measurement of the and b− meson lifetimes

PhyslcsLettersB 307 (1993)194-208 PHYSICS LETTERS B North-Holland

Measurement of the and B - meson lifetimes

ALEPH Collaboration

D. Buskulic, D. Decamp, C. Goy, J.-P. Lees, M.-N. Minard, B. Mours, B. Pietrzyk

Laboratowe de Physique des Parttcules (LAPP), IN2P3-CNRS, 74019 Annecy-le-Vteux Cedex, France

R. Alemany, F. Arizfizabal, P. Comas, J.M. Crespo, M. Delfino, E. Fernandez, M. Fernandez-Bosman, V. Gaitan, L1. Garrido, T. Mattison, A. Pacheco, C. Padilla, A. Pascual

Instttut de Fzstca d'Altes Energws, Umversttat Autonoma de Barcelona, 08193 Bellaterra (Barcelona), Spam 8

D. Creanza, M. de Palma, A. Farilla, G. Iaselli, G. Maggi, M. Maggi, S. Natali, S. Nuzzo, M. Quattromini, A. Ranieri, G. Raso, F. Romano, F. Ruggieri, G. Selvaggi, L. Silvestris, P. Tempesta, G. Zito

INFN Sezwne dl Bart e Dtparttmento di Flslca dell" Umverstth, 70126 Ban, Italy

Y. Chai, H. Hu, D. Huang, X. Huang, J. Lin, T. Wang, Y. Xie, D. Xu, R. Xu, J. Zhang, L. Zhang, W. Zhao

Insntute of H~gh-Energy Physws, Academia Stmca, Beqmg, China 9

L.A.T. Bauerdick 24, E. Blucher, G. Bonvicini, J. Boudreau, D. Casper, H. Drevermann, R.W. Forty, G. Ganis, C. Gay, R. Hagelberg, J. Harvey, S. Haywood, J. Hilgart, R. Jacobsen, B. Jost, J. Knobloch, I. Lehraus, T. Lohse 30, A. Lusiani, M. Martinez, P. Mato, H. Meinhard, A. Minten, A. Miotto, R. Miquel, H.-G. Moser, P. Palazzi, J.A. Perlas, J.-F. Pusztaszeri, F. Ranjard, G. Redlinger 25, L. Rolandi, J. Rothberg 3, T. Ruan, M. Saich, D. Schlatter, M. Schmelling, F. Sefkow, W. Tejessy, H. Wachsmuth, W. Wiedenmann, T. Wildish, W. Witzeling, J. Wotschack

European Laboratory for Partzcle Phystcs (CERN), 1211 Geneva 23, Swttzerland

Z. Ajaltouni, F. Badaud, M. Bardadin-Otwinowska, R. E1 Fellous, A. Falvard, P. Gay, C. Guicheney, P. Henrard, J. Jousset, B. Michel, J.-C. Montret, D. Pallin, P. Perret, F. Podlyski, J. Proriol, F. Prulhibre, F. Saadi

Laboratotre de Phystque Corpusculatre, Umversttd Blatse Pascal, IN2P3-CNRS, Clermont-Ferrand, 63177 Aubzbr e, France

T. Fearnley, J.D. Hansen, J.R. Hansen 2, P.H. Hansen, R. Mollerud, B.S. Nilsson 2

Ntels Bohr Instztute, 2100 Copenhagen, Denmark lo

I. Efthymiopoulos, A. Kyriakis, E. Simopoulou, A. Vayaki, K. Zacharladou

Nuclear Research Center Demokntos (NRCD), Athens, Greece

194 0370-2693/93/$ 06.00 © 1993 Elsevier Science Publishers B.V. All nghfs reserved.

Volume 307, number 1,2 PHYSICS LETTERS B 10 June 1993

J. Badier, A. Blondel, G. Bonneaud, J.C. Brient, G. Fouque, S. Orteu, A. Roug6, M. Rumpf, R. Tanaka, M. Verder~, H. Videau Laboratotre de Physique Nuclbatre et des Hautes Energies, Ecole Polytechmque, IN2P3-CNRS, 91128 Palatseau Cedex, France

D.J. Candlin, M.I. Parsons, E. Veitch

Department of Phystcs, Umverstty of E&nburgh, E&nburgh EH9 3JZ, UK ll

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M. Corden, C. Georgiopoulos, M. Ikeda, J. Lannutti, D. Levintha116 M. Mermikides t, L. Sawyer, S. Wasserbaech

Supercomputer Computations Research Instttute and Dept. of Phystcs, Florzda State Umversity, Tallahassee, FL 32306, USA 13,14,15

A. Antonelli, R. Baldini, G. Bencivenni, G. Bologna 5, F. Bossl, P. Campana, G. Capon, F. Cerutti, V. Chiarella, B. D'Ettorre-Piazzoli 26 G. Felici, P. Laurelli, G. Mannocchi 6 F. Murtas, G.P. Murtas, L. Passalacqua, M. Pepe-Altarelli, P. Picchi 5

Laboratori Naztonalt dell'INFN (LNF-INFN), 00044 FrascatL Italy

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Department of Phystcs and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK 1 l

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Department o f Phystcs, Imperzal College, London SW7 2BZ, UK 11

P. Girtler, E. Kneringer, D. Kuhn, G. Rudolph

Instttut for Expertmentalphyszk, Umversttiit lnnsbruck, 6020 lnnsbruek, Austria 19

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J.-J. Aubert, A.M. Bencheikh, C. Benchouk, A. Bonissent, J. Carr, P. Coyle, J. Drinkard 4, F. Etienne, D. Nicod, S. Papalexiou, P. Payre, L. Roos, D. Rousseau, P. Schwemling, M. Talby Centre de Physzque des Parucules, Facultk des Sciences de Lummy, IN2P3-CNRS, 13288 Marsezlle, France

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J. Boucrot 2, O. Callot, A. Cordier, M. Davier, L. Duflot, J.-F. Grivaz, Ph. Heusse, D.E. Jaffe, P. Janot, D.W. Kim zo, F. Le Diberder, J. Lefrangois, A.-M. Lutz, M.-H. Schune, J.-J. Veillet, I. Videau, Z. Zhang Laboratozre de l'Acckl&ateur Lm~azre, Umverslt~ de Parls-Sud. IN2P3-CNRS. 91405 Orsay Cedex, France

D. Abbaneo, G. Bagliesi, G. Batignam, L. Bosisio, U. Bottigli, C. Bozzi, G. Calderini, M. Carpinelli, M.A. Ciocci, R. Dell'Orso, I. Ferrante, F. Fidecaro, L. Fob, E. Focardi, F. Forti, A. Giassi, M.A. Giorgi, A. Gregorio, F. Ligabue, E.B. Mannelli, P.S. Marrocchesi, A. Messineo, F. Palla, G. Rizzo, G. Sanguinetti, P. Spagnolo, J. Steinberger, R. Tenchini, G. Tonelli, G. Triggiani, C. Vannini, A. Venturi, P.G. Verdini, J. Walsh Dtpartzmento dt Fzstca dell'Umversttiz, INFN Sez~one d~ Ptsa, e Scuola Normale Supertore, 56010 Ptsa, Italy

A.P. Betteridge, J.M. Carter, M.G. Green, P.V. March, Ll.M. Mir, T. Medcalf, I.S. Quazi, J.A. Strong, L.R. West Department of Physics, Royal Holloway & Bedford New College, Umverstty of London, Surrey TW20 OEX, UK 11

D.R. Botterill, R.W. Clifft, T.R. Edgecock, M. Edwards, S.M. Fisher, T.J. Jones, P.R. Norton, D.P. Salmon, J.C. Thompson Parucle Physzcs Dept, Rutherford Appleton Laboratory, Chdton, Dzdcot, Oxon OXl l OQX, UK 11

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J.G. Ashman, W. Babbage, C.N. Booth, C. Buttar, R.E. Carney, S. Cartwright, F. Combley, F. Hatfield, L.F. Thompson 2 Department of Physics, Umverstty of Sheffield, Sheffield $3 7RH, UK tl

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R. Della Marina, G. Giannini, B. Gobbo, F. Ragusa 22

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L. Bellantoni, W. Chen, D. Cinabro 27, J.S. Conway 31, D.F. Cowen 21, Z. Feng, D.P.S. Ferguson, Y.S. Gao, J. Grahl, J.L. Harton, R.C. Jared 7, B.W. LeClaire, C. Lishka, Y.B. Pan, J.R. Pater, Y. Saadi, V. Sharma, M. Schmitt, Z.H. Shi, A.M. Walsh, F.V. Weber, Sau Lan Wu, X. Wu, M. Zheng and G. Zobernig

Department o f Phystcs, Umverslty o f Wzsconsm, Madtson, WI 53706, USA 12

Received 15 March 1993 Editor: K. Winter

The lifetimes of the ~0 and B - mesons have been measured with the ALEPH detector at LEP. Semileptonlc decays

of ~0 and B - mesons were partially reconstructed by identifying events containing a lepton with an associated D *+ or D o meson. The proper time of the B meson was estimated from the measured decay length and the momentum and mass of the D-lepton system. A fit to the proper time of 77 D*+g - and 77 DOg - can&dates, combined with a constraint on the hfetlme ratio ( z_ /z o) arising from the relative rates of observed D*+g - and DOg - events,

+020 +007 (sys t . )ps ,z_ = 1 47 +022 +015 yielded the following hfetimes' z 0 = 1.52_0.18 (stat.)_o 13 ' -019 (stat.)_o 14 (syst.) ps, z - / Z o = 00g+o 19 (stat.)+o IS (syst) .

" ~ v - 0 . 1 5 12

1 Deceased. 2 Now at CERN, PPE Division, 1211 Geneva 23,

Switzerland. 3 Permanent address: Umverslty of Washington, Seattle,

WA 98195, USA. 4 Now at University of Califorma, Irvine, CA 92717, USA 5 Also Ist:tuto dl Fisica Generale, Unlversxt/i dl Tonno,

Tormo, Italy. 6 Also Istituto di Cosmo-Geofisica del C.N.R., Tonno,

Italy. 7 Permanent address: LBL, Berkeley, CA 94720, USA. 8 Supported by CICYT, Spain. 9 Supported by the National Science Foundation of China. 10 Supported by the Danish Natural Science Research

Council. 11 Supported by the UK Science and Engineering Research

Council. lZ Supported by the US Department of Energy, contract

DE-AC02-76ER00881 13 Supported by the US Department of Energy, contract

DE-FG05-87ER40319. 14 Supported by the NSF, contract PHY-8451274. 15 Supported by the US Department of Energy, contract

DE-FCOS-85ER250000. 16 Supported by SLOAN fellowship, contract BR 2703. 17 Supported by the Bundesministerium fur Forschung und

Technologic, Germany 18 Supported by the Directmn des Sciences de la Mati~re,

C.E A.

1. Introduction

Recen t exper imenta l i m p r o v e m e n t s have resulted

m precise measuremen t s o f the average B hadron life-

19 Supported by Fonds zur F6rderung der wissenschaftlichen Forschung, Austria.

2o Supported by the Korean Science and Engineering Foun- dation and Ministry of Educatmn.

21 Now at California Institute of Technology, Pasadena, CA 91125, USA.

22 Now at Dapartimento dl Flsica, Universat~ dl Milano, Malano, Italy.

23 Also at CERN, PPE Division, 1211 Geneva 23, Switzerland.

24 Now at DESY, Hamburg, Germany. 25 Now at TRIUMF, Vancouver, B.C., Canada. 26 Also at Umversit/t dl Napoli, Dlpartimento dl Scienze

Fisiche, Napoll, Italy. 27 Now at Harvard University, Cambridge, MA 02138,

USA. 28 Supported by the US Department of Energy, grant DE-

FG03-92ER40689 29 NOW at Unlverslth di Paxaa, Pavia, Italy. 30 Now at Max-Planck-Institut f. Kernphyslk, Heidelberg,

Germany. 31 Now at Rutgers University, Piseataway, NJ 08854, USA. 32 Now at Oxford University, Oxford OX1 3RH, UK. 33 Partially supported by Coloenclas, Colombia.

197


time [ 1,2], but measurements of the lifetimes of the individual B species are less precise [3 ]. Indirect mea-

surements of the ratio of the ~0 and B - lifetimes have been made as well [4,5].

Knowledge of the ratio of the ~o and B - lifetimes is relevant for a quantitative understanding of the im- portance of non-spectator effects and final state in- teractions in B meson decays. Such effects are large in the charm sector (where ZD+/ZDO ~-- 2.5), but are predicted to be much smaller for B decays [6].

This Letter reports a measurement of the ~0 and B - lifetimes with the ALEPH detector at LEP. Semilep-

tonic decays of fi0 and B - mesons were partially reconstructed by identifying events containing a lepton (e or At) with an associated D O or D *+ meson. The resulting D o -lepton (DOg - ) and D* +-lepton

(D* + g - ) event samples consist mostly of B - and ~-0 decays, respectively (charge conjugate modes are im- plied throughout this Letter). The separation orB meson species in this manner allows a measurement of their individual lifetimes.

2. The ALEPH detector

The ALEPH detector is described in detail else- where [7]. A high resolution vertex detector (VDET) consisting of two layers of silicon with double-sided readout was available for this analysis. It provides measurements in the r-~b and z directions at radii of 6.3 cm and 10.8 cm, with ~_ 12 Atm precision. The VDET provides full azimuthal coverage and polar angle coverage to I cos 01 < 0.85 for the inner layer only and [ cos 01 < 0.69 for both layers [8 ]. Outside VDET particles traverse the inner tracking chamber (ITC) and the time projection chamber (TPC). The ITC is a cylindrical drift chamber with eight axial wire layers at radii of 16 to 26 cm. The TPC measures up to 21 space points per track at radii between 40 and 171 cm, and also provides up to 330 measurements of the ionization ( d E / d x ) of each charged track. Tracking is performed in a 1.5 T magnetic field provided by a superconducting solenoid.

The electromagnetic calorimeter (ECAL) is a lead/wire-chamber sandwich operated in propor- tional mode. The calorimeter is read out in projective towers that subtend typically 15 mrad × 15 mrad in

solid angle and that are segmented m three longitu- dinal sections. The hadron calorimeter (HCAL) uses the iron return yoke as absorber. Hadronic showers are sampled by 23 planes of streamer tubes, with analog projective tower and digital hit pattern readout. The HCAL is used in combination with two layers of muon chambers outside the magnet for muon ldenfffication.

3. Event selection

The D*+g - and DOg - event samples were selected from approximately 260 000 hadronlc decays of the Z, collected m 1991 when the VDET became fully op- erational. Hadromc event selectmn based on charged tracks IS described in ref. [9 ].

The selection of muons and electrons is described in detad in ref. [ 10 ]. For this analysis, lepton candidates were required to have a momentum of at least 3 GeV/c. Electron candidates that had suffered a hard bremstrahlung due to interaction with detector mate- nal have been removed using the technique described in ref. [11].

D *+ and D O candidates were reconstructed from charged tracks that formed an angle of less than 45 ° with the lepton candidate. These charged tracks were also required to intersect an imaginary cylinder of ra- dius 2 cm and half-length 4 cm centered on the nom- inal interaction point, have at least 4 hits in the TPC, have a polar angle 0 such that I cos 0[ < 0.95 and have momentum greater than 200 MeV/c.

D *+ candidates were identified via the decay D *+ --+ DOn +, followed either by D O --+ K - n + or D o -+ K - n + n - n + n - . It is well known that the very low Q value for the decay D *+ -~ DOn + permits the identification of D *+ mesons with low background (a detailed presentation of reclusive D *+ selection is given in ref. [ 12 ] ). In this analysis, the favorable kinematic situation was explmted by requiring that the difference in mass between the D *+ and D o candidates lie within 1.5 MeV/c 2 (approximately two standard deviations of the experimental resolution) of the known value of 145.6 MeV/c z. Since, for these decays, the kaon will have the same electric charge as the lepton coming from the semileptonic decay of the B, this charge correlation was imposed in the reconstruction of D *+ mesons. For the subsample

198


where D O ~ K - n + the momentum of the D O was required to be greater than 5 GeV/c. The subsample with D o --+ K - n + n - n + n - suffers from greater

combinatorial background and therefore the following more stringent selection criteria were applied:

PDO > 8 GeV/c; if there are at least 40 d E / d x wire samples for the K track, its specific ionization must

be within two standard deviations of that expected for a kaon; and at least two of the D o decay tracks

have p > 1 GeV/c. If, for a given detected lepton, more than one combinat ion satisfied these selection criteria, the best combinat ion was selected, based on the values of the reconstructed D o mass and D* + -D o

mass difference.

The D ° g - sample consists of events with a lepton and a D o candidate, where the D o was not the decay product of a D *+. D o candidates were identified via the decay D O ~ K - n +. Again, K candidates were required to have the same charge as the lepton. For this sample, the powerful selection criterion involving the D * + - D ° mass difference was not applicable, making it necessary to apply stricter selection criteria. The D o candidates were required to have PDo > 8 GeV/c, PK > 2 GeV/c and pn > 1.5 GeV/c. Furthermore, the specific lonizaUon of both tracks, if at least 40 wire samples had been recorded, had to be within 2a of that expected of a kaon and a pion, respectively. To reject D o candidates coming from D *+ --+ D ° n +,

a search for the additional pion was performed. If a pion candidate yielding a D * + - D ° mass difference within 1.5 M e V / c z of the known value was found, the

D ° g - candidate was rejected. The efficiency for reconstructing the additional pion and rejecting D o ' s coming from D *+ decays was found to be 85%.

To improve the signal to background ratio and to

ensure well-measured decay lengths, additional selection criteria were placed on all the subsamples. The i nvanan t mass of the D (*)g (where D (*) can be D* + or D o ) system was required to be greater than 3 GeV/c 2. This criterion significantly reduced the combinatorial background, while keeping ,-~ 85% of the signal [ 13 ]. To exploit the high precision of the silicon vertex detector, the lepton track and the D o decay product tracks were required to have at least one VDET hit in both the r-~b and z projecnons (except for the decay D o --+ K - n + n - n + n - , where at least two of the four tracks were required to have VDET hits). Also, the D and B decay vertices were reconstructed (as will

%

o

~ 0 ha

5

0)

17 18 r r lK~ (Cev /e ~)

% ~o

o 25

~ 2o g

10

o 20

19 2 21

m KaTr

c)

6 17 1 8 19 2 21 mK~ (GeV/c=)

9 2 (aev/c')

Fig. 1 The mvarlant mass of D O candidates for the three subsamples, a) D*+g - , D o ---+ K n , b) D*+ g - , D o ~ K 3 n , c) DOg - , D o ---+ K n . The smooth curves are results of the fit described m the text. The mass region below 1.7 GeV/c 2 is excluded from the fit for the D o ~ K - n + samples to avmd a broad peak arising from the decay D O -+ K - n + n ° where the n o goes undetected.

be discussed in section 4) and the )~2 probability for each vertex fit was required to be greater than 1%.

The D o candidate mass spectra for the three subsamples are shown in fig. 1. For D o ~ K - n + the fitted curves consist of a Gaussian for the signal plus a linear background. The width of the Gausslan was fixed at 10 MeV/c 2, determined from a Monte Carlo simulation.

For D o ---, K - n + n - n + n - the use of the D o mass

as one of the criteria to select the best among several candidates for a given event causes the background to exhibit a broad peak centered on the D o mass. A

Gaussian, whose area and width were determined by considering the D o mass spectrum for events that fail the D* + - D o mass difference criterion, was combined with a straight line to describe this background. The signal was described by a Gaussian with the width fixed at 9 MeV/c 2.

The fitted D o mass and the fitted number of signal and background events within a window of ±2~ around the fitted mass for the three samples are shown in table 1.

199

Volume 307, number 1,2 PHYSICS LETTERS B

Table 1 Fitted D O mass and number of D O candidates and background events falling within a mass window of -t-2a.

Subsample Mass (MeV/c 2) Signal events Background events

D*+t - D ° ~ K - ~ + 1866+2 28.4-4-5.4 223=1.1 D*+g - D°-~K-zc+rc-n+n - 18644-2 40.74-7.2 6.7±4.0

DOg - D° ~ K - n + 1864-4-2 65.9-4-8.8 11.7=t=40

10 June 1993

4. Decay length and proper time

Events reconstructed with a D O mass within two standard deviat ions of the fi t ted D O mass were selected for the lifetime analysis, resulting in 77 D*+g- and 77 D°g- candidates. The decay length has been calculated for these events by reconstructing the pn - mary and B decay vertices in three dimensions.

The pr imary vertex reconstruction algori thm com- bines the average beam position, de termined from data for each run, with the track informat ion from the part icular event. After grouping the tracks into jets, tracks wathm each part icular jet were projected into the plane perpendicular to the jet direction. This re- moves any dependence on the lifetime of the particle in the approximat ion that the je t axis reproduces the direction of the b hadron. The pr imary vertex was then calculated as the point that was most consistent with the projected tracks and the beam envelope, which was taken as the average beam posi t ion with the dimensions of the LEP beam spot (N 150 a m x 10 a m × 1 cm). Using this algori thm on sxmulated bb events, an average resolution of the pr imary vertex posi t ion projected along the event sphericity axis of 85 a m is obtained.

The B decay vertex was obtained by first reconstructing the D o decay vertex using its known decay tracks and then extrapolating the neutral D O track backwards where it was combined with the lepton to form the B decay vertex (fig. 2 ). In the case of D*+g- events, the soft pion from the D *+ decay does not improve the resolution on the B decay length and was therefore not used in the reconstruction of the B vertex.

The best estimates of the B decay length 3 and its error aa are obtained by combining the reconstructed pr imary and secondary vertices with the B flight direction, using the formulas

200

Lepton 500 ,~rn

Fig. 2. Schematic representahon of a typical B decay into DOg-.

n,a[]lxj 1

d = ~ , j n, G71n j , a ~ = ~ , j n,a,Ttnj, (1)

to the B decay vertex position, n, is the vector of direction cosines of the B flight direction, and G71 is the inverse of the sum of the error matrices of the pr imary and B vertices. The uncertainty on the flight direction due to the missing neutrino induces a negli- gible error on the decay length. The resolution on the B decay length is typically about 300 #m, compared with an average B decay length of ~ 2.6 m m (assum- ing % = 1.49 ps and an average B momentum of 30 GeV/c ) .

The proper t ime for a decay is the decay length divided by flyc = p /m , however since these events contain an undetected neutrino, the B momentum is not known. A good approximat ion to the proper t ime t is obtained by using the D(*)g system when evaluating

a aa (2) t - (flyc)oe' a t - (flyC)oe"

Then ~ is defined as

~ c - (flY)De (3) (/?v)B "


g-

1000 [- " ~ MONTE CARLO aoo ~- 600 ~-

0 OS ' 'b8 I ' ' ' 12 ' ' ' 14 ' ' 16 1 '8 ' ' ' 2 ' ' 22 ~=(~7)./(#~')~ Fig. 3. Distribution 'of ~ (defined in the text).

A typical distribution of x for Monte Carlo signal events is shown in fig. 3. To perform a maximum likelihood fit for the lifetimes it is necessary to com- pute for each event the probability of observing a proper time t (as obtained from eq. (2)) given the lifetime z. The probability function F (t, at, T) is obtained by convoluting an exponential distribution with the properly normalised ~: distribution. Since this distribution depends on the selection criteria applied, separate ~ distributions are calculated for each subsample.

Due to the finite resolution on the decay length (and hence on the proper time) it is necessary to perform a second convolution with a Gausslan resolution function. It has been determined from a Monte Carlo simulation that the resolution on the proper time is best described by the sum of two Gaussians, where the widths of the Gaussians are given by at multiplied by a scale factor:

l - A 2 e x p [ ( t - t ° ) 2 ] Rres( t - t ° '~r t ) - V/~C1¢7~ 2i~f f - - -~]

e x p [- - + v/~c~r"--~ L 2 (c2a,) 2 J '

(4)

5. ~o and B - lifetimes

The ~o and B - lifetimes cannot be determined by performing separate fits on the two event samples.

Since both samples contain a mixture of ~0 and B - decays, one does not expect their distributions to be described by a single exponential. Furthermore, the

B-/-B ° mixture in the samples depends on the ratio of the lifetimes, as will be discussed below. There-

fore, to measure the T ° and B - lifetimes a simultaneous maximum likelihood fit to all the events was performed. Since each of the two samples contains a

mixture of ~-o and B - decays and of background, the likelihood function contains three components for each sample. The likelihood function is written as

ND*g

. . , )) + fo F(t, ,a, , ro) + fBGF~o(t, /

e NDOg

x ( I ~ f ° - F ( h ' a ' z - ) + f°°F(h 'a"z°) l=l

oo ) + f~GFdG(t,) , (5)

where F (t, a, r) is the probability function for the signal, as described in the previous section. The coefficients f_* and f0* are the fractions of the D*+g- sam-

ple arising from B - and ~0 decays, respectively. Sim- ilarly, f o and f0 ° are the fractions of the D°e- sam-

ple made up of B - and ~-0 decays. The coefficients fB*~ and f o are the background fractions of the samples, while the functions Fff~ (t) and F°o (t) are their normalised proper time distributions.

with parameters cl = 1.12 ± 0.06, c2 = 2.66 -4- 0.42 a n d / / 2 = 0.24 i 0.05. The second term in eq. (4) is necessary to model small non-Gaussian effects in the reconstruction of charged tracks. Due to the good resolution on proper time, the fitted lifetimes are rather insensitive to the precise values o f ct, c2, and A2.

Summarizing, the probability distribution that de- scribes the signal is obtained by convoluting an exponential decay function with the x distribution of fig. 3 and the resolution function of eq. (4).

5 1. Backgrounds

Background contamination arises from the following sources.

( 1 ) combinatorial background, i.e. candidates with a fake D(*);

(2) the process B -~ DsD(*)X, followed by D~- --* g - X , giving rise to a real D (*) and a real lepton;

(3) a real D (*) meson accompanied by a fake or non-prompt lepton, from Z ~ bb or Z ~ c~ events.

201

Volume 307, number 1,2 PHYSICS LETTERS B

Table 2 Background sources and their contnbuUons (in number of events) to the three subsamples.

10 June 1993

Subsample Combinatorial Fake lepton B ---+ D s D(*) X

D * + g - D ° - + K - n + 2.2±1 1 0.9±0.3 0 . 7 ± 0 3 D * + g - D° ~ K - n + n - n + n - 6.7±4.0 1 .5±05 1.0±0.4

DOg - D ° - + K - n + 11.7±4.0 1.9±0.7 1.9±0.7

~. 102

o

m

Ld

o)

-2 0 2 4 Proper time (ps)

-2.1o m

LLJ

- 2 4

Proper t , m e (ps)

&

o m

- 2 0 2 Proper t ime

4 (ps)

1(~

16

~)

- 2

MONTE CARLO

\ I I

Proper time (ps)

Fig 4. Proper time distributions for the three different samples for background due to source (1), a) D*+g - , D O ~ K n , b) D*+g - , D O ---+ K 3 n , c) DOg - , D O --* K n .

The smooth curves are results of the fit described m the text. d) shows the proper time distribution for events arising from background sources (2) and (3), as obtained from a Monte Carlo mmulation.

Source (1) is the dominant background and its contr ibution is determined from a fit to the D o mass distributions, and its magnitude is given in table 1 for the various subsamples. The proper t ime distribution

for this source has been determined from the data by selecting events from the sidebands of the D o peak. The same selection criteria described in section 3 have been applied to the background samples, except that the requirement on the D* + -D o mass difference in the case of the D*+g - events has been removed to increase the statistics. A function consisting of a Gaus- sian plus positive and negative exponential tails was used to describe these data (fig. 4a-c) .

The contribution from source (2) was calculated

from the measured branching ratios for this process [ 14] plus a Monte Carlo simulation to deter-

mine the detection efficiency. The proper time dis- t r ibution for this source was determined from the simulation and is well approximated by an exponential distribution with the mean b hadron lifetime,

Zb = 1.49 ± 0.07 ps [2]. The background from source (3) is estimated from

the known hadron-lepton mlsidentification probabilities and the measured inclusive D o and D *+ rates.

It can be further subdivided into three distinct com-

ponents, - cg events where the fake lepton comes from the

primary vertex, - bb events where the fake lepton comes from the

primary vertex, and - bb events where the fake lepton comes from the

decaying b hadron. The distribution of background source (3) in these three components and their proper time distributions have been determined from a Monte Carlo simulation. The proper time distribution for the sum of sources (2) and (3) for the D * + g - , D O --+ K - g + subsample is shown in fig. 4d. The corresponding distributions

for the other event samples are similar. The estimated number of events due to each back-

ground source for the different subsamples is shown

in table 2.

5 .2 . S a m p l e c o m p o s z t w n s

Each of the two event samples contains a mixture

of ~0 and B - decays, and the sample compositions

(the coefficients f 2 , fo*, f ° a n d f0 ° of eq. (5)) must be calculated to complete the specification of the likelihood function. The difficulty in evaluating the sample compositions arises from incomplete knowledge of the branching ratios of certain decay modes that contribute to the two samples. In particular, the branch-

202


ing ratios for decays of the type #1 B --* D(*)ngu have not been measured. This type of decay is impor tant because it contributes to the amount of B meson of the "wrong" species in the two samples.

The ~0 and B - content o f the two samples were calculated using the following method: the relevant

semileptonic branching ratios for ~o mesons were taken from measurements at the T(4S) energy. Where measurements were incomplete, reasonable assump- tions based on isospin conservation were applied. The B - branching fractions were then obtained from

B(B- --~ g - X ) = r - B ( B ° -+ *-X'), "C o

(6)

which derives from the expectation that the part ial semileptonic decay widths are equal. The sample co-

efficients were then calculated by considering the ~o and B - decay channels that contribute to the D * + g -

and D ° g - samples. As a consequence of this procedure, the coefficients f_*, f0*, f o and f0 ° appearing in the hkel ihood function (eq. (5)) depend on the lifetime ratio. The full calculation, given in detail in the Appendix, shows that the D* + g - sample contains

mostly ~0 decays and the D ° g - sample mostly B - . For example, i f the lifetimes were equal, one would obtain f0* = 0.73 and f * = 0.10 for the D*+g - sample and f_o = 0.64 and f0 ° = 0.20 for the D ° g - sample.

The technique of taking only the measured ~-0 branching fractions and calculating the B - branching fractions using eq. (6) prevents the int roduct ion of a l ifetime bias into the measurement, as would be the

case, for example, i f both the ~-o and B - branching fractions were taken from previous measurements.

~. 25

.~ 20 J ALEPH

a) f ~ D ;g -lepton

Proper hme (ps)

~" 3o u~ ~. 25

20

15

b) t ALEPH D°-Iepton

Proper brae (ps)

Ftg. 5. Proper Ume distributions with result of the fit overlaid for the two samples, a) D*+g- events, b) D°g- events. The solid curve shows the result of the full fit, includmg the event ratio constramt. The dashed curve corresponds to the fit without the event ratio reformation.

1 "10 +028 (stat.) ± 0.06 (syst.) ps , T-- : ~.Ju_027

where the sources of systematic error are discussed in section 6. The two lifetimes are consistent with the average b hadron lifetime and the ratio of the lifetimes is consistent with unity. The proper t ime distr ibutions for the two samples are shown in fig. 5, with the results of the fit overlaid (dashed curve).

As a check on the procedure, a measurement of the D O lifetime has been performed. The D O flight distance is calculated as the distance between the B and D O decay vertices. An unbinned l ikelihood fit to the 154 events yields

5.3. Fi t results too = 0.39 + 0.04 (star.) ps ,

A max imum likelihood fit to the proper Ume dis- t r ibutions of the D*+g - and DOg - events was performed to determine the two free parameters z0 and r_ . The resulting lifetime values are

in good agreement with the world average value qm = 0.420 zk 0.008 ps [ 16 ].

5.4. Event ratm constrmnt

1 ~ 4 + 0 2 5 + 0 0 6 Zo . . . . . . 023 (stat .)-oo5 (syst.) ps ,

#1 ~ ~ D(*)ngg is used to denote decays with non- resonant ~ producUon as well as decays of the type B D**gv.

The statistical precision of the lifetime measurement can be enhanced significantly i f the relative rates of D*+g - and DOg - events are taken into consider- ation. As for the sample composit ions, the expected ratio of the number of D*+g - events to the number

203


of DOg - events (R) is a function of the lifetime ra-

tio, via eq. (6). The dependence of R on the lifetime ratio was used with the observed ratio (Robs) to add a further constraint in the fit.

To measure Robs with greater statistical precision, the selection criteria requiring VDET hits and good

vertex probabilities have been removed. This resulted

in an increase of ~ 40% in the event samples. The observed event ratio was found to be

Robs --- 1.02 ± 0.17 :t: 0.05.

The systematic error arises from uncertainty in the fitting of the D o mass peak and in the background subtraction.

The expected ratio R was calculated as a function of

the lifetime ratio using the ~0 semileptonic branching fractions in a manner similar to that used in the calculation of the sample compositions. The D O branching

ratios for the channels selected and the selection efficiency for each channel were also necessary to calcu-

late R. It was assumed that equal numbers o f B ° and B - mesons are produced in Z decays. This is a reasonable assumption since B* mesons decay only by emitting a photon, and the B**-B mass difference is expected to lie well above the pion mass [ 15 ]. Fig. 6 shows a plot of the quantity R with its 1 a error ver-

sus the lifetime ratio 2"_/~0. The principal error arises

from uncertainty in the breakdown of N0 semilep-

tonic branching fractions. One can see from the plot that a value of the lifetime ratio of 2"-/2"o ~ 1 is pre- ferred, and in fact, using this event ratio information

alone, one obtains

T - 1 1 0 + 0 3 7 (stat.) (7) - - ~ ~ .~z . 024 "¢0

The statistical error here comes from the error on Robs. The error due to the spread of the curves is a systematic error which will be considered when evaluating the systematic uncertainty on the fitted lifetimes.

The information on the event ratio was combined with the decay length information in a coherent way by multiplying the likelihood function by the probability of observing a value of Robs, given a particular lifetime ratio. The total likelihood function is now given by

1~ 4 I ' ' 1 ' ' ' i . . . . . . . I '2

36 i 3 2

2s

2 ¢

2 4

16 J

12 j

0 04 OS 12 16 2 2 4 28

T . / T o

Fig. 6. The expected ratio R (number of D*+£ - events divided by number ofD°e - events) as a function of the ratio of the hfetlmes The area bounded by the curves represents a la variation of the ~0 branching fractions. The horizontal hne with the shaded area show the observed value and its error.

1

£ = '~0 V ~ O . o b s

[ (R(r-/2.o)-Robs) 2] x exp ~---ao2~ (S)

where aobs is the error on Robs, and £o IS given in eq. (5). The logarithm of £ was maximised to deter-

mine the two free parameters 2"_ and 2"0. The values obtained are

2.0 1-52 +020 = _ 18PS,

2"- 1 A T + 0 22 = " ' ~ ' - 0 . 1 9 p s ,

where the errors are statistical only. The correlation coefficient is 0.14. One may also consider the ratio of the lifetimes and their average to be the independent variables, in which case one obtains

T_ ° 0 - - = 0 9 6 + 19 • - 15,

TO

Tare = 1.49 +0 16 - 1 4 p S

where, again, the errors are statistical only. The re- sultlng curves of this simultaneous fit are superim- posed on the proper time distributions in fig. 5 (solid c u r v e s ) .

204

V o l u m e 307 , n u m b e r 1,2 P H Y S I C S L E T T E R S B 10 J u n e 1993

The fitted lifetime ratio results in following values for the sample composihons and the expected D* + g - - D°g- ratio:

f__* 0.10 +o08 = - 10 ,

3~* 0.73+o 1o = - 0 8 ,

f o 0 62+006 = " - 0 05

fo ° 0.1"7 +005 = " - 0 0 6 ,

R = 1 . 1 3 + 0 . 2 7 ,

where the errors include the statistical uncertainty on "L" /'/70.

6. Systemat ic uncertainties

the parameters that influence its shape. The b quark fragmentation function, the number of events of the type ~0 --+ D(.)ngu, and the event selection criteria have all been vaned to determine the effect on K and the resulting hfetimes.

The uncertainty due to the resolution function (eq. (4)) was estimated by allowing a variation of its parameters consxstent with their statistical errors plus a systematic error due to uncertainty in the Monte Carlo model of the decay length resolution.

The various contributions to the systematic error for the full fit with the event ratio constraint are pre- sented in table 3. The total systemaUc error is dominated by the uncertainty on the ~0 branching fractions. Furthermore, this uncertainty enters primarily through the calculation of R, the expected event ratio as a function of z-/T0. Systematic errors due to the different sources were combined m quadrature to obtain the total systematic error.

The following sources of systematic error have been considered: - uncertainties arising from lmprecase knowledge of the ~-o semdeptonic branching ratios; - uncertainties in the background fractions and in the parametrizatlons of the background proper time distributions; - uncertainties due to the smearing of the probability distribution used to correct for the missing neutrino (the x distribution); -uncer ta in t ies in the decay length resolution parametrization as obtained from the Monte Carlo simulation.

Imprecise knowledge ofB -° semlleptonlc branching fractions leads to uncertainties in the calculated sample compositions and the expected event ratio R. The ~-0 branching fractions have been varied within their experimental errors, taking into account correlations, as described m detail m the Appendix.

Uncertainties in the background fractions and proper time distributions have been considered. Dif- ferent background samples have been selected by varying the sideband regions and by using events with wrong-sign correlations, and alternative parametriza- tions of the proper time distributions have been studied.

The uncertainty In the x distribution used to correct for the missing neutrino has been estimated by varying

7. F inal results and conclusions

A maximum likehhood fit to the proper time distributions of 77 D*+g- and 77 D°t- candidates and the relative observed rates of D*+g- and D°g- events has yielded the following ~0 and B - lifetimes and hfetime ratio:

1 ~0+020 (stat.)+o07 (syst.) ps, 2" 0 = x . J z . 018 - 0 1 3

z- 1.47+o°292 (stat. ~+°15 (syst.) ps ~--- - - ] - - 0 14

__z- = 0.96+o19_ 15 (stat-) +°18-012 (syst.) . £0

Both z0 and z - are consistent with the average inclusive B hadron lifetime and the ratio of the lifetimes is consistent with unity.

The systematic error on the lifetimes is dominated by the uncertainty on the ~o semileptonic branching fractions, and m particular on the unmeasured ratio D/(D + D*) for decays of the type ~0 ~ D(.)~gu. Furthermore, this uncertainty arises primarily in the calculation of the expected event ratio R (as opposed to the coefficients f2, fo*, f -°and f0 ° ofeq. (5)). This implies that for future, higher statistics, measurements of the B - and ~o lifetimes, appropriate weighting of the event ratio information will be used to keep the

205


Table 3

Sources o f sys temat ic error on the fi t ted hfe t imes . The quant i t ies Be, B1, B2 and z, whmb are used to calculate the ~-o b ranch ing ratios, are def ined m the Appendix .

Source of error Cont r ibu t ion to sys temat ic error

zo (ps) z- (ps) z_ / z o

B ° b ranch ing rat ios

background t r e a t men t K dis t r ibut ion decay length resolut ion

total

B,

B1

B2

z

total

+00l +003 +003 -002 - 0 02 -002 +0 01 ±0.02 +0 03 --0.02 --0 02 +0 02 +0 04 +0 04 --003 - 0 03 --0 03 +006 +0 13 +0 17 --0 11 --0 12 --0 11

+006 +0.14 +0 18 --0.12 --013 - 0 12

±0 .02 +0 .03 i 0 . 0 3 ±0 .03 i 0 . 0 3 J:0.01 ~0 .01 ± 0 01 5:0.01

+007 +0.15 +0 18 --013 --0 14 -0.12

systematic errors from this source at or below the level of the statistical errors.

Acknowledgement

It is a pleasure to thank our colleagues from the SL division for the operat ion of LEP. We are indebted to the engineers and technicians at CERN and our home institutes for their contr lbuuons to ALEPH's success. Those of us not from member states thank CERN for its hospitality.

Appendix. Determination of sample compositions

Table 4 shows the six ~-0 decay channels considered in the determinat ion of the sample composi t ion coefficients. Possible modes with two or more non- resonant pions in the final state or with D** decaying into D ~*) plus two or more pions were assumed neg- hgible. The branching ratios of the modes considered have been determined in the following way:

( 1 ) B1 and B2 have been taken from measurements at CLEO and A R G U S [ 17,18 ];

(2) it was assumed that the inclusive semileptonic

branching ratio of ~0 mesons is given by the sum of the exclusive channels considered,

6

B, =_ e - x ) = B , .

t = l

This quanti ty has also been measured at CLEO and A R G U S [5,18,19];

(3) it was assumed that, in decays of the type B D(*)ngu the D(*)n states are produced with a fixed value of asospln, I = 1/2 (as is the case i f the decay proceeds via D** ). Then isospin conservation implies

B4 B6 n---- - - 2 ;

B3 B5

(4) the quanti ty

B5 B3 + B5

has not been measured. A value of z = 0.5 ± 0.5 was assumed.

The condations 2-4 allow the calculation of B3- B 6. The uncertainties on these branching ratios are large and highly correlated and thus not very mean- lngful. The quantitms Be, B1, B2 and z are the inde-

pendent quantit ies used to calculate the ~-0 semileptonic branching fractions. They have been var ied in- dependently for the evaluation of the systematic error on the fitted lifetimes. As explained in the main part of th~s Letter, the B - branching ratios were obtained using eq. (6).

The contributions to the D*+~- and DOg - samples were calculated using these branching ratios, the

206


Table 4 ~-o semileptonic branching ratios. The corresponding B - decay channels are also listed. The uncertainties on B 3 - B 6 are large and highly correlated and therefore are not shown.

~-0 BR (%) Corresponding B - decay

B 1 = B( -~ 0 ~ D * + g - u )

B 2 = B ( B 0 --+ D + g - u )

B 3 = B ( ~ "0 ___+ D*+zcOg-u)

B 4 = B ( B "0 ___+ D*Oz~+g-u)

B 5 = B(-B "0 ___+ D + n O g - u )

B 6 = B(-B 0 __, D O n + g - u )

Be = B(-B ° ~ g x )

= 4.74 ± 0.38

= 1.84±0.51

= 0.49

= 0.97

= 0.49

= 0.97

= 9.50 ± 1.40

B 1 = B ( B - --+ D*Og-u)

B f = B ( B - ---+ D O g - u )

B 3 = B ( B - --~ D*OzeOg-u)

B 4 = B ( B - ~ D * + ~ r - g - u )

B 5 = B ( B - ~ DO~Og-u)

B 6 = B ( B - --+ D + z c - g - u )

Table 5 Contributmns of ~-o and B - decays to the D*+g - and Dog - event samples.

D . + g - DOg-

~0 B .B1 + ~**B.B 3 £,~m(B.B 1 + c**B.B3) + c**(B4 + B6 ) B - ( z _ / r o ) [c**B,B4] ('c_/Zo) [BI + B 2 + e**(B 3 + Bs) + e**e,~mB.B4) ]

branching rat io for D *+ --+ DOn + (B. = 0.68 ±

0.03 [20] ) , and the re la t ive eff iciency for detect ing

channels B 3 - B 6 (c** = 0.70 4- 0.03, de t e rmined us-

ing a M o n t e Car lo s imula t ion) . The probabi l i ty that

a D * + g - even t is mis takenly recons t ruc ted as a D ° g -

even t (Cam = 0.15 4- 0.02) was also taken into ac-

count . Table 5 shows the ~-o and B - cont r ibut ions

to the D * + g - and Dog - samples.

References

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ARGUS Collab., H. Albrecht et al., Z. Phys. C. 54 (1992) 1.

[ 15 ] S. Godfrey and N. Isgur, Phys. Rev. D 32 ( 1985 ) 189. [16] Panicle Data Group, Phys. Rev D 45, Part 2 (1992). [ 17 ] CLEO Collab., D. Bortoletto et al., Phys. Rev. Lett.

63 (1989) 1667; CLEO Collab., R. Fulton et al., Phys. Rev. D 43 ( 1991 ) 651, ARGUS Collab., H. Albrecht et al., preprint DESY 92-039, February 1992.

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measurement of the and b− meson lifetimes

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