Measurements of |Vcb|, form factors and branching fractions in the decays B0 → D∗+ℓ−νℓ and B0 → D+ℓ−νℓ

$Page 1: Measurements of |Vcb|, form factors and branching fractions in the decays B0 → D∗+ℓ−νℓ and B0 → D+ℓ−νℓ$
13 March 1997

PHYSICS LETTERS B

ELSEVIER Physics Letters B 395 (1997) 373-387

Measurements of (V&l, form factors and branching fractions in the decays g+ D*+&-Q and @)+ D+&-&,

ALEPH Collaboration

D. Buskulic a, I. De Bonis a, D. Decamp a, P. Ghez a, C. Goy a, J.-P. Lees a, A. Lucotte a, M.-N. Minard a, J.-Y. Nief a, P. Odier a, B. Pietrzyk a, M.P. Casado b, M. Chmeissani b,

P. Comasb, J.M. Crespo b, M. Delfino b, I. Efthymiopoulosb>i, E. Fernandezb, M. Fernandez-Bosman b, Ll. Garridobp15, A. Juste b, M. Martinez b, S. Orteub, C. Padillab,

I.C. Park b, A. Pascual b, J.A. Perlas b, I. Riu b, F. Sanchez b, F. Teubert b, A. Colaleo ‘, D. Creanza c, M. de PalmaC, G. Gelao c, M. GironeC, G. Iaselli ‘, G. Maggi ‘, M. Maggi ‘,

N. Marinelli c, S. Nuzzo c, A. Ranieri c, G. Raso ‘, F. Ruggieri ‘, G. Selvaggi ‘, L. Silvestris ‘, P. TempestaC, A. Tricomi c*3, G. Zito ‘, X. Huang d, J. Lin d, Q. Ouyang d, T. Wang d,

Y. Xie d, R. Xu d, S. Xued, J. Zhang d, L. Zhang d, W. Zhaod, D. Abbaneoe, R. Alemany e, A.O. Bazarko e, P. Bright-Thomas e, M. Cattaneo e, F. Cerutti e, P. Coyle e, H. Drevermanne,

R.W. Fortye, M. Franke, R. Hagelberge, J. Harvey e, P. Janote, B. Jost e, E. Kneringere, J. Knobloch”, I. Lehraus e, G. Lutters e, P. Mato e, A. Minten e, R. Miquel e, L1.M. Mir e~2,

L. Moneta e, T. Oest e,20, A. Pacheco e, J.-F. Pusztaszerie, F. Ranjarde, P. Rensing ey12, G. Rizzo e, L. Rolandi”, D. Schlattere, M. Schmellinge724, M. Schmitte, 0. Schneidere, W. Tejessy e, I.R. Tomaline, A. Venturi”, H. Wachsmuthe, A. Wagnere, Z. Ajaltouni f, A. Barresf, C. Boyer f, A. Falvard f, P. Gay f, C. Guicheney f, P. Henrard f, J. Jousset f,

B. Michel f, S. Monteil f, J-C. Montret f, D. Pallin f, P. Perret f, F. Podlyski f, J. Proriol f, P. Rosnet f, J.-M. Rossignol f, T. Fearnley s, J.B. Hansen s, J.D. Hansen g, J.R. Hansen s, P.H. Hansen a, B.S. Nilssons, B. Rensch s, A. W%in3nen s, A. Kyriakis h, C. Markou h, E. Simopoulou h, I. Siotis h, A. Vayaki h, K. Zachariadou h, A. Blonde1 i, G. Bonneaud i,

J.C. Brient i, P. Bourdon’, A. Rouge i, M. Rumpf i, A. Valassi ip6, M. Verderi i, H. Videau i,21, D.J. Candlinj, M.I. Parsonsj, E. Focardi k,21, G. Parrini k, M. Corden”, C. Georgiopoulose,

D.E. Jaffel, A. Antonelli m, G. Bencivenni m, G. BolognamF4, F. Bossi m, P. Campana”, G. Capon m, D. Casper m, V. Chiarellam, G. Felici m, P. Laurelli m, G. Mannocchi m,5,

F. Murtas m, G.P. Murtas m, L. Passalacqua m, M. Pepe-Altarellim, L. Curtis n, S.J. Dorris n, A.W. Halley”, I.G. Knowles”, J.G. Lynch”, V. O’Shea”, C. Raine”, J.M. Starr”,

K. Smith”, P. Teixeira-Dias”, A.S. Thompson”, E. Thomson”, F. Thomson”, R.M. Turnbull n, U. Becker O, C. Geweniger O, G. Graefe’, P. Hanke O, G. Hansper O,

0370-2693/97/$17.00 @ 1997 Elsevier Science B.V. All rights reserved. PZI SO370-2693(97)00071-3

374 ALXPH ~o6~boration/Physics Letters 3 395 (1997) 373-387

V. Hepp O, E.E. Kluge O, A. PutzerO, M. Schmidt O, J. Sommer O, H. Stenzel O, K. Tittel O, S. Werner O, M. Wunsch O, R. Beuselinck P, D.M. Binnie P, W. Cameron P, PJ. Dornanp,

E.B. Martin *, A. Moutoussi P, J. Nash P, J.K. Sedgbeer P, A.M. Stacey P, M.D. Williams P, G. Dissertori 9, P Girtler 4, D. Kuhn 4, G. Rudolph 9, A.P. Betteridge r, C.K. Bowdery r,

P. Colrain’, G. Crawford’, A.J. Finchr, F. Foster r, G. Hughes r, T, Sloan r, M.I. Williams r, A. Galla ‘, I. Giehl ‘, A.M. Greene ‘, C. Hoffmann~, K. Jakobs s, K. Kleinknecht s, G. Quast ‘, B. Renk ‘, E. Rohne s, H.-G. Sander ‘, P. van Gemmerens, C. Zeitnitz s,

J J Aubert t*21, A.M. Bencheikh t, C. Benchouk t, A. Bonissent t, G. Bujosat, D. Calvet t, . .

J. Car-r t, C. Diaconu t, F. Etienne t, N. Konstant~i~s t, P Payre t, D. Rousseau t, M. Talby t, A. Sadouki t, M. Thulasidas t, K. Trabelsi t, M. Aleppo”, F. RagusaU*21, R, Berlich”,

W. Blum “, V. Btischer “, H. Diet1 “, F. DydakVs21, G. Ganis”, C. Gotzhein “, H. Kroha”, G, Liitjens “, G. Lutz “, W. Manner ‘, H.-G. Moser “, R. Richter “, A. Rosado-Schlosser “,

S. Schael’, R. Settles ‘, H. Seywerd ‘, R. St. Denis “, H. Stenzel”, W. Wiedenmarm “, G. Wolf ‘, J. Boucrot”, 0. Callot w, Y. Choi wv26, A. CordierW, M. Davier w, L. DuflotW,

J.-F. Grivaz w, Ph. Heusse w, A. H6ckerW, A. Jacholkowska”, M. Jacquet w, D.W. Kim w+19, F. Le Diberder w, J. Lefranr;ois w, A.-M. Lutz w, I. Nikolic w, H.J. Park ws19, M.-H. Schune w,

S. Simion”, J.-J. Veillet w, I. Videau w, D. ZerwasW, P. AzzurriX, G. Bagliesi ‘, G. Batignani”, S. BettariniX, C. BozziX, G. CalderiniX, M. CarpinelliX, M.A. Ciocci’, V. Ciulli x, R. Dell’Orso ‘, R. Fantechi x, I. Ferrante”, L. FoA ‘,I, F. Forti ‘, A. Giassi ‘,

M.A. Giorgi ‘, A. Gregorio ‘, F. Ligabue ‘, A. Lusiani ‘, P.S. Marrocchesi ‘, A. Messineo x, F. PallaX, G. Sanguinetti ‘, A. Sciaba”, l? SpagnoloX, J. Steinberger x, R. Tenchini ‘,

C. Tonellix~25, C. V~ni~ ‘, PG. Verdini X, G.A. Blair y, L.M. Bryant y, J.T. Chambers Y, Y. GaoY, M.G. Greeny, T. Medcalfy, l? Perrodoy, J.A. Strongy,

J.H. von Wimmersperg-Toeller Y, D.R. Botterill ‘, R.W. Clifft ‘, T.R. Edgecock ‘, S. HaywoodZ, l? Maley z, P.R. NortonZ, J.C. Thompson ‘, A.E. Wright”,

B. Bloch-Devaux aa, P. Colas aa, S. Emery =, W. Kozanecki aa, E. LanGon aa, M.C. Lemaire aa, E. Locci aa, l? Perez aa, J. Rander aa, J.-F. Renardy aa, A. Roussarie aa, J.-P. Schuller =,

J. Schwindlingaa, A. Trabelsi aa, B. Vallage aa, S.N. Blacka’, J.H. Dannab, R.l? Johnson ab, H.Y. Kimab, A.M. Litke &, M.A. McNeil ab, G. Taylor&, C.N. Booth”, R. Boswell ac,

C.A.J. Brew ac, S. Cartwrightac, F. Combley ac, A. Koksal ac, M. Letho ac, W.M. Newton”, J. Reeve ac, L.F. Thompson ac, A. Bohrerad, S. Brandt ad, G. Cowanad, C. Grupenad,

J. Minguet-Ro~iguez ad, F. Rivera ad, P Saraivaad, L. Smolik ad, F. Stephan ad, M. Apollonio ae, L. Bosisio ae, R. Della Marina ae, G. Giannini ae, B. Gobbo ae,

G. Musolino ae, J. Rothbergaf, S. Wasserbaech af, S.R. Armstrongag, P. Elmer ag, Z. Feng ag,27, D.P.S. Ferguson ag, Y.S. Gao ag,2g, S. Gonzalez w, J. Grahl ag, T.C. Greening ag,

O.J. Hayes ag, H. Hu as, P.A. McNamara IBaa, J.M. Nachtman aa, W. Orejudos as, Y.B. Panag, Y. Saadiaa, I.J. Scottag, A.M. Walsh agv23, J. Walshag, Sau Lan Wu”g, X. Wu ag,

J.M. Yamartinoag, M. Zheng ag, G. Zobernig ag a Laboratoire de Physique des Particules (LAPP), ~~2P3-~~S, 74019 Annecy-le-Keux Cede& France

b lnstitut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona), Spain7 c Dipartimento di Fisica, INFN Sezione di Bari, 70126 Bari, Italy

ALEPH Collaboration/Physics Letters B 395 (1997) 373-387 375

d Institute of High-Energy Physics, Academia Sinica, Beijing, People’s Republic of China 8 e European Laboratory for Particle Physics (CERN), 1211 Geneva 23, Switzerland

f Laboratoire de Physique Corpusculaire, Vniversite Blaise Pascal, lN2P3-CNRS, Clermont-Ferrand, 43177 Aubiere, France g Niels Bohr Institute, 2100 Copenhagen, Denmark9

’ Nu~~ar Research Center Demok~tos (NR~D), Athens, Greece i ~boratoire de Physique Nucleaire et des Hautes Energies, Ecole Po~yte~~ique, IN2P3-CNRS, 91128 Pa~aiseau Cedex, France

j Department of Physics, University of Edinburgh, Edinburgh El@ 3JZ, United Kingdom lo k Dipartimento di Fisica, Vniversita di Firenze, INFN Sezione di Firemze, 50125 Firenze, Italy

e Supercomputer Computations Research Institute, Florida State University Tallahassee, FL 32306-4052, USA I3714 m Laboratori Nazionali dell’INFN (LNF-INFN), 00044 Frascati, Italy

n Departmetrt of Physics and Astronomy, University of Glasgow, Glasgow G12 SQQ, United Kingdom lo O lnstitut fiir Hochenergiephysik, Universittit Heidelberg, 69120 Heidelberg, Germany I6

P Department of Physics, Imperial College, London SW7 2I32, United Kingdom lo 4 Insti~t~r Experimenta~hys~~ Vniversi~t Innsb~~k, 6020 lansb~ck, ~st~a i8

I‘ Depa~e~t of Physics, Vn~versi~ of Lancasten ~n&aster LA1 4YB, United Kingdom lo s Institut fir Physik, Universitiir Mainz, 55099 Mainz, Germany I6

’ Centre de Physique des Particutes, Fact&t? des Sciences de Luminy, IN2P3-CNRS, I3288 Marseille, France u Dipartimento di Fisica, Vniversita di Milan0 e INFN Sezione di Milano, 20133 Milano, Italy

v Max-Plan&-Institutfr Physik, Werner-Heisenberg-Institut, 80805 Miinchen, Germany I6 w Laboratoire de l’Acce%+ateur Lineaire, Universite’ de Paris-Sud, IN2P3-CNRS, 91405 Orsay Cedex, France

’ Dipartimeato di Fisica dell’Vniversitir, INFN Sezione di Pisa, e Scuola Normale Superiore, 56010 Piss, Italy Y Department of Physics, Royal Holloway & Bedford New College, University of London, Surrey TW20 OEX, United Kingdom 10

’ Particle Physics Dept., Ruthe~ord Appleton ~borato~~ ~hi~to~ Didcot, Oxon OXI I OQX, United Kingdom lo aa CEA, D~N~e~i~e de Physique des ~a~‘~u~es~ ME-Salty, 9Il9I eif-sur-~ve~e Cedex, Franlee ab Institute for Particle Physics, Vniversi~ of California at Santa Cruz, Santa Cruz, CA 95064, USA2=

ac Department of Physics, University of Shefield, She@eld S3 7RH, United Kingdom I0 ad Fachbereich Physik, Universitiit Siegen, 57068 Siegen, Germany I6

ae Dipartimento di Fisica, Universita di Trieste e INFN Sezione di Trieste, 34127 Trieste, Italy ‘t Experimental Elementary Particle Physics, University of Wa,shington, WA 98195, Seattle, USA

ag Department of Physics, University of Wisconsin, Madison, WI 53706, USA l1

Received 17 October 1996 Editor: K. Winter

Abstract

Two samples of exclusive semileptonic decays, 579 rr”-+ D*+eTf events and 261 k?+ Df&-Tt events, are selected from approximately 3.9 million hadronic Z decays collected by the ALEPH detector at LEP From the reconstructed differential decay rate of each sample, the product of the hadronic form factor F(w) at zero recoil of the DC*)+ meson and the CKTkl matrix element /V&l are measured to be F o*+(l)l&l = (31.9% 1.8,,f 1.9+) x lo-s,&+(l)/vcb/ = (27.8 f 6_gstat f 6.5,& x 10m3. The ratio of the form factors &+ ( 1) and Fn--t ( 1) is measured to be &C ( 1 >/Foe+ ( 1) = 0.87 f 0.22,t,t i 0.2&t. A value of l&l is extracted from the two samples, using theoretical constraints on the slope and curvature of the hadronic form factors and their normalization at zero recoil, with the result IX&} = (34.4 f 1.6,,, f

2.3,,, f 1.4m) x 10e3. The branching fractions are measured from the two integrated spectra to be Br(?-+ D*+J?-Ye) =

(5.53 f 0.26stat & 0.52,,&%, Br(?--+ D+!-Tf) = (2.35 f 0.20,t,t k 0.44,&%. @ 1997 Elsevier Science B.V.

t Now at CERN, 1211 Geneva 23, Switzerland. 2 Supported by Direccicin GeneraI de Investigaci6n Cientifica y

Tecnica, Spain. 3 Also at Dipartimento di Fisica, INFN, Sezione di Catania,

Catania, My. 4 Also Istitnto di Fisica Generale, Universita di Torino, Torino,

I&y. 5 Also Istituto di Cosmo-Geofisica de1 C.N.R., Torino, Italy. 6 Supported by the Commission of the European Communities,

contract EW3CHBICT941234. 7 Supported by CICYT, Spain. * Supported by the National Science Foundation of China.

376 ALEPH Collaboration/Physics Letters B 395 (1997) 373-387

1. Introduction

The Heavy Quark Effective Theory (HQET) is a well established theoretical framework in which heavy

hadron properties and related observables can be stud- ied reliably in a well defined limit of QCD [l-3]. HQET relates all hadronic form factors in B semileptonic decays to a single universal form factor, the Isgur-Wise function, and fixes its normalization at

zero recoil of the charm meson. This property allows for an almost model-independent determination of the

CKM matrix element 1 &,I from the study of exclusive semileptonic B meson decays.

To date all measurements of 1 vcb 1 based on exclusive semileptonic B decays have been performed from the

differential decay rate of g--+ D*+&-Ff [ 4-71. In the limit of zero lepton mass, the differential decay rate is:

’ Supported by the Danish Natural Science Research Council. lo Supported by the UK Particle Physics and Astronomy Research

Council.

I1 Supported by the US Department of Energy, grant DE-FG0295

ER40896.

I2 Now at Dragon Systems, Newton, MA 02160, USA.

l3 Supported by the US Department of Energy, contract DE-FG05-

92ER40742. l4 Supported by the US Department of Energy, contract DE-FCOS-

85ER250000.

r5 Permanent address: Universitat de Barcelona, 08208 Barcelona,

Spain. l6 Supported by the Bundesministerium fti Bildung, Wissenschaft,

Forschung und Technologie, Germany. l7 Supported by the Direction des Sciences de la Matiere, C.E.A.

l8 Supported by Fonds zur Fordernng der wissenschafthchen

Forschung, Austria. lg Permanent address: Kangnung National University, Kangnung,

Korea.

*O Now at DESY, Hamburg, Germany.

*’ Also at CERN, 1211 Geneva 23, Switzerland. ** Supported by the US Department of Energy, grant DE-FGO3-

92ER40689. 23 Now at Rutgers University, Piscataway, NJ 08855-0849, USA. 24 Now at Max-Plank-Institiit fiir Kemphysik, Heidelberg,

Germany. 25 Also at Istituto di Matematica e Fisica, Universita di Sassari,

Sassari, Italy. 26 Permanent address: Sung Kyun Kwan University, Suwon, Korea.

27 Now at The Johns Hopkins University, Baltimore, MD 21218, USA.

28 Now at Harvard University, Cambridge, MA 02138, USA.

G2F s(O) = -g-pm&+(mBO - mD*+)2

X K(w)(w2 - 1)“2~&+(@)]I’&j2, (1)

where w, the scalar product of the two meson four- velocities, is related to q2, the mass squared of the

!Zve system: 0 = (m$ +m&,,+ -q2)/(2mB0mD~*~+). K(w) is a known kinematic function and .Fo*+ (w) is

the hadronic form factor of the decay Be-+ D*+!-Ft. The strategy used [ 81 is to measure .F&+ ( 1) ]I&,/

from dI/dw by extrapolation to o = 1 (point of zero recoil of the D*+ meson) and to determine I Vcb I using the theoretical prediction of Fn*+ ( 1). The theoretical uncertainty in this determination is of order 3% [ 91.

The semileptonic decay I?--, D+C-Ft can also be used to measure I Vcb 1, though it is more difficult ex- perimentally. In the limit of zero lepton mass the dif-

ferential decay rate of $--, D+&?t is:

G -m3+(mgo+mo+)2 48~~ D

x (W2 - l)3’2~;+(w)I&,,12. (2)

At zero recoil, dIu+ /dw is much more suppressed than dlYD.+/dw due to helicity mismatch between initial and final states. The strategy to extract Fo+ ( 1) /v&l

is identical to that used for the decay g--+ D*+FFl and the theoretical uncertainty in the determination of

I Vcb I is of the same order [ 101. In this letter an update of a previous measurement

[ 61 of .?o*+ ( 1) l&b] from the decay g--+ D*+&?t is presented and a measurement of Fo+ ( 1) I &b 1 based on

the study of the decay !?--+ D+l-Ff is reported. The new analysis allows a comparison of the form factors Fo.+ (w) and &+ (0) which are predicted to be identical in the infinitely heavy quark limit. The value of the ratio &*+ ( 1) /Fo+ ( 1) provides an important test of the predictions of HQET. A value of IV&] is also extracted by combining both decays and using constraints [ 91 on the slope and curvature of the hadronic form factors .&*+ (w) and &+ (w) .

2. The ALEPH detector

The ALEPH detector and its performance are described in detail in Refs. [ 11,121: only a brief descrip- tion of the apparatus properties is given in this section.

ALXPH Collaboration/Physics Letters B 395 (1997) 373-387 377

Charged particles are detected in the central part of the detector with three concentric devices, a precision vertex detector (VDET) , a multi-wire drift chamber

(ITC) and a large time projection chamber (TIC). S~~oun~ng the beam pipe, the VDET consists of two concentric layers of double-sided silicon detectors, po- sitioned at average radii of 6.5 cm and 11.3 cm, and covering 85% and 69% of the solid angle, respectively.

The intrinsic spatial resolution of the VDET is 12 pm for the r# coordinate and between 11 pm and. 22 pm for the z coordinate, depending on the polar angle of the charged particle. The ITC, at radii between 16 cm and 26 cm, provides up to 8 coordinates per track in the rg view while the TPC measures up to 21 three- dimensional points per track at radii between 30 cm

and 180 cm. The TPC also serves to identify charged particle species with up to 338 measurements of the specific ionization (dE/d.r). The three detectors are immersed in an axial magnetic field of 1.5 T and together provide a transverse momentum resolution of c~(pr) /pr = 0.0006 x or @ 0.005 (pi in GeVlc).

shape in the ECAL and, when available, by the specific ionization information from the TPC. Muons are identified from their hit pattern in the HCAL and from the presence of at least one associated hit in the muon chambers. Electrons and muons are required to have momentum greater than 2 GeVfc and 3 GeVlc, respectively.

-0 3.1. B -+ D*+C-Fl event selection

D*+ candidates are reconstructed in the channel D*+-+ Do& and the Do candidates in the three

decay modes: Do-+ K-v+, Do--+ R-&7-r-=+ and Do+ K$r-rr+. The mass difference between the Do& and the Do candidates is required to be within 2.1 MeV/c2 (2.5 standard deviations) of 145.4 MeV/$. The event selection is similar to that described in Ref. [6].

Electrons and photons are identified in the elec- tromagnetic calorimeter (ECAL) , a lead-proportional chamber sandwich segmented into 0.9” x 0.9” pro- jective towers which are read out in three sections in depth, Muons are identified in the hadron calorimeter (HCAL) , a 7 interaction length yoke interleaved

with 23 layers of streamer tubes, together with two additional double layers of muon chambers. The visi- ble energy flow in the detector is determined with an algorithm [ 121 which combines measurements from

different detector components.

Charged kaon candidates for which dE/dx information is available are required to have /ok/ < 2, where Xx is the number of standard deviations between the

measured and the expected ionization for the kaon

hypothesis. In the channel Do--t K-‘&7.r-&, candidate kaons with momenta less than 2 GeVlc are rejected. Candidate Kg’s are reconstructed in the channel Kg-+ W-G’. They must have a momentum larger than 0.5 GeVlc, a decay length larger than 0.5 cm, and a reconstructed mass within 15 MeV/c2 of the nominal K$ mass. Reconstructed Do candidates are required to have a vertex separated from the interaction point by more than twice the resolution on the Do

reconstructed decay distance.

3. Event selection and ~o~~ction

The analysis presented in this letter is based on approximately 3.9 million hadronic Z decays recorded with the ALEPH detector from 1991 to 1995 and selected as described in Ref. [ 131.

Exclusive semileptonic decays $-+ D*+C-Fe and Be --+ D+&-Ff are selected in hadronic events where a

lepton is associated with a D*+ or D’, respectively, in the same hemisphere. Throughout this letter, ‘lepton” refers to either electron or muon, and charge conjugate reactions are implied.

Reconstructed D*+ candidates are combined with

an identified lepton from the same hemisphere. The angle between the D*+ and the lepton is required to be less than 45”. The D*Q?- system is required to have an invariant mass less than 5.3 GeV/c*. To ensure a good B meson vertex reconstruction, the lepton and at least two of the Do tracks are required to have one or more VDET hits. The x2 probabilities of the vertex fit for both Do and D*+l- vertices 29 must be larger than 1%. To ensure a precise m~urement of the B meson direction and cons~uen~y a good w recons~ction, the distance of the D*+&- vertex from the interaction point projected onto the D*+e- direction is required to

The lepton identification is described in detail in 2g The D*+P’ vertex is determined from the lepton and the Do Ref. [ 141. Electrons are identified by their shower candidates.


Table 1 Branching fraction of physics background processes used in this analysis.

Channels contributing Branching to D*+f?- and D+P fraction (%)

B--+ D*+GFF-Q 1.25 f 0.22

Ir” + D*+%-Oe-F[ 0.63 It 0.11

Ea ----f D*+K”P-Fj 1.25 f 0.22

$“-t D*+T-v, 2.06 f 0.41

B-t D*+X, 13.0 f 3.70

Channels contributing to D+f?

B--+ D+?r--!-Ft

Bo -+ D+Pae-i+

Bs” + D+K”f?-Ft

Ea --+ D+~i3,

&+ D+X,

B” + D*+e-i7,

Branching fraction (%)

0.32 zt 0.22

0.16 f 0.11

0.32 f 0.22

0.69 f 0.14

4.00 f 3.30

5.53 & 0.58

be greater than 1 mm. The selection results in a sample of 1266 D*+!- candidates with a reconstructed Do mass within 2.5 standard deviations ((+ = 10 MeV/c* for Do+ K-r+ and Do--t Kfr-n-+ and 8 MeVlc* for Do-+ K-&W-&) of the Do nominal mass.

-0 3.2. B -+ D+C-Ft event selection

D+ candidates are reconstructed in the channel Df-+ K-n-+&. The momenta of the two pions are required to be greater than 1 GeVlc for the energetic pion and greater than 0.5 GeV/c for the other, and candidate kaons are selected as in the Do+ K-&r-+r+

channel. Reflections from D,‘- K-K+z-+ are rejected if the K-K+ mass is within 6 MeV/c* of the 4 meson mass or the K-z-+ mass is within 100

MeV/c* of the K*’ mass and if the reconstructed K+K-r- mass is within 20 MeVIe* of the nominal D,“ mass. Reconstructed D+ candidates are required to have a vertex separated from the interaction point by more than five times the resolution of the D+

decay distance. Reconstructed D+ candidates are combined with an

identified lepton from the same hemisphere using the same selection criteria as in the D*+F event selection. An additional requirement is placed on the distance between the D+ vertex and the D? vertex projected onto the D+ direction which is required to be greater than -0.5 mm. The selection results in a sample of 1609 D+!- candidates with a reconstructed D+ mass within 2.5 standard deviations (CT = 8 MeVlc2) of the D+ nominal mass.

3.3. w reconstruction

The reconstruction of the w variable is performed on an event by event basis using the B meson direction and the neutrino energy [ 61. The B meson direction is determined from the vector joining the DC*)+!- vertex and the primary vertex. The resolution is inversely proportional to the decay length, and is approximately one degree at a decay-length of three millimeters. The neutrino energy is estimated with a rms precision of 2.6 GeV from the missing energy in the hemisphere containing the D (*)+e- candidate [ 151. The rms resolution in w is 0.07 for both channels corresponding to 13% of the allowed kinematical ranges, 1 < w <

-0 1.504 for the B --+ D*+FFj channel and 1 < w <

1.589 for the $+ D+C-Fl channel.

4. Sample composition and background rejection

4.1. Background sources

The two main classes of background sources that contribute to the D(*)? sample are physics background events where the DC*)+ and the lepton candidates are both real and combinatorial background events. Combinatorial background events come from either a fake DC*)’ in association with a real or a fake lepton, or a fake lepton in association with a real DC*)+.

Physics background processes contributing to the D*+!.- and DfF samples and their measured or estimated branching ratios are listed in Table 1. Processes

ALEPH Collaboration/Physics Letters B 395 (1997) 373-387

Table 2 The D(*)+e- samples composition without (initial) and with (final) background rejection requirements.

379

Sample composition D*‘%?- sample initial tinal initial

D+f?- sample final

yield 126&h 36 741+27 1562140 466% 23

Bo --f (D*++ D*+&-i$ D+IT*) 249 f 26 791 8 B--t D(*)+XL!-ii, 263 rt 46 74f13 163f53 28flO B--t DC*)+& 71f20 15f 5 50f22 7f 4

20-t D(*)+r-‘ij; 23rt 5 5f 1 31f 6 4f 1 comb. background 204 j; 27 68+ 9 661 f47 85& 6 signal 705 f 68 579 f 32 408 f 88 261f23

involving a D*+ meson in the final state contribute 3o to both D*+C- and D+C3”” samples while processes involving a D+ meson contribute to the D+P’ sample only. Some of these processes have not been measured and are estimated from other measurements or by analogy with known decays. The branching

ratios of B---t D(*)“71--&?f, Ba+ D(*)+zr*&?l

and $-+ D(“)+K*LY~ are estimated from measured values [ 161 of Br(B---+ D(*)+rr-P~~) and

Br($+ D*z--e-Z~), using isospin and tlavour

SU(3) symmetry. The branching ratios of r;“-+ D(*)+Y’i?, are estimated from the inclusive measurement Br(b-+ X~-Y~) [ 177, ~su~ng that three- fourths of b+ XT-Y, involve a D*+ meson and the other one-fourth involve a D+ meson. The branching ratios of the inclusive double charmed B decays B--+ D*+X, and &+ D+X, are based on measurements [ 181 of B+ D(*j+DX.

For the D*+t- combinatorial background, fake D*+‘s arise from the combination of a fake Do with a random slow pion or from the combination of a real Do with a random slow pion. The first combination leads to a smooth Do mass distribution under the Do . mass peak in the D*+e- sample. It is fitted with a second order polynomial function and its rate is estimated from the integral of the fitted function within the Do mass window. The rate of the second type of combination is estimated by assuming that the probability to associate a random soft pion to a genuine

3o The decay process p-+ D*+PFl is the signal in the D*?P sample, and the main physics background component in the DsC

sample. The Br($+ D *?PFl) value in Table 1 is the one measured from the D*+P sample (see Section 5.1).

Do!? pair is the same as to associate a second soft pion to a reconstructed D*+L- combination. This leads to a contribution of less than 1% of the signal at 95% confidence level. The fake lepton combinatorial background is estimated by applying a 1% probability of hadron ~sidentifica~on (based on Ref. [ 141) to D*+-hadron combinations selected with the same criteria as D*+&- combinations.

The DfP combinatorial background is estimated in a similar way. In addition, reflections from D,‘-+ K-K+a” are reduced to less than 2% of the signal, as estimated from Monte Carlo, with specific cuts as described in Section 3. Reflections from

A,+ -+ pK-& and D*+-+ D*( --+ K-&X)rr+ are negligible.

4.2. Background rejection

The expected composition of the D*+P and D+C- samples after event selection is presented in Table 2. The background level is clearly high especially in the D+P sample: the fraction of D*+e- (D+!-) events originating from physics background processes is 28% (32%) and from combinatorial background is 16% (42%).

To reduce the level of background in the two selected samples; three additional requirements are used. The contribution of the process B---t D(*)+?r-e-Fg in both samples is reduced by rejecting events where an additional charged particle is consistent with the B vertex. Events with an additional charged track in a 45” cone around the DC*)+&- direction, having the same charge as the lepton, momentum greater than 0.5 GeVlc, one or more VDET hits in r4 and z

380 ALEPH Ca~~boration/Plzysi Letters B 39.5 (1997) 373-387

coordinates, and forming an invariant mass with the D(*)+C- system lower than 5.3 GeVlc2 are selected. They are rejected if the charged track passes closer

to the B vertex than to the interaction point and if its impact parameter with respect to the 3 vertex is less than 4cr. This r~~rement removes 77% of the B---t Df*)+~--e-Ft background while keeping 96% of the signal. For the channels Dt+ K-rrfrr+ and Do-+ K-~-+~-rr~, events with an additional track having a charge opposite to that of the lepton and sat- isfying the same criteria as described above but with

the impact parameter calculated with respect to the D vertex instead of the B vertex, are rejected. This requirement removes 30% of the remaining combinatorial background while keeping 99% of the signal.

To reject background D(*)+C- events with additional neutral particles originating from B decay, a missing mass variable ML,, quantifying the consis-

tency between the neutrino energy, the B direction of flight, the B mass and the D(*)+C- four-momentum is used as described in Ref. [ 61. Candidates with &Q$, greater than 1 GeV2/c4 are rejected. This requirement removes 49% of the &-+ D(*)+~/K’~-~~ while keeping 83% of the signal.

The contribution of background processes g--+ D*+e-Fg, D*+--+ D+?r’/r (referred to hereafter as D+&$-) to the D+e- sample can be further reduced by rejecting D+&- pairs correlated with a go or a y. Since Br(D*+-+ D+y) is small compared to Br(D*++ D+7r”) [ 191, only rr” are considered. Due

to the soft vi momentum, no explicit reconstruction of the n-2 is attempted. Photons with energy greater than 500 MeV are selected in a 4.5” cone around the Di direction. A mass difference variable is defined as AMY = M(D’y) - (MD*+ t- Mo+)/Z, which is expected to be close to zero for photons coming from D+rig-. Events where at least one photon fulfills ]AiiM,{ < 20 MeV/c2 are rejected. This requirement removes 54% of the D+&f?- background while keeping 83% of the D+.!- signal. Fig. 1 shows the mass difference AM, for signal and background events estimated as described in Section 4.1.

The expected compositions of the D*+e- and D+C- samples after background rejection requirements are described in Table 2. The contribution of physics and combinatorial background events in the final D(*)‘&- sample have been strongly reduced. The expected fraction of physics background D*+e- (D+e-) events is

-0.05 0 0.05 0.1 0.15 0.2

AM, (C&/c*)

Fig. 1. The reconstructed AM, for data (points), and backgrounds (histograms). If several photons are available, the one with AM, closest to zero is selected. The arrows indicate the excluded region. The rightmost bin contains overflows and events with no photon candidate. The vertical scale is broken for better readability.

13% (25%). The expected fraction of combinatorial background D*+C- (D”J? ) events is 9% ( 18%). The reconstructed o dis~ibut~ons of the final D*+C- and D+L- samples are presented in Fig. 2 along with the main background contributions.

The reconstruction efficiencies for g--+ D*+e-Ye

and $--+ D+C-Fj decays are estimated from Monte Carlo simulation. Differences in efficiency of the VDET hits and vertices probabi~ty r~uirements between data and Monte Carlo are investigated in detail on inclusive D*+, D+, D*+C- and D? samples and corrections are applied to the simulation efficiencies [ 61. The variation of the reconstruction efficiencies as a function of w for all reconstructed decay channels is presented in Fig. 3.

5. Measurement of FJp+(l)l&,l and .?%+(l)I%l

The method used to extract &++ ( 1) IV&,] and Fo+ ( 1) f k&l from the differential event rate dN( D*+L- ) /dw and diV( D+&- )/do is described in this section. The systematic error quoted for each

ALEPH ~a~~b~ratian/P~ys~cs I.&m B 395 (1997) 373-387 381

(a) n*+i sample ALEPH Data Phys bkg

i 1:2 1:3 1:4 1:5

w

i? @ 150 (b) D’l sample

l Data ‘G ‘E

Phys bkg

r5 100 [Eza Comb bkg

ALEPH

j

50 + +++ I

0 I 1.1 1.2 1.3 1.4 1.5

Fig. 2. Reconstructed w distributions for (a) 2-t D*+!?Zl and

(b) $--+ D+eYf event candidates. The points are data. The black histograms are the combinato~~ background contibutions. The shaded histograms correspond to the various physics backgrounds reconstructed from dedicated Monte Carlo. The D‘trr$!-‘ contribution in (b) is not shown, since it is to be measured from data (see Section 5.2).

result is described in the next section.

The combinatorial background contribution to dN(D*‘e- ) /dw is measured from data in each bin of w as described in Section 4.1 while physics background contributions are taken from dedicated Monte Carlo simulation, with total number of events as given in Table 2.

The physics function which describes the

dN(D*+F)/dw distribution of the final p--+ D*+&-Ft sample after background subtraction is

&i pi6 Q(w) = 26-GBBr(b+ B’)Br(D*+-+ DOS-+) W

TBO dIb*+ ( W) x Br(D’-+ I&~)~

dw e(w) 9

where Br( Do--+ mu) is the br~ching ratio of the Do decay. Its value for the three decay channels is given in Table 3. The quantity es9 = 97.40 _j, 0.24% [ 131 is

0.064 I

Fig, 3. Reconstruction efficiency for (a) g--+ D*+l-Pt decay

and (b) B0-t D+(-iro,)P-Ft decay as a function of w. The curves am the second order polynomial fits used to parameterize the efliciency in the fit.

Table 3 Branching fractions and lifetimes used [ 191. The quoted errors are used for the estimation of systematic uncertainties.

Branching fractions (%)

Lifetimes (ps)

r,, /rhad

Br(b-+ B*) Br(b--t Bt) Br(D*+-+ Do&) Br(D*“-+ Di&)

Br(D*+--+ D+r) Br(DO-+ K-T+) Br(D’-t K-n+rr-rr+) Br(DO--t K$rr-n+) Br(D+d K-r+r+)

22.12 * 0.20 31.8 f 2.2 11.2 f 1.9 68.3 xt 1.4 30.6 + 2.5 1 1+2.1 . -0.7

3.83 i 0.12

7.5 f 0.4

2.7 f 0.2

9.1 i 0.6

1.56 i 0.06

1.62 i 0.06

1.61 f 0.10

the hadronic event selection efficiency and E(W) is the w-dependent selection efficiency. The latter is parameterized for each Do decay channel by a second order polynomial. The differential decay width din*+ /do is

382

Table 4

ALEPH Collaboration/Physics Letters B 395 (1997) 373-387

Results of the different fits described in the text. The systematic errors are described in Section 6.

linear fit

quadratic constrained fit

Channel jCoc*,+(l)lKbl(x10-3)

D*+e 31.9 f 1.8stat & 1.9,,t D+e 27.8 zt 6.&m i 6.5,,1

D*+& 32.0 rt 2.1,~ + 2.0,pt D+.? 31.1 f 9.9,m i 8.6,,t

2 aD(*)+

0.31 f 0.17stat f o.os,,, -0.05 rt: 0.53s~t f 0.38,,t

0.37 jI 0.26,ra f 0.14S, 0.20 zh 0.98,Q.t It 0.50,,

Correlation

92% 99%

94% 99%

given in Eq. ( 1) . The unknowns in the physics function ‘P(w) are

/I&,/ and 3n*+ (w) . The dependence of 3&i. (w) on w is assumed to be linear:

30*+(w) =3u*+(l)[l -a&+(w- 111 *

A binned maximum likelihood fit is performed on the dN(D*+P ) /dw distribution. The fitting function is the convolution of the physics function Q(w) and the w-dependent resolution function.

The results are given in Table 4. Fig. 4a shows the result of the fit. The corresponding product 3u*+ (w) } I&,/ is shown in Fig. 4b. The values of

3u.+ (w ) 1 k&j for specific values of $ are useful for tests of the factorization in hadronic decays; they are

given in Table 5. From the integrated physics function, the branching

ratio of Be--+ D*+&-Ff is measured to be

Br(& D*+e-&) = (5.53 f 0.26,, & 0.52,&%.

All background contributions to dN( D+C- ) /dw are estimated as described in the previous section

except for the D*+C component corresponding to the partially reconstructed D”‘rrzC- decay. The value of 3u+ ( 1) / V&f is extracted by fitting simu~t~~usly the dN( DfC- ) /dw and dN(D*+P ) /dw distributions so that the D+?rzl- background component in dN( D+&- ) /dw is determined from data.

The physics function describing the dN( D’C- ) /dw distribution after subtracting all backgrounds except the rem~ning D+$L- component is:

0 I 1.1 1.2 1.3 1.4 1.5

w

Fig. 4. (a) The ~ffe~nti~ rate d~(D*~~-)/d~ of $_+ D*+ -- i! V[ candidates after all cuts and background subtraction. The points are data with statistical error bars, and the histogram is the number of events predicted by the fit. (b) _YFn++ (w) j&j as a function of w, the shaded band and the white bands indicating the statistical and systematic uncertainties, respectively. The points are data after correction for resolution effects.

Q(u) = 2?zBr(b-+ B”) 99

x Br(D+-+ K-&V+) 2 fi

+ Br( D*+-+ D’rO/r) dJ&+(o,e,*+(w)] .

The w-dependent SehXtion effiCienCieS ED+ ( w) for the Be--+ D+&-V~ signal and ED*+(W) for the

Table 5 Values of Fn+ (w) /l&j and F&+(u) IV&l for q2 corresponding to the masses of some particles (note that the same q2 corresponds to different w depending on the decay), extracted from the results of the linear fit given in Table 4. The values are also given for the maximum w. The first uncertainties are statistical and the second are systematic. The entries are largely correlated.

~D*+(@)/v,bl(xIo-3) &+(W)lv,bj (x10-3)

o=l 31.9il.Xfl.P 27.8 i 6.8 zt 6.5

@(q$) 28.0 f 0.9 f 1.5 28.2 f 2.3 f 3.6

“(““;’ 27.6i 1.1 f 1.5 28.5 f 1.2 f 2.6

@(m,+) 27.2 i 1.3 f 1.4 28.5 f 1.6 i 2.5

0 ( NZ?r+ ) 26.9 f 1.4 z!z 1.4 28.6 f 2.0 f 2.5

CP= D*+

26.9 zb 1.4 f 1.4 28.4 f 1.1 zt 2.6

CAP” D”

28.6 f 2.1 f 2.0

I? -+ D*+l?Yf background are both parameterized by second order polynomials. The differential decay widths dFD*+/dw and dFo+ /do are given in Eqs. ( I.) and (2) , respectively. The form factor &+ (w) in dl?o+/do is assumed to have a linear dependence on u, as for &W (0) in ND*+ /du:

A binned maximum likelihood fit is simulta-

neously performed on the dLN(D”C- ) /dw and dN(D*+P)/dw distributions. The signal and background components of the dN(D+.!- ) /dw distribution are convolved with different w-resolution

functions. The w-resolution function for background Df&- events is worsened due to the missing &. The four free parameters in the fit are

_&+( l>]I&,j, a;,, Fo++( 1)/&J, and a&+. The results for &+ ( 1) jVh,l and a$+ are given in Table 4. Their statistical uncertainties include by construc- tion the uncertainty on the D*+P contribution. Val- ues of &*+( 1) lV&,j and a&+ obtained from this simultaneous fit are indistinguishable from those obtained from the previous fit (see Section 5.1) of the dN(D*+&-) /dw distribution alone. Fig. 5a shows the result of the fit. The corresponding product Fo+ (w) /V&l is shown in Fig. Sb. V&es of .17$+ ( w ) j I&,/ for specific values of the 2 are also given in Table 5.

From the integrated physics function @n+ (u) , the

branching ratio of g--t D+L’-Fl is measured to be

w

Fig. 5. (a) The differential event rate dN(D’P)/dur of

Bo - D%!-i;p candidates after all cuts and background subtraction. The points are data with statistical error bars. The dotted histogram is the contribution of the D%:P background, the

dashed histogram is the contribution of the 9-t D+e-‘i;e signal and the solid histogram the sum of the two. (b) Fn.+ (0) 1 v&,1 as a function of w (see caption of Fig. 4 for details).

ALEPH

1 ! ___“_._____... ,,‘” . . . . . . . . . . _..__..~..._____.~.________~ _._.

0.5

1 1.1 1.2 I.3 1.4 I.5

w

Fig. 6. The measured ratio of 7n+(w) and ZJ&+(w), with statistical error bars.

Br(go--t D”CYt) = (2.35 f 0.20,,, f 0.44,,,,) % .

Fig. 6 shows that the ratio of FrJ+ (w) and 3;>*+ (w} is consistent with unity over the whole common range of o. At w = 1 this ratio is measured from the results of the previous fits to be


in agreement with the theoretical prediction [lo] ~+(l)/~*+(l) = 1.08f0.06~.

The same quantity is also measured to be consistent

with unity with better accuracy at wgz, the m~imum --a

value of w for the B -+ D*+e-Vf decay,

The independence of .&+ (w) /Fn*+ (w) over the whole range of w is also quantified by verifying that the difference of the fitted slopes is in agreement with

the theoretical value [9] (a;, - a&,)th 2c 0.08,

a;, - a;*+ = -0.36 & 0.58,&t i O-31,,.

These are the first direct tests of the prediction of HQET that the same hadronic form factor can describe

the decays I?--+ D*+&-Fl and I?--+ DC&-F!. This

prediction can be exploited to extract /I&, / from the two decays, by using the Isgur-Wise function &(w) itself. A second-order p~~eterization

&(o) = 1 - a&J - 1) -t ca(w - 1>2

is chosen and a theoretical constraint [9] co II 0.72~; - 0.09 is used. The form factors Fo*+(@) and Fo+ (w) are parameterized similarly, with slopes and curvatures related to those of 3co(o) by the relations [9] a&+ = ug - 0.06, fzk+ = 4 + 0.02, co*+ = Co - 0.06 - O.O6a;, co+ = Co + 0.01 + 0.02$. These relations allow the constraint between ui and CO to be transformed into constraints between a&,,+ and coC*,+ . The results are given in Table 4. In spite of the increased uncertainty, this result is chosen since it relies on a less arbitrary p~~eterization of the form factors [ 91.

The measurement of 1 &,I is done by fitting directly the Isgur-Wise function with the parameterization given above and taking the normalizations at w =

1 to be e*+(l) = 0.91 f 0.03m (see Ref. [9] and references therein) and $+(1)/e*+ ( 1) = 1.08 f 0.06&. The fitted values of the two remaining free parameters, which are 95% correlated, are

Iv,/ = (34.4 + 1.6,,, f 2.3,,, f 1.4& X 10-3,

a; = 0.30* 0.12,, rt 0.14,,,, f 0.13&)

where the third error arises from the theoretical uncertainty on the inputs.

6. Systematic uncertainties

The various sources of systematic uncertainties are su~~ized in Table 6. They are described in more

detail below. Since 3( 1) IV&] is propo~onal to the square root of the branching fraction of the B decay, it will be half as sensitive than the branching fractions to quantities like other branching fractions and efficiencies, provided the slope a2 is unaffected. This is

generally true for the D*V” channel, where the signal and the background have similar shapes. For the D+&- channel however, the signal vanishes rapidly at low W, while the background is roughly constant. Any systematic uncertainty affecting the background level will affect both the normalization and the slope, with a comparatively higher impact on F( 1) ]I& 1 than for the D*+P channel. Correlations between the D*+P and the DfP measurements are taken into account in the deter~nation of all uncertainties. The correlation between the total systematic uncertainti~ on F( 1) /V&,1 and a2 is 48% for the D*+&- channel and 93% for the D? channel. The systematical uncertainty on the ratio To+ ( 1) /Fn*+ ( 1) is largely domi- nated by the uncertainty on Fu+ ( 1) . The systematical uncertainties on IV&l and ~2: are similar to the uncertainties on .?$*t ( 1) j &/ and a$,,, but with a larger sensitivity to the ba~k~ound and to the simulation.

Branching f~ac~~o~s: The systematic uncertainties related to the fraction of hadronic Z decays to bb

pairs and the D*+, Do and D+ branching fractions are estimated by the effect of their variation within the quoted uncertainties in Table 3. Correlations in the measured Do branching fractions are taken into account. The branching ratios Br( D*+-+ Do,+) and Br(D*“-+ D+?ra/r) are also taken to be fully anti-

correlated. Backgrounds: The contribution of each physics

background is varied within uncertainties given in Table 1, taking into account their possible correlation. The fraction of narrow resonant D(*)+v/K~-P~ decays in the Monte Carlo simulation is varied between 0 and 100% (with a central value of 46% [ 161) to account for the lack of knowledge of the non-resonant

part. The use of a first order polynomial instead of a

second order one to describe the fake D background component in the D mass spectrum fit changes the background estimate slightly. The contribution of fake

AL.EPH Collaboration/Physics Letters B 395 (1997) 373-387 385

Table 6 Systematic uncertainties. All contributions are given in percent with respect to the measured value except for a”,+ and a&+, where absolute uncertainties are quoted.

Source FD*+(l)j%bl a* D*+ Bru++ FD+(l)/%b/ a-2

D+ Bra+

Braack ratios Br(D--+ KFZ?~) Br(D*+--t Do@+) Pb; /rhad

Br(b-+ B”) subtotal

Background B-i D*X&-i+ B--t D(*)+&

Bo -f D(*)+T-& fake DC*) fake lepton

subtotal

Simulation Fragmentation e efficiency Vertex efficiency Photon efficiency Efficiency shape MC statistics 0 resolution

subtotal

B” Eifetinre

Total

2.0 3.8 10.0 0.13 9.5 1.4 2.8 6.0 0.11 2.7 0.5 _ 0.9 0.5 0.9 2.9 5.8 2.9 5.8 3.8 7.5 12.0 0.17 11.5

1.7 0.02 2.2 9.8 0.18 4.3 0.3 0.7 2.3 0.04 1.4

0.2 0.4 1.8 0.04 0.5 0.8 1.6 2.2 0.01 2.2 0.1 0.4 1.1 0.02 0.5 2.0 0.02 3.5 10.5 0.20 5.1

1.7 0.02 2.3 3.6 0.03 4.7 1.0 2.0 2.0 0.01 2.0 1.5 2.9 11.2 0.13 10.5

6.0 0.04 6.0 0.6 0.02 0.3 4.5 0.10 0.4 1.6 0.05 1.6 8.4 0.19 3.9 1.5 0.05 4.7 0.10 - 3.4 0.08 4.5 17.1 0.27 13.7

2.6 1.5 3.3 0.01 1.4

6.1 0.08 9.5 23.5 0.38 18.6

D*’ events in the D*Q- sample and of the reflection from D$-+ K-Ki7rf in the D+!- sample are varied by 100% of their estimated contribution given in Section 4.1. The uncertainty on the fake lepton mis- identification probability (electron or muon) is estimated to be 20%, based on Ref. [ 141.

~i~~~a~i~~: The mean B hadron energy has been measured by ALEPH to be Xn = 0.715 rt: 0.015 [ 151 relative to the beam energy. The quoted uncertainty corresponds to the variation of the efficiency when Xn is varied within errors. The uncertainty on the lepton efficiency is taken to be 2%, based on Ref. [ 141.

The data vs. Monte Carlo efficiency ratio of the VDET hits and vertex probability requirements men- tioned in Section 4.2 are varied within errors.

Photon reconstruction affects the selected D”C- sample in two ways. The efficiency for associating the Df with a random photon affects directly the D”W efficiency. This effect is checked by comparing in data

and Monte Carlo the probability to associate a random photon to D’TI$~- events, where no photon is expected. The photon reconstruction efficiency directly affects the level of remaining D+gtJ- events. This effect is checked by comparing the number of D+gze- events passing and failing the photon rejection cut on data and Monte Carlo, as illustrated by the agreement between data and Monte Carlo in Fig. 1. The quoted uncertainty corresponds to the statistical error of these two successful checks.

The uncertainty related to the w resolution is taken to be half of the change in parameters when the fit is performed with a perfect resolution. Degrading the o resolution by ~bi~~ily shifting the missing energy or smearing the vertices inside their estimated uncertainty or by not using the soft pion in the D*+&- channel does not change the result by more than this uncertainty.

The uncertainty related to the dependence of the ef-

386 AL.EPH Co~laboration/Physi~s L.etters B 39.5 (1997) 373-387

ficiency with w corresponds to the change if the fit is performed with a linear instead of quadratic parameterization of the efficiency vs 0.

3 lifetimes: A change in B” lifetime affects F( 1) lV&,l in two correlated ways. An increase in the lifetime directly decreases the partial width corresponding to a fixed branching ratio. However the branching ratio also decreases because the require-

ment on the decay length above 1 mm favour long Iifetime events. A change in the B+ and Bf lifetimes within errors also affects the proportion of physics background but this has a negligible effect on the

final results.

7. Conclusion

The differential decay rates dr/du for the decays

B” --+ D*+C-Fl and p-+ D+J?Ff are measured. Us-

ing a linear w dependence for the hadronic form factors

F&.(w) and~o~(~),thevaluesof~~*+~1)l~bl and F*+ ( 1) j&l and of the slopes a&+ and a& are:

Fj*+(1)Iv,,,l = (31.9f l&,,,f 1&y& x 10-3,

a;*+ = 0.31 i: 0.17,, i 0.08,,, ,

and

&S (1) I&,] = (27.8 * 6.8,mt f 6.5,& X 1O-3 ,

a;+ = -0.05 rt 0.53,,,, f 0.3&t.

The values of &*+ (1) /I&J and a&+ are in agreement with the previous ALEPH measurement [ 61 up- dated for new Do branching ratios [ 193 and are more

precise. The ratio of the form factors .&++ (0) and Fn+ (w)

at o = 1 and o = WE% and the difference of their

slopes are measured to be

3I>+(l)

FD*+(l) = 0.87 f 0.22g@ i 0.21,y,t,

FD+ (0s: )

&*+ (@;;?f ) = 1.06 f 0.09,, f 0.1 lsyst,

a;+ - a& = -0.36 1J10.58,~~~ f 0.31syst.

[5] D. Bortoletto et al. (CLEO Coil.), Phys. Rev. Lett. 63, (1989) 2667; R. Fultou et al. (CLEO COIL), Phys. Rev. D 43, (1991) 651; B. Barish et al. (CLEO Coil.), Phys. Rev. D 51 (1995) 1014.

These measured values are in agreement with theoret- [6] D. Buskulic et al. (ALEPH Coil.), Pbys. L&t. B 359 (1995)

ical predictions from HQET. They represent the first 236.

direct tests of HQET prediction of the universality of the Isgur-Wise function.

1 v& 1 iS USUdly derived from FD*+ ( 1) 1 v& 1, although the linear parameterization of the form factor is arbitrary. It is however possible to use a quadratic parameterization of the form factor with only a small loss of precision using theoretical relations between the slope and curvature of the hadronic form factors and their calculated values at o = 1. i&b/ and the slope of the Isgur-Wise function are then measured to be

j&l = (34.4xt 1.6,&t & 2.3,,, f 1.4& x 10-3,

a;4 = 0.30 It 0.12,,,, + 0.14,,,, i 0.13& .

The integrated spectra of the two semileptonic B” decay channels yield the following branching frac-

tions:

Br($-+ D*+e-Fl) = (5.53 i 0.26Stit f 0.52,,,,)%,

Br(&+ D+&?t) = (2.35 f 0.20Stit * 0.44,YSt> % .

Acknowledgements

We are grateful to Irinel Cap&i, Laurent Lellouch and Matthias Neubert for useful discussions. We wish to thank our colleagues from the accelerator division for the successful operation of LEP. We are indebted to the engineers and technicians at CERN and our home institutes for their contribution to the good per-

formance of ALEPH. Those of us from non-member countries thank CERN for its hospitality.

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[3] M. Neubert, Phys. Rep. 245 (1994) 259. [4] H. Albrecht et al. (ARGUS Coil.), Phys. L.&t. B 197 (1989)

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Documents

Measurements of |Vcb|, form factors and branching fractions in the decays B0 → D∗+ℓ−νℓ and B0 → D+ℓ−νℓ