about 2.5 times largerthan that of the D° [1].

In a pure spectator model the semileptonic branch-ing ratio of b hadrons is expected to be ;zz: 13 - 15%.At the T(4S), where for kinematical reasons only B+and B° mesons can be produced, the average valueof the b semileptonic branching ratio has been mea-sured to be 10.3 f 0.7%, possibly indicating the pres-ence of non-spectator contributions. Improved mea-surements of the average, and more importantly of ex-clusive, semileptonic branching ratios will give muchgreater I " into the applicability of the spectatormodel to the b and c sectors.

in this paper we report on a measurement of the av-erage semileptonic branching ratios of b and c quarksobtained from a saraple of 127 083 hadronic Z decayscollected using the ALEPH detector at LEP. Within this

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sample of events electrons andmuons are identified and

their momentum (p) and its component transverse to

their associated jet axes (pi) are measured . The differ-ent p,p.i distributions of leptons from b and c decaysallow a simultaneous fit of both semileptonic branch-

ing ratios to be performed. The method uses a binnedmaximumlikelihood fit to the p, pl distributions of theobserved leptons, with the fragmentation function ofthe heavy flavour quarks constrained to follow that of

Peterson et al . [2] . Within the framework of this model

the mean valucs ,f the fragmentation parameters (XÉ)

and (xÉ) are also obtained .

2. THE ALEPH DETECTOR':AND LEPTON IDEN-TIFICATION

The ALEPH detector has been described in detail

elsewhere [3], so only a brief description is given here.Charged tracks are measured over the angular rangeIcos 01 < 0.95, with 0 the polar angle, by an inner cylin-drical drift chamber (ITC) and alarge cylindrical timeprojection chamber (TPC). These are immersed in amagnetic field of 1 .5 Tesla and together measure themomentum of charged particles with a resolution of

bylp = 0.0008p(GeV/c)-1 ®0.003 [3,4] . TheTPC alsoprovides up to 330 measurements of the specific ion-ization (dEldx) of each charged track. For electronsin hadronic events the dEldx resolution is 4.6% for330 ionization samples. The electromagnetic calorime-ter (ECAL), which surrounds the TPC but is inside

G. Taylor (ALEPH Collaboration) /Sen :ileptonic decayratesandfragmentation parametersofbandc states

the coil of the superconducting solenoid, is used tomeasure electromagnetic energy and, together with theTPC, to identify electrons . It is a lead-proportionaltube calorimeter with cathode-pad readout which hasa resolution for electromagnetic showers of bE/E =

0.025 ® 0.20/x, with E in GeV. It covers the angu-lar region 1 cos 9 1 < 0.98 and is finely segmented intoprojective towers, each subtending an angle of approx-imately 0.8° by 0.8°. They are read out in three longi-Ludinal segments corresponding to thicknesses of 4, 9,and 9 radiation lengths . Muons are identified by thehadron calorimeter (HCAL), composed of the iron ofthe magnet return yoke interleaved with 23 layers ofstreamer tubes, and the muon chambers, an additionaltwo layers of streamer tubes surrounding the calorime-ter . The tubes of the HCAL have a pitch of 1 cm andmeasure ; in two dimensions ; tracks from penetratingparticles within the angular range Icos 9! < 0.98 . Theenergy of hadronic showers is measured by means of acopper pad readout arranged in projective towers, eachsubtending an angle of approximately 3.8° by 3.8° , withan energy resolution of bEIE = 0.85/x, with E inGeV. The muon chambers, covering the same angularrange as the HCAL, are read out by cathode stripsboth parallel and perpendicular to the streamer tubes .Therefore each layer provides a three-dimensional co-ordinate for charged tracks which penetrate the 7.5 in-teraction lengths of material between the interactionpoint and the streamer tubes.

The selection of hadronic events is based on chargedtracks . Each event is required to have at least five"good" charged tracks, where a "good" track is onethat passes through a cylinder of 2 cm radius and 20 cmlength around the interaction point, has I cos 01 < 0.95,and has at least four TPC coordinates . The sum oftheir energies must be greater than 20% of the centre-of-mass energy. This selection has an efficiency of 95%,and the background from TT and two-photon eventshas been estimated to be less than 0.25% . A total of127 083 hadronic Z decays were selected by these cuts .

Leptons are identified in the ALEPH detector bymatching a charged track measured in the TPC and

159

ITC with either an energy deposit consistent with be-ing from an electron in the ECAL, or a pattern of hitsin the HCAL and muon chambers consistent with be-ing from a muon . The identification of leptons withthe ALEPH detector has been discussed elsewhere [5],but someimprovements to the methods presented therehave been made. Electrons are identified by comparingthe ECAL energy deposits in the four towers aroundthe extrapolation of each charged track with that ex-pected for an electron of the measured momentum.This energy must be greater than the expected valueminus 1.6 standard deviations. The average depth ofthe energy deposition in the ECAL is also measuredand required to be in the range -1.8Q to +3.Oo" ofthe -value expected for an electron. At least 50 TPCionization samples are required for an electron candi-date, and a candidate is rejected if the dE/dx is morethan 2.5 standard deviations below the expected value .The same methods as presented in Ref. [5] are used toremove photon conversions and Dalitz pairs from theprompt electron signal and to estimate in the data theefficiency and background to electron identification .

Muons are identified using both the pattern of firedplanes in the HCAL and the three-dimensional coor-dinates of the muon chambers. The requirement ofRef. f5] of having at least one hit in the last threeplanes of the HCAL has been replaced by the require-ment that the track extrapolates to within 4a of a hitin the muon chambers. The rest of the cuts are thesame. The efficiency of the muon chambers has beenmapped using Z -~ IL+FL- events. The efficiency andbackgrounds to muon identification are estimated inthe data by the techniques of Ref. [5] . For this analy-sis, where the highest level of lepton purity is required,lepton identification was restricted to the angular rangecos 01 < 0.6 .

3 . JET RECONSTRUCTION AND P1

The motivation behind using a lepton's momentumand its component transverse to an associated jet axisto distinguish between the contributions from b and cquark decays have been discussed in a previous publica-

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60 80 100Purity (b-4e)(%)

Figure 1:

The variation of selection efficiency withpurity in semileptonic b decays, as the pl cut on thelepton is increased. Values for both the new and olddefinitions of jet axis and pl are shown.

tion [5]. In previous ALEPH analyses [5,6] jet axes wereformed using only information from charged tracks andthe transverse momentum of a lepton was measuredwith respect to the momentum vector of the corre-sponding jet after that lepton had been removed fromthe jet. Detailed Monte Carlo studies [7] have shownthat an improved separation between leptons from pri-mary b decay and those from other sources may beobtained by including in the jet definition some of theneutral electromagnetic and hadronic energy measuredin the calorimeters . The detailed algorithm to makeuse of both neutral and charged energy, without dou-ble counting, has been described in a previous publica-tion [8] . With the use of this algorithm, the average re-constructed energy iL a well-contained hadronic eventis 91 GeV with an r.m.s . of 8GeV. The charged, elec-tromagnetic and hadronic energy fractions observed areon average 59%, 26% and 15% respectively.

With the neutral energy included in the jet defi-nition no discernable difference was observed betweenincluding or excluding the lepton from the definition ofthe jet axis . The more natural definition of includingthe lepton in the jet axis was adopted. The variation ofefficiency with purity in semileptonic b decays, as thep.i cut on the lepton is increased, is shown in Fig. 1,for both the new and the old jet and pl definitions .The efficiency is quoted with respect to the number of

leptons from primary b decay which have p > 3 GeV/c.

It is clear that a substantially higher purity, in the high

pl region, can be obtained using the new definition of

jet axis and pl . The new definition also gives a pu-rity which increases as the p.i cut is increased whileusing the old definition the purity is seen to fall offat very high p1. This somewhat strange behaviour

obtained using the old definition was associated withan increased contribution from primary c decays in thehigh p.i region . This effect was caused by an instabilityin the old pi definition due to the rather low chargedtrack multiplicity of semileptonic c decays .

In the above studies and in the subsequent analysisthe jets were formed using the scaled-invariant-massclustering algorithm [9]. The jet resolution parameterof this algorithm was chosen such that sets of tracksand calorimetric objects were clustered only as longtheir scaled invariant mass was less than 6 GeV.

4. FITTING B(b -> R) AND B(c -* f)In order to extract simultaneously the branching

ratios B(b -+ f) and B(c -+ Q) the lepton sample is di-vided into bins in p and pl. The two branching ratiosare then extracted using a binned maximumlikelihoodfit to the binned p, pl spectra of the inclusive leptoncandidates . The fitting method is similar to that usedin Ref. [5] to measure the partial widths of the Z decay-ing to bb and cc . The number of leptons above back-ground in each bin contains contributions from fourdistinct sources of prompt leptons; primary-c decay,primary-b decay, b -4 c --+ f and b -~ T --> t:

NI(p, pl) = Nhadron(A AL) + Nnon-prompt(A p1 )

+E(p,p1) x [2Nce B(c -* P) E Wk((XÉ) )Ppri(T>> P1-)k

-}-2N66 B(b -~ Q)1Wk((XÉ))pbpri(p,pl)k

+2Nb -b B(b --; c)B(c -+ 1) E Wk((xɻPbsec(p ' p-L)k

--2N66B(b -f T)B(T -~ f)~Wk((XÉ))p (p,pl), " (1)k

The F,1, represent sums over six bins in XE, theb or c hadron energy divided by the LEP beam en-

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F-

G. Taylor (ALEPHCollaboration) ISendlepionic decay rates andfragmentation parametersofbandcstates

Momentum (GeV/c)

Figure 2 :

Projections onto p of the spectrum of ob-served electron and muon candidates with no cut onP1 . AIso shown are the fits to Eqn . 1, broken downinto their various contributions . In the electron casethe results of the fit are shown extrapolated down to 2GeV/c to illustrate the consistency in that region .

ergy, while the Wk((oE)) are fragmentation functionsderived from the LUND-6.3 parton-shower model [10] .Within the LUND program, the fragmentation functionof Peterson et al., is used at the quark level, as a func-tion of z = (E + Pll)hadron/(E + p)quark. pk(p,pl) rep-resents the probability that a heavy hadron undergoingsemileptonic decay with xE in bin k results in a leptonin the bin p, pl and is derived from a full Monte-Carlosimulation including detector effects .

In the fit the Standard Model values of 0.217 and0.171 are used for Nb&/Nhad and NcE/Nhad respectively,B(b --+ -r) is set to 0.31 - B(b -+ 1), according to phase-space calculations [11], and B(T --+ t) is taken to be0.178 f 0.004 [121 .

Four variables are allowed to float freely in the fit :

B(b -> t), B(c -+ t), (XÉ) and (xÉ) . The muons andelectrons are fitted separately in order to check for con-

sistency. The fits are made with six bins in both p and

p1.

The results from these fits are given in Table 1 . To

give a visual impression of these fits, projections ontothe p axis of the data and the best fit are shown in

Fig. 2 for electrons and muons, and projections onto

Transverse momentum (GeV/c)

Figure 3:

Projections onto pl of the spectrum of ob-served electron and muon candidates for p > 3GeV/c .Also shown are the fits to Eqn . 1, broken down intotheir various contributions .

the pl . axis are shown in Fig. 3 .

The fits of the branching ratios are restricted to therange p > 3GeV/c, and use a total of 3644 electroncandidates and 5513 muon candidates . The model fitsthe data well . Results from the independent muon andelectron fits are in good agreement .

The systematic errors were obtained by varying inturn the efficiencies, backgrounds, fragmentation pa-rameters and branching ratios within their estimatederrors . A breakdown of the contribution to these sys-tematic errors from the various component sources isgiven in Table . 2 . The total systematic error for eachchannel was calculated by adding in quadrature the in-dividual contributions. In both cases the largest contri-butions to the systematic error camefrom uncertaintiesin the lepton identification efficiencies and in the levelof predicted background.

The resulting errors on B(b --> t) and (zÉ) which aresensitive mainly to the relatively pure high-p1 region,are small . B(c --> t) and (zÉ) have larger systematicerrors because they are more sensitive to the low plregion where the background is relatively high .

Since the independent results from the electron and

muon channels give consistent results they can be av-

eraged, taking proper account of common systematic

162 (i. Taylor (ALEPHCollaboration) /Semileptonic decay rates andfragmentation parametersofb and c states

Table 1 : The semileptonic decay rates and fragmentation parameters of the b and c quarks from the individualelectron and muon channels. The first error is statistical and the second is systematic .

Table 2: Individual contributions to the systematic errors on the branching ratios and fragmentation param-eters for the electron sample (e), muon sample (u) and common to both (e + p) .

Table 3 .

Electrons and MuonsB(b -> e)

9.90 ± 0.41 ± 0.29B(c-1) 9.33±0.45±0.95AE)

0.714 ± 0.021 ± 0.006(XÉ)

0.465 ± 0.033 ± 0.020

Table 3 :

The Semileptonic decay rates and fragmen-tation parameters of the b and c quarks from the com-bined electron and muon channels . The first error isstatistical and the second is systematic .

errors, to give the combined lepton results shown in

5 . HIGHER ORDER D* RESONANCESFor all of the results given above the Monte Carlo

prediction for the p, p.1 distribution ofleptons from pri-mary b decay was obtained using the model of Kr6nerand Schuler [13] . This model assumes that the semilep-tonic decays of b states are sat�ra_ted by the decaysB -+ Dev and B -+ D*Qü. From measurements atthe T(4S) [14] there is some evidence for contributions

from decays of the type B -> D**w and B --> D*(n7r)Qü .These contributions may account for as much as 40%of the inclusive spectrum . The presence of such addi-tional decays has the effect of softening the lepton mo-mentum spectrum for B's decaying at rest, and hencethe p1 distribution for the measurements made above .While the extent of this contribution is not well knownit does have a significant effect on the determinationof the branching ratio B(b -; f) . To evaluate quantita-tively the effect of these higher order resonances the fitwas redone with a Monte Carlo sample which includeda 7.5% contribution from the decay B --> D**Pv and anequal amount from B -+ D*7rw . The fit results fromthis new Monte Carlo are given in Table. 4 . The valueof B(b --> t) measured increased by 4% which is largerthan the corresponding systematic error quoted in Ta-ble . 3 . The changes to the other fit parameters werewithin the quoted systematic errors . The systematicerrors quoted in Table . 4 contain contributions fromthese higher order resonances corresponding to 50% ofthe effect of introducing them.

Source Variation(%) (xE) (X )B(c --+ t) B(b -->_Q)

Hadron Misidentification (e) 20 0.012 0.002 0.3 0.07 --Non-Prompt Background (e) 20 0.008 0.002 1 .0 0.15Efficiency (e) 3 0.012 0.008 0.4 0.30Hadron Misidentification ( ;L) 100 0.060 0.003 1.1 0.20Non-Prompt Background 17 0.015 0.001 0.8 0.10Efficiency 3 0.013 0.008 0.4 0.30B(b --> c) (e + Ft) 7 0.003 0.000 0.3 0.03NablNQQ (e +.u) 2 0.007 0.000 0.1 0.14

eq (e + l') 5 0.007 0.000 0.2 0.02

Electrons MuonsB(b -~ 1) 9.63 ± 0.57 ± .0.36 10.23±0.60±0.42B(c -> 1) 9.44 ± 0.60 ± .1.20 9.17±0.68±1 .40(ME) 0.720 ± 0.028 ± .0.008 0.706 ± 0.031 ± 0.009ME) 0.475 ± 0.041 ± .0.021 0.431 ± 0.055 ± 0.064

B(bB(c --~(XE)ME)

G. Taylor (ALEPHCollaboration) ISendleptonic decay ratesandfragmentationparanzet®rs ofb and cstates

Table 4:

The semileptonic decay rates and fragmen-tation parameters of the b and c quarks from the com-bined electron and muon channels after correcting fora 15% contribution from D** and D*7r decays . The firsterror is statistical and the second is systematic, includ-ing a contribution for uncertainties in the level of theD** and D*(n7r) decays.

After D** Correctionsf) 10.30 0.43 .0.3535Q)

8.86f 0.43 f .0.980.719 f 0.021 f .0.0060.469 f 0.033 f .0.021

Bearing in mind that the fit results are quite sen-sitive to the detailed shape of the generated leptonmomentum spectra, and that not everybody uses thesame shape to analyse their data, the results obtainedfor B(b -4 R are reasonably consistent with previousmeasurements from the T(4S) [14], the continuum atenergies around 30 Gev/c [15] and at the Z pole [16] .These measurements of B(b -+ 1), which lie mostly in arange between 10% and 11 .5%, are on the other hand,lower than the naive spectator model predictions of 13to 15% . These measurement would appear to indicatethe presence of non spectator model contributions to b

quark decay.

6 . CONCLUSIONSThe semileptonic branching ratios and fragmenta-

tion parameters of both b and c quarks have been mea-sured from an analysis of inclusive lepton production inZ decays . The results obtained are seen to be sensitiveto the amount of higher order resonances produced insemileptonic b decays . The final results obtained to-gether with their systematic errors are summarized inTable . 4.

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4. W.B. Atwood et al., Performance of the AlephTime Projection Chamber, CERN/PPE 91-24(Feb. 1991), to be published in Nucl. Inst . andMeth .

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14. ARGUS Collaboration, H. Albrecht et al., preprintDESY 90-088 .J . Alexander, in: Les Recontres de Physique de laVallee d'Aosta (La Thuile, March 1990 : resultto be published in Phys . Rev. D.CLEO Collaboration, R . Fulton et al., Phys .Rev. D 43, (1990) 3 .

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