arX

iv:1

112.

0702

v1 [

hep-

ex]

3 D

ec 2

011

BABAR-PUB-11/014SLAC-PUB-14811

Study of B → Xuℓν decays in BB events tagged by a fully reconstructed B-meson

decay and determination of |Vub|

J. P. Lees, V. Poireau, and V. TisserandLaboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),

Universite de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France

J. Garra Tico and E. GraugesUniversitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain

M. Martinelliab, D. A. Milanesa, A. Palanoab, and M. Pappagalloab

INFN Sezione di Baria; Dipartimento di Fisica, Universita di Barib, I-70126 Bari, Italy

G. Eigen and B. StuguUniversity of Bergen, Institute of Physics, N-5007 Bergen, Norway

D. N. Brown, L. T. Kerth, Yu. G. Kolomensky, G. Lynch, and K. TackmannLawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA

H. Koch and T. SchroederRuhr Universitat Bochum, Institut fur Experimentalphysik 1, D-44780 Bochum, Germany

D. J. Asgeirsson, C. Hearty, T. S. Mattison, and J. A. McKennaUniversity of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1

A. KhanBrunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom

V. E. Blinov, A. R. Buzykaev, V. P. Druzhinin, V. B. Golubev, E. A. Kravchenko, A. P. Onuchin,S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, K. Yu. Todyshev, and A. N. Yushkov

Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia

M. Bondioli, D. Kirkby, A. J. Lankford, M. Mandelkern, and D. P. StokerUniversity of California at Irvine, Irvine, California 92697, USA

H. Atmacan, J. W. Gary, F. Liu, O. Long, and G. M. VitugUniversity of California at Riverside, Riverside, California 92521, USA

C. Campagnari, T. M. Hong, D. Kovalskyi, J. D. Richman, and C. A. WestUniversity of California at Santa Barbara, Santa Barbara, California 93106, USA

A. M. Eisner, J. Kroseberg, W. S. Lockman, A. J. Martinez, T. Schalk, B. A. Schumm, and A. SeidenUniversity of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA

C. H. Cheng, D. A. Doll, B. Echenard, K. T. Flood, D. G. Hitlin, P. Ongmongkolkul, F. C. Porter, and A. Y. RakitinCalifornia Institute of Technology, Pasadena, California 91125, USA

R. Andreassen, M. S. Dubrovin, Z. Huard, B. T. Meadows, M. D. Sokoloff, and L. SunUniversity of Cincinnati, Cincinnati, Ohio 45221, USA

P. C. Bloom, W. T. Ford, A. Gaz, M. Nagel, U. Nauenberg, J. G. Smith, and S. R. WagnerUniversity of Colorado, Boulder, Colorado 80309, USA

R. Ayad∗ and W. H. Toki

2

Colorado State University, Fort Collins, Colorado 80523, USA

B. SpaanTechnische Universitat Dortmund, Fakultat Physik, D-44221 Dortmund, Germany

M. J. Kobel, K. R. Schubert, and R. SchwierzTechnische Universitat Dresden, Institut fur Kern- und Teilchenphysik, D-01062 Dresden, Germany

D. Bernard and M. VerderiLaboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France

P. J. Clark and S. PlayferUniversity of Edinburgh, Edinburgh EH9 3JZ, United Kingdom

D. Bettonia, C. Bozzia, R. Calabreseab, G. Cibinettoab, E. Fioravantiab, I. Garziaab,

E. Luppiab, M. Muneratoab, M. Negriniab, A. Petrellaab, L. Piemontesea, and V. SantoroINFN Sezione di Ferraraa; Dipartimento di Fisica, Universita di Ferrarab, I-44100 Ferrara, Italy

R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro,

M. Nicolaci, P. Patteri, I. M. Peruzzi,† M. Piccolo, M. Rama, and A. ZalloINFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy

R. Contriab, E. Guidoab, M. Lo Vetereab, M. R. Mongeab, S. Passaggioa, C. Patrignaniab, and E. Robuttia

INFN Sezione di Genovaa; Dipartimento di Fisica, Universita di Genovab, I-16146 Genova, Italy

B. Bhuyan and V. PrasadIndian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India

C. L. Lee and M. MoriiHarvard University, Cambridge, Massachusetts 02138, USA

A. J. EdwardsHarvey Mudd College, Claremont, California 91711

A. Adametz, J. Marks, and U. UwerUniversitat Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany

F. U. Bernlochner, M. Ebert, H. M. Lacker, and T. LueckHumboldt-Universitat zu Berlin, Institut fur Physik, Newtonstr. 15, D-12489 Berlin, Germany

P. D. Dauncey and M. TibbettsImperial College London, London, SW7 2AZ, United Kingdom

P. K. Behera and U. MallikUniversity of Iowa, Iowa City, Iowa 52242, USA

C. Chen, J. Cochran, W. T. Meyer, S. Prell, E. I. Rosenberg, and A. E. RubinIowa State University, Ames, Iowa 50011-3160, USA

A. V. Gritsan and Z. J. GuoJohns Hopkins University, Baltimore, Maryland 21218, USA

N. Arnaud, M. Davier, G. Grosdidier, F. Le Diberder, A. M. Lutz,B. Malaescu, P. Roudeau, M. H. Schune, A. Stocchi, and G. Wormser

Laboratoire de l’Accelerateur Lineaire, IN2P3/CNRS et Universite Paris-Sud 11,Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, France

D. J. Lange and D. M. Wright

3

Lawrence Livermore National Laboratory, Livermore, California 94550, USA

I. Bingham, C. A. Chavez, J. P. Coleman, J. R. Fry, E. Gabathuler, D. E. Hutchcroft, D. J. Payne, and C. TouramanisUniversity of Liverpool, Liverpool L69 7ZE, United Kingdom

A. J. Bevan, F. Di Lodovico, R. Sacco, and M. SigamaniQueen Mary, University of London, London, E1 4NS, United Kingdom

G. CowanUniversity of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom

D. N. Brown and C. L. DavisUniversity of Louisville, Louisville, Kentucky 40292, USA

A. G. Denig, M. Fritsch, W. Gradl, A. Hafner, and E. PrencipeJohannes Gutenberg-Universitat Mainz, Institut fur Kernphysik, D-55099 Mainz, Germany

K. E. Alwyn, D. Bailey, R. J. Barlow,‡ G. Jackson, and G. D. LaffertyUniversity of Manchester, Manchester M13 9PL, United Kingdom

R. Cenci, B. Hamilton, A. Jawahery, D. A. Roberts, and G. SimiUniversity of Maryland, College Park, Maryland 20742, USA

C. DallapiccolaUniversity of Massachusetts, Amherst, Massachusetts 01003, USA

R. Cowan, D. Dujmic, and G. SciollaMassachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA

D. Lindemann, P. M. Patel, S. H. Robertson, and M. SchramMcGill University, Montreal, Quebec, Canada H3A 2T8

P. Biassoniab, A. Lazzaroab, V. Lombardoa, N. Neriab, F. Palomboab, and S. Strackaab

INFN Sezione di Milanoa; Dipartimento di Fisica, Universita di Milanob, I-20133 Milano, Italy

L. Cremaldi, R. Godang,§ R. Kroeger, P. Sonnek, and D. J. SummersUniversity of Mississippi, University, Mississippi 38677, USA

X. Nguyen and P. TarasUniversite de Montreal, Physique des Particules, Montreal, Quebec, Canada H3C 3J7

G. De Nardoab, D. Monorchioab, G. Onoratoab, and C. Sciaccaab

INFN Sezione di Napolia; Dipartimento di Scienze Fisiche,Universita di Napoli Federico IIb, I-80126 Napoli, Italy

G. Raven and H. L. SnoekNIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands

C. P. Jessop, K. J. Knoepfel, J. M. LoSecco, and W. F. WangUniversity of Notre Dame, Notre Dame, Indiana 46556, USA

K. Honscheid and R. KassOhio State University, Columbus, Ohio 43210, USA

J. Brau, R. Frey, N. B. Sinev, D. Strom, and E. TorrenceUniversity of Oregon, Eugene, Oregon 97403, USA

E. Feltresiab, N. Gagliardiab, M. Margoniab, M. Morandina,

4

M. Posoccoa, M. Rotondoa, F. Simonettoab, and R. Stroiliab

INFN Sezione di Padovaa; Dipartimento di Fisica, Universita di Padovab, I-35131 Padova, Italy

E. Ben-Haim, M. Bomben, G. R. Bonneaud, H. Briand, G. Calderini,

J. Chauveau, O. Hamon, Ph. Leruste, G. Marchiori, J. Ocariz, and S. SittLaboratoire de Physique Nucleaire et de Hautes Energies,IN2P3/CNRS, Universite Pierre et Marie Curie-Paris6,Universite Denis Diderot-Paris7, F-75252 Paris, France

M. Biasiniab, E. Manoniab, S. Pacettiab, and A. Rossiab

INFN Sezione di Perugiaa; Dipartimento di Fisica, Universita di Perugiab, I-06100 Perugia, Italy

C. Angeliniab, G. Batignaniab, S. Bettariniab, M. Carpinelliab,¶ G. Casarosaab, A. Cervelliab, F. Fortiab,

M. A. Giorgiab, A. Lusianiac, B. Oberhofab, E. Paoloniab, A. Pereza, G. Rizzoab, and J. J. Walsha

INFN Sezione di Pisaa; Dipartimento di Fisica, Universita di Pisab; Scuola Normale Superiore di Pisac, I-56127 Pisa, Italy

D. Lopes Pegna, C. Lu, J. Olsen, A. J. S. Smith, and A. V. TelnovPrinceton University, Princeton, New Jersey 08544, USA

F. Anullia, G. Cavotoa, R. Facciniab, F. Ferrarottoa, F. Ferroniab,

M. Gasperoab, L. Li Gioia, M. A. Mazzonia, and G. Pireddaa

INFN Sezione di Romaa; Dipartimento di Fisica,Universita di Roma La Sapienzab, I-00185 Roma, Italy

C. Bunger, O. Grunberg, T. Hartmann, T. Leddig, H. Schroder, and R. WaldiUniversitat Rostock, D-18051 Rostock, Germany

T. Adye, E. O. Olaiya, and F. F. WilsonRutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom

S. Emery, G. Hamel de Monchenault, G. Vasseur, and Ch. YecheCEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France

D. Aston, D. J. Bard, R. Bartoldus, C. Cartaro, M. R. Convery, J. Dorfan, G. P. Dubois-Felsmann, W. Dunwoodie,R. C. Field, M. Franco Sevilla, B. G. Fulsom, A. M. Gabareen, M. T. Graham, P. Grenier, C. Hast, W. R. Innes,

M. H. Kelsey, H. Kim, P. Kim, M. L. Kocian, D. W. G. S. Leith, P. Lewis, S. Li, B. Lindquist, S. Luitz, V. Luth,

H. L. Lynch, D. B. MacFarlane, D. R. Muller, H. Neal, S. Nelson, I. Ofte, M. Perl, T. Pulliam, B. N. Ratcliff,

A. Roodman, A. A. Salnikov, R. H. Schindler, A. Snyder, D. Su, M. K. Sullivan, J. Va’vra, A. P. Wagner,

M. Weaver, W. J. Wisniewski, M. Wittgen, D. H. Wright, H. W. Wulsin, A. K. Yarritu, C. C. Young, and V. ZieglerSLAC National Accelerator Laboratory, Stanford, California 94309 USA

W. Park, M. V. Purohit, R. M. White, and J. R. WilsonUniversity of South Carolina, Columbia, South Carolina 29208, USA

A. Randle-Conde and S. J. SekulaSouthern Methodist University, Dallas, Texas 75275, USA

M. Bellis, J. F. Benitez, P. R. Burchat, and T. S. MiyashitaStanford University, Stanford, California 94305-4060, USA

M. S. Alam and J. A. ErnstState University of New York, Albany, New York 12222, USA

R. Gorodeisky, N. Guttman, D. R. Peimer, and A. SofferTel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel

P. Lund and S. M. SpanierUniversity of Tennessee, Knoxville, Tennessee 37996, USA

5

R. Eckmann, J. L. Ritchie, A. M. Ruland, C. J. Schilling, R. F. Schwitters, and B. C. WrayUniversity of Texas at Austin, Austin, Texas 78712, USA

J. M. Izen and X. C. LouUniversity of Texas at Dallas, Richardson, Texas 75083, USA

F. Bianchiab and D. Gambaab

INFN Sezione di Torinoa; Dipartimento di Fisica Sperimentale, Universita di Torinob, I-10125 Torino, Italy

L. Lanceriab and L. Vitaleab

INFN Sezione di Triestea; Dipartimento di Fisica, Universita di Triesteb, I-34127 Trieste, Italy

V. Azzolini, F. Martinez-Vidal, and A. OyangurenIFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain

H. Ahmed, J. Albert, Sw. Banerjee, H. H. F. Choi, G. J. King, R. Kowalewski,

M. J. Lewczuk, C. Lindsay, I. M. Nugent, J. M. Roney, R. J. Sobie, and N. TasneemUniversity of Victoria, Victoria, British Columbia, Canada V8W 3P6

T. J. Gershon, P. F. Harrison, T. E. Latham, and E. M. T. PuccioDepartment of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

H. R. Band, S. Dasu, Y. Pan, R. Prepost, and S. L. WuUniversity of Wisconsin, Madison, Wisconsin 53706, USA

We report measurements of partial branching fractions for inclusive charmless semileptonic Bdecays B → Xuℓν, and the determination of the CKM matrix element |Vub|. The analysis is basedon a sample of 467 million Υ (4S) → BB decays recorded with the BABAR detector at the PEP-IIe+e− storage rings. We select events in which the decay of one of the B mesons is fully reconstructedand an electron or a muon signals the semileptonic decay of the other B meson. We measurepartial branching fractions ∆B in several restricted regions of phase space and determine the CKMelement |Vub| based on four different QCD predictions. For decays with a charged lepton momentump∗ℓ > 1.0 GeV in the B meson rest frame, we obtain ∆B = (1.80±0.13stat.±0.15sys.±0.02theo.)×10−3

from a maximum likelihood fit to the two-dimensional MX – q2 distribution. Here, MX refers tothe invariant mass of the final state hadron X and q2 is the invariant mass squared of the chargedlepton and neutrino. From this measurement we extract |Vub| = (4.31± 0.25exp. ± 0.16theo.)× 10−3

as the arithmetic average of four results obtained from four different QCD predictions of the partialrate. We separately determine partial branching fractions for B0 and B− decays and derive a limiton the isospin breaking in B → Xuℓν decays.

PACS numbers: 13.20.He, 12.15.Hh, 12.38.Qk, 14.40.Nd

I. INTRODUCTION

A principal physics goal of the BABAR experiment isto establish CP violation in B meson decays and to testwhether the observed effects are consistent with the Stan-dard Model (SM) expectations. In the SM, CP -violating

∗Now at Temple University, Philadelphia, Pennsylvania 19122,

USA†Also with Universita di Perugia, Dipartimento di Fisica, Perugia,

Italy‡Now at the University of Huddersfield, Huddersfield HD1 3DH,

UK§Now at University of South Alabama, Mobile, Alabama 36688,

USA¶Also with Universita di Sassari, Sassari, Italy

effects result from an irreducible phase in the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [1, 2].Precise determinations of the magnitude of the matrixelement |Vub| will permit more stringent tests of the SMmechanism for CP violation. This is best illustrated interms of the unitarity triangle [3], the graphical repre-sentation of one of the unitarity conditions of the CKMmatrix, for which the side opposite to the angle β is pro-portional to the ratio |Vub|/|Vcb|. The best way to deter-mine |Vub| is to measure the decay rate for B → Xuℓν(here X refers to a hadronic final state and the index cor u indicates whether this state carries charm or not),which is proportional to |Vub|2.There are two approaches to these measurements,

based on either inclusive or exclusive measurements ofsemileptonic decays. The experimental uncertainties onthe methods are largely independent, and the extraction

6

of |Vub| from the measured branching fractions relies ondifferent sets of calculations of the hadronic contributionsto the matrix element. For quite some time, the resultsof measurements of |Vub| from inclusive and exclusive de-cays have been only marginally consistent [4, 5]. Globalfits [6, 7] testing the compatibility of the measured an-gles and sides with the unitarity triangle of the CKMmatrix reveal small differences that might indicate po-tential deviations from SM expectations. Therefore, it isimportant to perform redundant and improved measure-ments, employing different experimental techniques anda variety of theoretical calculations, to better assess theaccuracy of the theoretical and experimental uncertain-ties.

Although inclusive branching fractions exceed those ofindividual exclusive decays by an order of magnitude, themost challenging task for inclusive measurements is thediscrimination between the rare charmless signal and themuch more abundant decays involving charmed mesons.To improve the signal-to-background ratio, the events arerestricted to selected regions of phase space. Unfortu-nately these restrictions lead to difficulties in calculat-ing partial branching fractions. They impact the conver-gence of Heavy Quark Expansions (HQE) [8, 9], enhanceperturbative and nonperturbative QCD corrections, andthus lead to significantly larger theoretical uncertaintiesin the determination of |Vub|.We report herein measurements of partial branching

fractions (∆B) for inclusive charmless semileptonic Bmeson decays, B → Xuℓν [10]. This analysis extendsthe event selection and methods employed previously byBABAR to a larger dataset [11]. We tag Υ (4S) → BBevents with a fully reconstructed hadronic decay of oneof the B mesons (Breco). This technique results in a lowevent selection efficiency, but it uniquely determines themomentum and charge of both B mesons in the event, re-ducing backgrounds significantly. For charged B mesonsit also determines their flavor. The semileptonic decayof the second B meson (Brecoil) is identified by the pres-ence of an electron or a muon and its kinematics areconstrained such that the undetectable neutrino can beidentified from the missing momentum and energy of therest of the event. However, undetected and poorly re-constructed charged particles or photons lead to largebackgrounds from the dominant B → Xcℓν decays, andthey distort the kinematics, e.g., the hadronic mass MX

and the leptonic mass squared q2.

For the Breco sample, the two dominant backgroundsources are non-BB events from continuum processes,e+e− → qq(γ) with q = u, d, s, or c, and com-binatorial BB background. The sum of these twobackgrounds is estimated from the distribution of thebeam energy-substituted mass mES, which takes thefollowing form in the laboratory frame: mES =√

(s/2 + ~pB · ~pbeams)2/E2beams − ~p 2

B. Here ~pB refers tothe momentum of the Breco candidate derived from themeasured momenta of its decay products, Pbeams =(Ebeams, ~pbeams) to the four-momentum of the colliding

beam particles, and√s to the total energy in the Υ (4S)

frame. For correctly reconstructed Breco decays, the dis-tribution peaks at the B meson mass, and the width ofthe peak is determined by the energy spread of the col-liding beams (typically less than 1 MeV). The size ofthe underlying background is determined from a fit tothe mES distribution.

We minimize experimental systematic uncertainties,by measuring the yield for selected charmless semilep-tonic decays relative to the total yield of semileptonicdecays B → Xℓν, after subtracting combinatorial back-grounds of the Breco selection from both samples.

In order to reduce the overall uncertainties, measure-ment of the signal B → Xuℓν decays is restricted toregions of phase space where the background from thedominant B → Xcℓν decays is suppressed and theo-retical uncertainties can be reliably assessed. Specifi-cally, signal events tend to have higher charged leptonmomenta in the B-meson rest frame (p∗ℓ ), lower MX ,higher q2, and smaller values of the light-cone momen-tum P+ = EX − |~pX |, where EX and ~pX are energy andmomentum of the hadronic system X in the B mesonrest frame.

The observation of charged leptons with momenta ex-ceeding the kinematic limit for B → Xcℓν presented firstevidence for charmless semileptonic decays. This wasfollowed by a series of measurements close to this kine-matic limit [12–16]. Although the signal-to-backgroundratio for this small region of phase space is favorable, thetheoretical uncertainties are large and difficult to quan-tify. Since then, efforts have been made to select largerphase space regions, thereby reducing the theoretical un-certainties. The Belle Collaboration has recently pub-lished an analysis that covers about 88% of the signalphase space [17], similarly to one of the studies detailedin this article.

We extract |Vub| from the partial branching fractionsrelying on four different QCD calculations: BLNP byBosch, Lange, Neubert, and Paz [18–20]; DGE, thedressed gluon exponentiation by Andersen and Gardi [21,22]; ADFR by Aglietti, Di Lodovico, Ferrara, and Riccia-rdi [23, 24]; and GGOU by Gambino, Giordano, Ossolaand Uraltsev [25]. These calculations differ significantlyin their treatment of perturbative corrections and theparameterization of nonperturbative effects that becomeimportant for the different restrictions in phase space.

This measurement of |Vub| is based on combined sam-ples of charged and neutral B mesons. In addition, wepresent measurements of the partial decays rates for B0

and B− decays separately. The observed rates are foundto be equal within uncertainties. We use this observationto set a limit on weak annihilation (WA), the processbu→ ℓ−νℓ, which is not included in the QCD calculationof the B → Xℓν decay rates. Since final state hadronsoriginate from soft gluon emission, WA is expected tocontribute to the decay rate at large values of q2 [26, 27].

The outline of this paper is as follows: a brief overviewof the BABAR detector, particle reconstruction and the

7

data and Monte Carlo (MC) samples is given in Sec-tion II, followed in Section III by a description of theevent reconstruction and selection of the two event sam-ples, the charmless semileptonic signal sample and theinclusive semileptonic sample that serves as normaliza-tion. The measurement of the partial branching fractionsand their systematic uncertainties are presented in Sec-tions IV and V. The extraction of |Vub| based on four setsof QCD calculations for seven selected regions of phasespace is presented in Section VI, followed by the conclu-sions in Section VII.

II. DATA SAMPLE, DETECTOR, AND

SIMULATION

A. Data sample

The data used in this analysis were recorded with theBABAR detector at the PEP-II asymmetric energy e+e−

collider operating at the Υ (4S) resonance. The totaldata sample, corresponding to an integrated luminosityof 426 fb−1 and containing 467 million Υ (4S) → BBevents, was analyzed.

B. The BABAR detector

The BABAR detector and the general event reconstruc-tion are described in detail elsewhere [28, 29]. Forthis analysis, the most important detector features arethe charged-particle tracking, photon reconstruction, andparticle identification. The momenta and angles ofcharged particles are measured in a tracking system con-sisting of a five-layer silicon vertex tracker (SVT) and a40-layer, small-cell drift chamber (DCH). Charged parti-cles of different masses are distinguished by their ioniza-tion energy loss in the tracking devices and by the DIRC,a ring-imaging detector of internally reflected Cherenkovradiation. A finely segmented electromagnetic calorime-ter (EMC) consisting of 6580 CsI(Tl) crystals measuresthe energy and position of showers generated by electronsand photons. The EMC is surrounded by a thin super-conducting solenoid providing a 1.5 T magnetic field andby a steel flux return with a hexagonal barrel sectionand two endcaps. The segmented flux return (IFR) is in-strumented with multiple layers of resistive plate cham-bers (RPC) and limited streamer tubes (LST) to identifymuons and to a lesser degree KL.

C. Single particle reconstruction

In order to reject misidentified and background tracksthat do not originate from the interaction point, we re-quire the radial and longitudinal impact parameters tobe r0 < 1.5 cm and |z0| < 10 cm. For secondary tracksfrom KS → π+π− decays, no restrictions on the impact

parameter are imposed. The efficiency for the reconstruc-tion of charged particles inside the fiducial volume of thetracking system exceeds 96% and is well reproduced byMonte Carlo (MC) simulation.

Electromagnetic showers are detected in the EMC asclusters of energy depositions. Photons are required notto be matched to a charged track extrapolated to the po-sition of the shower maximum in the EMC. To suppressphotons from beam-related background, we only retainphotons with energies larger than 50 MeV. Clusters cre-ated by neutral hadrons (KL or neutrons) interacting inthe EMC are distinguished from photons by their showershape.

Electrons are primarily separated from chargedhadrons on the basis of the ratio of the energy depositedin the EMC to the track momentum. This quantityshould be close to 1 for electrons since they depositall their energy in the calorimeter. Most other chargedtracks are minimum ionizing, unless they shower in theEMC crystals.

Muons are identified by a neural network that com-bines information from the IFR with the measured trackmomentum and the energy deposition in the EMC.

Within the acceptance of SVT, DCH, and EMC, de-fined by the polar angle in the laboratory frame, 0.410 <θlab < 2.54 rad, the average electron efficiency for labo-ratory momenta above 0.5 GeV is 93%, largely indepen-dent of momentum. The average hadron misidentifica-tion rate is less than 0.2%. Within the same polar-angleacceptance, the average muon efficiency rises with labo-ratory momentum and reaches a plateau of about 70%above 1.4 GeV. The muon efficiency varies between 50%and 80% as a function of the polar angle. The averagehadron misidentification rate is about 1.5%, varying byabout 0.5% as a function of momentum and polar angle.

Charged kaons are selected on the basis of informationfrom the DIRC, DCH, and SVT. The efficiency is higherthan 80% over most of the momentum range and varieswith the polar angle. The probability of a pion to bemisidentified as a kaon is close to 2%, varying by about1% as a function of momentum and polar angle.

Neutral pions are reconstructed from pairs of photoncandidates that are detected in the EMC and are as-sumed to originate from the primary vertex. Photonpairs having an invariant mass within 17.5 MeV of thenominal π0 mass are considered π0 candidates. The over-all detection efficiency, including solid angle restrictions,varies between 55% and 65% for π0 energies in the rangeof 0.2 to 2.5 GeV.

K0S→ π+π− decays are reconstructed as pairs of tracks

of opposite charge with a common vertex displaced fromthe interaction point. The invariant mass of the pair isrequired to be in the range 490 < mπ+π− < 505 MeV.

8

D. Monte Carlo simulation

We use MC techniques to simulate the response of theBABAR detector [30] and the particle production and de-cays [31], to optimize selection criteria and to determinesignal efficiencies and background distributions. Theagreement of the simulated distributions with those indata has been verified with control samples, as shownin Section IVD; the impact of the inaccuracies of thesimulation is estimated in Section V.The size of the simulated sample of generic BB events

exceeds the BB data sample by about a factor of three.This sample includes the common B → Xcℓν decays.MC samples for inclusive and exclusiveB → Xuℓν decaysexceed the size of the data samples by factors of 15 ormore.Charmless semileptonic B → Xuℓν decays are sim-

ulated as a combination of resonant three-body decayswith Xu = π, η, η′, ρ, ω, and decays to nonresonanthadronic final states Xu. The branching ratios assumedfor the various resonant decays are detailed in Table I.Exclusive charmless semileptonic decays are simulatedusing a number of different parameterizations: for B →πℓν decays we use a single-pole ansatz [32] for the q2 de-pendence of the form factor with a single parameter mea-sured by BABAR [33]; for decays to pseudoscalar mesonsη and η′ and vector mesons ρ and ω we use form fac-tor parameterizations based on light-cone sum calcula-tions [34, 35].The simulation of the inclusive charmless semileptonic

B decays to hadronic states with masses larger than2mπ is based on a prescription by De Fazio and Neu-bert (DFN) [36] for the triple-differential decay rate,d3Γ / dq2 dEℓ dsH (Eℓ refers to the energy of the chargedlepton and sH = M2

X) with QCD corrections up toO(αs). The motion of the b quark inside the B me-son is incorporated in the DFN formalism by convolvingthe parton-level triple-differential decay rate with a non-perturbative shape function (SF). This SF describes thedistribution of the momentum k+ of the b quark insidethe B meson. The two free parameters of the SF are ΛSF

and λ1SF. The first relates the B meson mass mB to the

b quark mass, mSFb = mB − ΛSF, and λ1

SF is the averagemomentum squared of the b quark. The SF parameter-ization is of the form F (k+) = N(1 − x)ae(1+a)x, where

x = k+/ΛSF ≤ 1 and a = −3(ΛSF)2/λ1

SF − 1. The firstthree moments Ai of the SF must satisfy the followingrelations: A0 = 1, A1 = 0 and A2 = −λ1SF/3.The nonresonant hadronic state Xu is simulated with

a continuous invariant mass spectrum according to theDFN prescription. The fragmentation of the Xu systeminto final state hadrons is performed by jetset [37]. Theresonant and nonresonant components are combined suchthat the sum of their branching fractions is equal to themeasured branching fraction for inclusive B → Xuℓν de-cays [38], and the spectra agree with the DFN prediction.In order to obtain predictions for different values of ΛSF

and λ1SF, the generated events are reweighted.

TABLE I: Branching fractions and their uncertainties [38] forexclusive B → Xuℓν decays

mode B(B0 → Xuℓν) B(B− → Xuℓν)

B → πℓν (136± 7) · 10−6 (77± 12) · 10−6

B → ηℓν (64± 20) · 10−6

B → ρℓν (247± 33) · 10−6 (128± 18) · 10−6

B → ωℓν (115± 17) · 10−6

B → η′ℓν (17± 22) · 10−6

We estimate the shape of background distributionsby using simulations of the process e+e− → Υ (4S) →BB with the B mesons decaying according to measuredbranching fractions [38].For the simulation of the dominant background from

B → Xcℓν decays, we have chosen a variety of differ-ent form factor parameterizations. For B → Dℓν andB → D∗ℓν decays we use parameterizations [39] basedon heavy quark effective theory (HQET) [40–43]. Inthe limit of negligible charged lepton masses, decays topseudoscalar mesons are described by a single form fac-tor for which the q2 dependence is expressed in termsof a slope parameter ρ2D. We use the world averageρ2D = 1.18± 0.06 [44], updated with recent precise mea-surements by the BABAR Collaboration [45, 46]. De-cays to vector mesons are described by three form fac-tors, of which the axial vector form factor dominates.In the limit of heavy quark symmetry, their q2 depen-dence can be described by three parameters for whichwe use the most precise BABAR measurements [45, 47]:ρ2D∗ = 1.20 ± 0.04 [45, 47], R1 = 1.429 ± 0.074, andR2 = 0.827 ± 0.044 [47]. For the simulation of semilep-tonic decays to the four L=1 charm states, commonly re-ferred to as D∗∗ resonances, we use calculations of formfactors by Leibovich, Ligeti, Stewart, and Wise [48]. Wehave adopted the prescription by Goity and Roberts [49]for nonresonant B → D(∗)Xℓν decays.

III. EVENT RECONSTRUCTION AND SIGNAL

EXTRACTION

A. Reconstruction of hadronic B decays tagging

BB events

Υ (4S) → BB events are tagged by the hadronic de-cays of one of the B mesons based on a semi-exclusivealgorithm that was employed in an earlier analysis [11].We look for decays of the type Breco → D(∗)Y ±, whereD(∗) is a charmed meson (D0, D+, D∗0, or D∗±) andY is a charged state decaying to up to five chargedhadrons, pions or kaons, plus up to two neutral mesons(K0

Sor π0). The following decay modes of D mesons

are reconstructed: D0 → K−π+, K−π+π0, K−π+π−π+,K0

Sπ+π− and D+ → K−π+π+, K−π+π+π0, K0

Sπ+,

9

K0Sπ+π+π−, K0

Sπ+π0 with K0

S→ π+π−. D∗ mesons

are identified by their decays, D∗+ → D0π+, D+π0,and D∗0 → D0π0, D0γ. Pions and photons from D∗ de-cays are of low energy and therefore the mass difference∆M = m(Dπ)−m(D) serves as an excellent discrimina-tor for these decays.Among the very large number of Breco decay chains we

only retain those with a signal purity P = S/(S +B) >20%, where S and B, derived from MC samples, de-note the signal and background yields. The kinematicconsistency of the Breco candidates with B meson de-cays is checked using mES and the energy difference,∆E = (PB · Pbeams − s/2)/

√s. We restrict the Breco

mass to mES > 5.22 GeV and require ∆E = 0 GeVwithin approximately three standard deviations, wherethe ∆E resolution depends on the decay chain. If anevent contains more than one Breco candidate, the decaychain with the highest χ2 probability is chosen. For thispurpose we define

χ2total = χ2

vertex +

(

MD

(∗)reco

−MD(∗)

σD

(∗)reco

)2

+

(

∆E

σ∆E

)2

. (1)

Here the first term is taken from a vertex fit for tracksfrom Breco decays, the second relates reconstructed andnominal masses [38], M

D(∗)reco

and MD(∗) , of the charm

mesons (D0, D+, D∗0 orD∗±), with the resolution σD

(∗)reco

,

and the third term checks the energy balance ∆E com-pared to its resolution σ∆E . The number of degrees offreedom is therefore defined as Ndof = Ndof

vertex + 2. Theresulting overall tagging efficiency is 0.3% for B0B0 and0.5% for B+B− events.

B. Selection of inclusive B → Xℓν decays

In order to minimize systematic uncertainties, we mea-sure the yield of selected charmless semileptonic decays ina specific kinematic region normalized to the total yieldof semileptonic B → Xℓν decays. Both semileptonicdecays, the charmless and the normalization modes, areidentified by at least one charged lepton in events that aretagged by a Breco decay. Both samples are background-subtracted and corrected for efficiency. Using this nor-malization, the systematic uncertainties on the Breco re-construction and the charged lepton detection cancel inthe ratio or are eliminated to a large degree.The selection criteria for the charmless and the total

semileptonic samples are chosen to minimize the statisti-cal uncertainty of the measurement as estimated from asample of fully simulated MC events that includes bothsignal and background processes.A restriction on the momentum of the electron or

muon is applied to suppress backgrounds from secondarycharm or τ± decays, photon conversions and misidenti-fied hadrons. This is applied to p∗ℓ , the lepton momen-tum in the rest frame of the recoiling B meson, which is

accessible since the momenta of the Υ (4S) and the recon-structed B are known. This transformation is importantbecause theoretical calculations refer to variables thatare Lorentz-invariant or measured in the rest frame ofthe decaying B meson. We require p∗ℓ to be greater than1 GeV, for which about 90% of the signal is retained.For electrons and muons the angular acceptance is de-

fined as 0.450 < θ < 2.473 rad, where θ refers to thepolar angle relative to the electron beam in the labo-ratory frame. This requirement excludes regions wherecharged particle tracking and identification are not effi-cient. We suppress muons from J/ψ decays by reject-ing the event if a muon candidate paired with any othercharged track of opposite charge (and not part of Breco)results in an invariant mass of the pair that is consistentwith the J/ψ mass. A similar requirement is not imposedon electron candidates, because of their higher selectionefficiency. We also reject events if the electron candidatepaired with any other charged track of opposite charge isconsistent with a γ → e+e− conversion.A variety of processes contributes to the inclusive

semileptonic event samples, i .e. candidates selected bya Breco decay and the presence of a high momentum lep-ton. In addition to true semileptonic decays tagged by acorrectly reconstructed Breco, we consider the followingclasses of backgrounds:

• Combinatorial background: the Breco is not cor-rectly reconstructed. This background originatesfrom BB or continuum e+e− → qq(γ) events. Inorder to subtract this background, the yield of trueBreco decays is determined from an unbinned max-imum likelihood fit to the mES distribution (Sec-tion IIID).

• Cascade background: the lepton does not origi-nate from a semileptonic B decay, but from sec-ondary decays, for instance from D mesons, includ-ing Ds → τν, or residual J/ψ background.

• τ background: electrons or muons originate fromprompt τ leptons, primarily fromB → Xτν decays.

• Fake leptons: hadrons are misidentified as leptons,primarily muons.

The last three sources of background are combined andin the following are referred to as “other” background.

C. Selection of inclusive B → Xuℓν decays

A large fraction of B → Xcℓν decays is expected tohave a second lepton from cascade decays of the charmparticles. In contrast, in B → Xuℓν decays secondaryleptons are very rare. Therefore, we enhance signalevents by selecting events with only one charged leptonhaving p∗ℓ > 1 GeV.In semileptonic B meson decays, the charge of the pri-

mary lepton is equal to the sign of the charge of the b

10

(GeV)X M∆-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Ent

ries

/ 32

MeV

0

50

100

150

200

250

300

350

)2 (GeV2 q∆-3 -2 -1 0 1 2 3

2E

ntrie

s / 1

20 M

eV

020406080

100120140160180200220

(GeV)+ P∆-0.4 -0.2 0 0.2 0.4

Ent

ries

/ 14

MeV

0

50

100

150

200

250

300

350

FIG. 1: Resolution for MC simulated for signal B → Xuℓν events passing all event selection criteria, (left) MX reco −MX true,(center) q2reco − q2true, and (right) P+,reco − P+,true. The curve shows a fit results for the sum of two Gaussian functions.

quark. Thus for B+B− events in which the Breco andthe lepton originate from different B decays in the event,we impose the requirement QbQℓ < 0, where Qb is thecharge of the b quark of the Breco and Qℓ is the chargeof the lepton. For B0B0 events this condition does notstrictly hold because of flavor mixing. Thus, to avoid aloss in efficiency, this requirement is not imposed. Thehadronic state Xu in charmless semileptonic decays is re-constructed from all particles that are not associated withthe Breco candidate or the charged lepton. The measuredfour-momentum PX is defined as

PX =

Ntrk∑

i=1

P trki +

Nγ∑

i=1

P γi , (2)

where the summation extends over the four-vectors of thecharged particles and photon candidates. From this four-vector, other kinematic variables,M2

X = P 2X = E2

X −p2X ,q2, and P+, can be calculated.The loss of one or more charged or neutral particles

or the addition of tracks or single electrons from photonconversions degrade the reconstruction ofXu and the res-olution of the measurement of any related kinematic vari-ables. In order to reduce the impact of missing chargedparticles and the effect of single electrons from γ → e+e−

conversions, we impose charge conservation on the wholeevent, Qtot = QBreco + QX + Qℓ = 0. This requirementrejects a larger fraction of B → Xcℓν events because oftheir higher charged multiplicity and the presence of verylow momentum charged pions from D∗± → D0π±

soft de-cays which have low detection efficiency.The resolution functions determined from MC simula-

tion of signal events passing the selection requirementsare shown in Fig. 1 for the variables MX , q2, and P+.Each of these distributions has a narrow core contain-ing 30%, 50%, and 30% of the B → Xuℓν events, withwidths of 25MeV, 250MeV2, and 10MeV, respectively.The remaining events have a considerably poorer resolu-tion, primarily because of lost secondary particles fromthe decay of the hadronic Xu.

In B → Xℓν decays, where the state X decays hadron-ically, the only undetected particle is a neutrino. Theneutrino four-momentum Pν can be estimated from themissing momentum four-vector Pmiss = PΥ (4S)−PBreco −PX −Pℓ. For correctly reconstructed events with a singlesemileptonic decay, the missing mass squared, MM 2 =P 2miss, is consistent with zero. Failure to detect one or

more particles in the event creates a tail at large positivevalues; thus MM 2 is used as a measure of the quality ofthe event reconstruction. Though MM 2 is Lorentz in-variant, the missing momentum is usually measured inthe laboratory frame, because this avoids the additionaluncertainty related to the transformation into the c.m.frame. We require MM 2 to be less than 0.5 GeV2. Be-cause of the higher probability for additional unrecon-structed neutral particles, a neutrino or KL, the MM 2

distribution is broader for B → Xcℓν decays, and thisrestriction suppresses this background more than signalevents.

In addition, we suppress the B → D∗ℓν backgroundby exploiting the small Q-value of the D∗ → Dπsoft de-cays which result in a very low momentum pion. Forenergetic D∗ mesons, the momenta pπsoft

and pD arealmost collinear, and we can approximate the D∗ di-rection by the πsoft direction and estimate the D∗ en-ergy by a simple approximation based on the Eπsoft

,ED∗ ≈ mD∗×Eπsoft

/145 MeV. Using the measured Breco

and charged lepton momenta, and the four-momentum ofthe D∗ derived from any pion with c.m. momentum be-low 200 MeV, we estimate the neutrino mass for a poten-tial B → D∗ℓν decay as MM 2

veto = (PB−PD∗−Pℓ)2. For

true B → D∗ℓν decays, this distribution peaks at zero.Thus, we veto D∗ decays to low momentum charged orneutral pions by requiring, respectively, MM 2

veto(π+soft) <

−3 GeV2 or MM 2veto(π

0soft) < −2 GeV2. This is achieved

without explicit reconstruction of the D meson decays,and thus avoids large losses in rejection power for thisveto.

We reduce B → D∗ℓν background by vetoing eventswith a charged or neutral kaon (K0

S→ π+π−), that orig-

11

inate primarily from the decays of charm particles.A summary of the impact of the signal selection cri-

teria on the high-energy lepton sample, for the signal,semileptonic and nonsemileptonic background samples ispresented in Table II, in terms of cumulative selectionefficiencies. Combinatorial background is not included;it is subtracted based on fits to the mES distributions,as described in Section IIID. The overall efficiency forselecting charmless semileptonic decays in the sample oftagged events with a charged lepton is 33.8%; the back-ground reduction is 97.8% for B → Xcℓν and 95.3% for“other”.

TABLE II: Comparison of the cumulative selection efficien-cies for samples of signal B → Xuℓν decays and B → Xcℓνand “other” backgrounds. The efficiencies are relative to thesample of Breco-tagged events with a charged lepton.

Selection B → Xuℓν B → Xcℓν OtherOnly one lepton 99.3% 98.1% 95.8%Total charge Q=0 65.5% 52.9% 49.1%MM 2 44.2% 17.8% 17.8%D∗ℓν (π+

s ) veto 40.6% 9.9% 14.4%D∗ℓν (π0

s) veto 34.8% 6.3% 9.1%Kaon veto 33.8% 2.2% 4.7%

On the basis of the kaon and the D∗ veto, two datasamples are defined:

• signal-enriched: events that pass the vetoes; thissample is used to extract the signal;

• signal-depleted: events rejected by at least one veto;they are used as control sample to check the agree-ment between data and simulated backgrounds, in-cluding the poorly understood B → D∗∗ℓν decays.

D. Subtraction of combinatorial background

The subtraction of the combinatorial background ofthe Breco tag for the signal and normalization samplesrelies on unbinned maximum-likelihood fits to the mES

distributions. For signal decays the goal is to extract thedistributions in the kinematic variables p∗ℓ , MX , q2, andP+. Because the shapes and relative yields of the signaland background contributions depend on the values ofthese kinematic variables, the continuum and combina-torial background subtraction is performed separately forsubsamples corresponding to events in bins of these vari-ables. This results in more accurate spectra than a singlefit to the full sample of events in each selected region ofphase space.For the normalization sample, the fit is performed for

the full event sample, separately for B0 and B− tags.ThemES distribution for the combinatorial Breco back-

ground can be described by an ARGUS function [50],

fbkg(m) = Nbkgm√

1−m2e−ξ(1−m2), (3)

where m = mES/mESmax and mES

max is the endpointof the mES distribution which depends on the beam en-ergy, and ξ determines the shape of the function. Nbkg

refers to the total number of background events in thedistribution.For signal events, the mES distribution resembles a

resolution function peaking at the B meson mass witha slight tail to lower masses. Usually the peak of themES distribution is empirically described by a CrystalBall function [51], but this ansatz turned out to be in-adequate for this dataset because the Breco sample iscomposed of many individual decay modes with differentresolutions. We therefore follow an approach previouslyused in BABAR data [52] and build a more general func-

tion, using a Gaussian function, fg(x) = e−x2/2, and thederivative of tanhx, ft(x) = e−x/(1 + e−x), to arrive at

fsig(∆) =

C2

(C3−∆)n if ∆ < αC1

σLft(

∆σL

) if α 6 ∆ < 0rσ1ft(

∆σ1) + 1−r

σ2fg(

∆σ2) if ∆ > 0.

(4)

Here ∆ = mES − mES, where mES is the maximum ofthe mES distribution. C1, C2 and C3 are functions of theparameters mES, r, σ1, σ2, σL, α, and n, that ensure thecontinuity of fsig.Given the very large number of parameters, we first

perform a fit to samples covering the full kinematic rangeand determine all parameters describing fsig and the AR-GUS function. We then repeat the fit for events in eachbin of the kinematic variables, with only the relative nor-malization of the signal and background, and the shapeparameter ξ of the ARGUS function as free parameters.Figure 2 shows the mES distribution for the inclusivesemileptonic sample, separately for charged and neutralB mesons.

5.22 5.24 5.26 5.28

Ent

ries

/ 0.5

MeV

0

5000

10000

(GeV)ESm5.24 5.26 5.28

0

5000

10000

FIG. 2: The mES distribution for the inclusive semileptonicsample, for fully reconstructed hadronic decays of B− (left)and B0 mesons (right). The solid line shows the result ofthe maximum-likelihood fit to signal and combinatorial back-grounds; the dashed line indicates the shape of the back-ground described by an ARGUS function.

Finally, we correct for the contamination from cascade

12

background in the number of neutral B mesons, due tothe effect of B0-B0 mixing, in each bin of the kinematicvariables. We distinguish neutral B decays with right-and wrong-sign leptons, based on the flavor of the Breco

decay. The contribution from cascade decays is sub-tracted by computing the number of neutral B mesonsNB0 as

NB0 =1− χd

1− 2χdNB0

rs− χd

1− 2χdNB0

ws, (5)

whereNB0rsandNB0

wsare the number of neutralB mesons

with right and wrong sign of the charge of the accompa-nying lepton, and χd = 0.188 ± 0.002 [38] is the B0-B0

mixing parameter.The performance of the mES fit has been verified using

MC simulated distributions. We split the full sample intwo parts. One part, containing one third of the events,is treated as data, and is similar in size to the total datasample. The remaining two thirds represent the simu-lation. The fit procedure, described in Section IV, isapplied to these samples and yields, within uncertain-ties, the charmless semileptonic branching fraction thatis input to the MC generation.

IV. SIGNAL EXTRACTION AND PARTIAL

BRANCHING FRACTION MEASUREMENT

A. Signal yield

Once continuum and combinatorial BB backgroundshave been subtracted and the mixing correction has beenapplied, the resulting differential distributions of thekinematic variables are fitted using a χ2 minimizationto extract Nu, the number of selected signal events. Theχ2 for these fits is defined as

χ2 =∑

i

[N i − (CsigNi,MCu + CbkgN

i,MCbkg )]2

σ(N i)2 + σ(N i,MC)2, (6)

where, for each bin i of variable width, N i is the num-

ber of observed events, and N i,MCu and N i,MC

bkg are thenumber of MC predicted events for signal and back-ground, respectively. The statistical uncertainties σ(N i)and σ(N i,MC) are are taken from fits to themES distribu-tions in data and MC simulations. The scale factors Csig

and Cbkg are free parameters of the fit. The differentialdistributions are compared with the sum of the signal andbackground distributions resulting from the fit in Figs. 3and 4. For the B → Xuℓν signal contributions we distin-guish between decays that were generated with values ofthe kinematic variable inside the restricted phase spaceregions, and a small number of events, Nout

u , with valuesoutside these regions. This distinction allows us to re-late the fitted signal yields to the theoretical calculationsapplied to extract |Vub|.

B. Partial branching fractions

We obtain partial branching fractions for charmlesssemileptonic decays from the observed number of signalevents in the kinematic regions considered, after correc-tion for background and efficiency, and normalization tothe total number of semileptonic decays B → Xℓν ob-served in the Breco event sample. For each of the re-stricted regions of phase space under study, we calculatethe ratio

∆Ru/sl =∆B(B → Xuℓν)

B(B → Xℓν)=N true

u

N truesl

=(Nu)/(ǫ

uselǫ

ukin)

(Nsl −BGsl)

ǫslℓ ǫsltag

ǫuℓ ǫutag

. (7)

Here, N trueu and N true

sl refer to the true number of signaland normalization events. The observed signal yield Nu

is related to N trueu by Nu = ǫuselǫ

ukinǫ

ul ǫ

utagN

trueu , where ǫusel

is the efficiency for detecting B → Xuℓν decays in thetagged sample after applying all selection criteria, ǫkin isthe fraction of signal events with both true and recon-structed MX , P+, q

2, or p∗ℓ within the restricted regionof phase space, and ǫul refers to the efficiency for select-

ing a lepton from a B → Xuℓν decay with a momentump∗ℓ > 1 GeV in a signal event tagged with efficiency ǫutag.

Similarly, N truesl is related to Nsl, the fitted number of

observed Breco accompanied by a charged lepton withp∗ℓ > 1 GeV, through N true

sl = (Nsl−BGsl)/ǫslℓ ǫ

sltag. Here,

BGsl is the remaining peaking background estimatedfrom MC simulation and Nsl is obtained from the mES

fit to the selected semileptonic sample and ǫslℓ refers tothe efficiency for selecting a lepton from a semileptonic Bdecay with a momentum p∗ℓ > 1 GeV in an event taggedwith efficiency ǫsltag. We obtain Nsl = 237, 433± 838 andBGsl = 20, 705± 132.The ratio of efficiencies in Eq. (7) accounts for dif-

ferences in the final states and the different lepton mo-mentum spectra for the two classes of events, and theirimpact on the tagging. The efficiencies for Breco taggingand lepton detection are not very different, and thus theefficiency ratio is close to one.We convert Eq. (7) to partial branching fractions by

using the total semileptonic branching fraction, B(B →Xℓν) = (10.75± 0.15)% [38].The regions of phase space, fitted event yields, efficien-

cies introduced in Eq. (7), and partial branching fractionsare listed in Table III; the regions are one-dimensional inMX , P+, or p

∗ℓ , or two-dimensional in the plane MX ver-

sus q2. In the following, we will refer to the latter asMX – q2. Two fits have been performed with no addi-tional kinematic restrictions, apart from the requirementp∗ℓ > 1 GeV: a fit to the lepton momentum spectrum anda fit to the two-dimensional histogram MX – q2. Sincethe same events enter both fits, the correlation is veryhigh. The fact that the results are in excellent agreementindicates that the distribution of the simulated signal andbackground distributions agree well with the data.

13

-100

0

0 2 4

100

200300

0

1000

2000

3000 (a)

MX(GeV)

Ent

ries/

0.31

GeV

Ent

ries/

bin

0

200

1000

2000

3000

0

420P+(GeV)

Ent

ries/

0.22

GeV

Ent

ries/

bin

(b)

0

100

2000

200

400

600

0 10 20q2(GeV2)

Ent

ries/

2 G

eV2

Ent

ries/

bin

(c)

MX<1.7 GeV

MX<1.7 GeV

0

100

200

0

500

1000(d)

1 1.5 2 2.5p* (GeV)

Ent

ries/

2 G

eVE

ntrie

s/2

GeV

FIG. 3: Measured distributions (data points) of (a) MX , (b) P+, (c) q2 with MX < 1.7 GeV, and (d) p∗ℓ . Upper row: comparison

with the result of the χ2 fit with varying bin size for the sum of two scaled MC contributions (histograms), B → Xuℓν decaysgenerated inside (white) or outside (light shading) the selected kinematic region, and the background (dark shading). Lowerrow: corresponding spectra with equal bin size after background subtraction based on the fit. The data are not corrected forefficiency.

0

100

200

300

0

500

1000

1500(a)

0 10 20q2(GeV2)

Ent

ries/

bin

Ent

ries/

2 G

eV2

-100

0

100

200

300

0

1000

2000

3000

4000 (b)

0 2 4Mx(GeV)

Ent

ries/

bin

Ent

ries/

0.33

GeV

FIG. 4: Projections of measured distributions (data points) of (a) q2 and (b) MX with varying bin size. Upper row: comparisonwith the result of the χ2 fit to the two-dimensionalMX – q2 distribution for the sum of two scaled MC contributions (histograms),B → Xuℓν decays (white) and the background (dark shading). Lower row: corresponding spectra with equal bin size afterbackground subtraction based on the fit. The data are not corrected for efficiency.

Correlations between the different analyses are re-ported in the entries above the main diagonal of Table IV.

In addition, a series of fits to the lepton momentumspectrum has been performed with the lower limit onp∗ℓ increasing from 1.0 GeV to 2.4 GeV. The resultsare presented in Section VI; the measurement at p∗ℓ >1.3 GeV gives the smallest total uncertainty and is also

quoted in Table III.

Consistency checks have been performed. The analysisdone on data samples collected in different data-takingperiods, or separating the lepton flavor or charge have allyielded the same results, within experimental uncertain-ties.

14

TABLE III: List of the fitted numbers of signal events Nu, the number of events generated outside the kinematic selectionNout

u , the efficiencies, the partial branching fractions ∆B(B → Xuℓν) and the χ2 per degree of freedom for the different selectedregions of phase space. The first uncertainty is statistical, the second systematic. The p∗ℓ > 1 GeV requirement is implicitlyassumed.

Region of phase space Nu Noutu ǫuselǫ

ukin (ǫslℓ ǫ

slt )/(ǫ

uℓ ǫ

ut ) ∆B(B → Xuℓν) (10

−3) χ2/ndofMX < 1.55 GeV 1033± 73 29± 2 0.365 ± 0.002 1.29 ± 0.03 1.08± 0.08 ± 0.06 7.9/8MX < 1.70 GeV 1089± 82 25± 2 0.370 ± 0.002 1.27 ± 0.04 1.15± 0.10 ± 0.08 6.6/8P+ < 0.66 GeV 902± 80 54± 5 0.375 ± 0.003 1.22 ± 0.03 0.98± 0.09 ± 0.08 3.4/9MX < 1.70 GeV, q2 > 8 GeV2 665± 53 39± 3 0.386 ± 0.003 1.25 ± 0.03 0.68± 0.06 ± 0.04 23.7/26MX – q2 1441 ± 102 0± 0 0.338 ± 0.002 1.18 ± 0.03 1.80± 0.13 ± 0.15 31.0/29p∗ℓ > 1.0 GeV 1470 ± 130 8± 2 0.342 ± 0.002 1.18 ± 0.03 1.80± 0.16 ± 0.19 21.6/14p∗ℓ > 1.3 GeV 1329 ± 121 61± 5 0.363 ± 0.002 1.18 ± 0.09 1.52± 0.13 ± 0.14 20.4/14

TABLE IV: Correlation coefficients for measurements in different kinematic regions. The entries above the main diagonal referto correlations (statistical and systematic) for pairs of measurements of the partial branching fractions; the entries below thediagonal refer to the correlations (experimental and theoretical) for pairs of |Vub| measurements.

Phase space restrictionMX < 1.55 MX < 1.70 P+ < 0.66 MX < 1.70GeV, MX – q2 p∗ℓ > 1.3

GeV GeV GeV q2 > 8 GeV2 p∗ℓ > 1.0 GeV GeVMX < 1.55 GeV 1 0.77 0.74 0.50 0.72 0.57MX < 1.70 GeV 0.81 1 0.86 0.55 0.94 0.73P+ < 0.66 GeV 0.69 0.81 1 0.46 0.78 0.61MX < 1.70 GeV, q2 > 8 GeV2 0.40 0.46 0.38 1 0.52 0.46MX – q2 0.58 0.88 0.67 0.34 1 0.74p∗ℓ > 1.3 GeV 0.53 0.72 0.58 0.40 0.72 1

C. Partial branching fractions for B0 and B−

All the fits, except those to the p∗ℓ distribution, havebeen repeated separately for charged and neutral Breco

tags. In this case, we extract the true signal yields fromthe measurements by the following relations to determinethe partial branching fractions:

N0meas = PB0

true→B0reco

N0true + PB−

true→B0reco

N−true,

N−meas = PB0

true→B−

recoN0

true + PB−

true→B−

recoN−

true,

where the cross-feeds probabilities, PB−

true→B0reco

and

PB0true→B−

reco, are computed using MC simulated events

and are typically of the order of (2 - 3)%.Figure 5 shows the q2 distributions of B → Xuℓν

events after background subtraction, for charged andneutral B decays, with MX < 1.7 GeV. Fitted yields,efficiencies, and partial branching fractions are given inTable V.

D. Data - Monte Carlo comparisons

The separation of the signal events from the noncom-binatorial backgrounds relies heavily on the MC simula-tion to correctly describe the distribution for signal andbackground sources. Therefore, an extensive study has

been devoted to detailed comparisons of data and MCdistributions.A correction applied to the simulation improves the

quality of the fits to the kinematic distributions in re-gions that are dominated by B → Xcℓν background, es-pecially in the high MX region. In the simulation, weadjust λD∗∗ , the ratio of branching fractions of semilep-tonic decays to P -waveD mesons and nonresonant charmstates decaying to D(∗)X , over the sum of all D(∗)ℓν and“other” background components,

λD∗∗ =B(B → D∗∗ℓν) + B(B → D(∗)Xℓν)

B(B → D(∗)ℓν) + B(B → Xother). (8)

This ratio has been determined from data by performinga fit on the MX – q2 distribution of the signal-depletedsample without kinematic selection. The resulting dis-tribution of this fit is shown in Fig. 6. We measureλD∗∗ = 0.73 ± 0.08, where the error takes into accountthe fact that χ2/ndof = 2. Other determinations, usingsignal-enriched samples, give statistically consistent re-sults. This adjustment improves the quality of the fits inregions where backgrounds dominate, but it has a smallimpact on the fitted signal yield. We have verified thatusing D∗∗ MC correction factors determined separatelyon each analysis do not change significantly the resultswith respect to our default strategy, where λD∗∗ is deter-mined for the most inclusive sample available, namely the

15

TABLE V: Summary of the fits to separate samples of neutral and charged B decays. For details see Table III.

B0 decays Nu Noutu ǫuselǫ

ukin (ǫslℓ ǫ

slt )/(ǫ

uℓ ǫ

ut ) ∆B(B → Xuℓν) (10

−3) χ2/ndof

MX < 1.55 GeV 458± 48 12± 1 0.360 ± 0.004 1.49 ± 0.07 1.09 ± 0.12 ± 0.11 19.0/9MX < 1.70 GeV 444± 53 12± 1 0.370 ± 0.004 1.45 ± 0.07 1.12 ± 0.11 ± 0.11 16.6/9P+ < 0.66 GeV 434± 52 27± 3 0.367 ± 0.004 1.38 ± 0.06 1.09 ± 0.13 ± 0.11 9.1/9MX < 1.70 GeV, q2 > 8 GeV2 262± 38 16± 2 0.380 ± 0.005 1.43 ± 0.06 0.61 ± 0.09 ± 0.06 15.8/26MX – q2 553± 72 0± 0 0.328 ± 0.003 1.36 ± 0.08 1.58 ± 0.21 ± 0.20 14.8/29

B− decays Nu Noutu ǫuselǫ

ukin (ǫslℓ ǫ

slt )/(ǫ

uℓ ǫ

ut ) ∆B(B → Xuℓν) (10

−3) χ2/ndof

MX < 1.55 GeV 591± 56 17± 2 0.370 ± 0.003 1.18 ± 0.04 1.12 ± 0.11 ± 0.11 3.1/9MX < 1.70 GeV 669± 63 14± 1 0.370 ± 0.003 1.17 ± 0.07 1.27 ± 0.14 ± 0.13 3.3/9P+ < 0.66 GeV 491± 61 28± 4 0.379 ± 0.004 1.11 ± 0.03 0.96 ± 0.12 ± 0.12 2.0/9MX < 1.70 GeV, q2 > 8 GeV2 406± 41 24± 2 0.392 ± 0.004 1.43 ± 0.03 0.74 ± 0.08 ± 0.08 26.9/26MX – q2 859± 79 0± 0 0.345 ± 0.003 1.07 ± 0.03 1.91 ± 0.18 ± 0.22 36.7/29

)2(GeV2q0 5 10 15 20 25

2E

ntrie

s / 2

GeV

0

10

20

30

40

50

60

70

80(b)

0 10 20

2E

ntrie

s / 2

GeV

-20

0

20

40

60

80

100

120

140(a)

FIG. 5: Comparison of the measured q2 distributions (datapoints) for MX < 1.7 GeV for charmless semileptonic decaysof (a) charged and (b) neutral B mesons to the results ofthe fit (histogram), after B → Xcℓν and “other” backgroundsubtraction.

signal-depleted sample of the analysis without kinematicrequirements.

Figures 7 and 8 show comparisons of data and MC dis-tributions, after subtraction of the combinatorial back-ground, for signal-enriched and signal-depleted event

samples. All the selection criteria have been applied,except those affecting directly the variable shown. Thespectra are background-subtracted based on the resultsof the mES fit performed for each bin of the variableshown. The uncertainties on data points are on the yieldsof the bin-by-bin fits. The data and MC distributions arenormalized to the same area. The overall agreement isreasonable, taking into account that the uncertainties arepurely statistical. The effects that introduce differencesbetween data and simulation are described in Section V;their impact is assessed and accounted for as systematicuncertainty.

V. SYSTEMATIC UNCERTAINTIES

The experimental technique described in this article,namely the measurement of a ratio of branching fractions,ensures that systematic uncertainties due, for example,to radiative corrections or differences between B± andB0 or B0 production rate and lifetime, are negligible.A summary of all other statistical and systematic un-certainties on the partial branching fractions for selectedkinematic regions of phase space is shown in Table VI forthe complete data sample, and in Table VII for chargedand neutral B samples separately.

The individual sources of systematic uncertainties are,to a good approximation, uncorrelated and can thereforebe added in quadrature to obtain the total systematicuncertainties for partial branching fraction. In the fol-lowing, we discuss the assessment of the systematic un-certainties in detail.

To estimate the systematic uncertainties on the ratio∆Ru/sl, we compare the results obtained from the nom-inal fits with results obtained after changes to the MCsimulation that reflect the uncertainty in the parameterswhich impact the detector efficiency and resolution orthe simulation of signal and background processes. Forinstance, we lower the tracking efficiency by randomlyeliminating a fraction of tracks (corresponding to the es-

16

)2 (GeV2q0 5 10 15 20 25

0

1000

2000

3000

)2 (GeV2q0 5 10 15 20 25

0

1000

2000

3000 (b)

)2 (GeV2q0 5 10 15 20 25

0

1000

2000

30000 5 10 15 20 25

Ent

ries

/ bin

0

100

200

300

400

0 5 10 15 20 25

Ent

ries

/ bin

0

100

200

300

400

(a)

0 5 10 15 20 25

Ent

ries

/ bin

0

100

200

300

400

)2 (GeV2q0 5 10 15 20 25

0

500

1000

1500

2000

)2 (GeV2q0 5 10 15 20 25

0

500

1000

1500

2000(d)

)2 (GeV2q0 5 10 15 20 25

0

500

1000

1500

20000 5 10 15 20 25

Ent

ries

/ bin

0

1000

2000

3000

4000

0 5 10 15 20 25

Ent

ries

/ bin

0

1000

2000

3000

4000(c)

0 5 10 15 20 25

Ent

ries

/ bin

0

1000

2000

3000

4000

FIG. 6: Fit results to the MX – q2 distribution for the signal-depleted sample. The q2 distribution is reported separately forthe four MX bins: (a) MX ≤ 1.5 GeV, (b) 1.5 < MX ≤ 2.0 GeV, (c) 2.0 < MX ≤ 2.5 GeV and (d) 2.5 < MX ≤ 3.0 GeV. Thethree MC contributions shown here are: B → Xuℓν decays vetoed by the selection (no shading), B → Dℓν, B → D∗ℓν and“other” background (light shading), and the B → D∗∗ℓν component as defined in the text (dark shading).

timated uncertainty) in the MC sample, redo the eventreconstruction and selection on the recoil side, performthe fit, and take the difference compared to the resultsobtained with the nominal MC simulation as an estimateof the systematic uncertainty. The sources of systematicuncertainties are largely identical for all selected signalsamples, but the size of their impact varies slightly.

A. Detector effects

Uncertainties in the reconstruction efficiencies forcharged and neutral particles, in the rate of tracksand photons from beam background, misreconstructedtracks, failures in the matching of EMC clusters tocharged tracks, showers split-off from hadronic interac-tions, undetected KL, and additional neutrinos, all con-tribute to the event reconstruction and impact the vari-ables that are used in the event selection and the analysis.For all these effects the uncertainties in the efficienciesand resolution have been derived from comparisons ofdata and MC simulation for selected control samples.From the study of the angular and momentum distri-

butions of low momentum pions in D∗ samples, we es-timate the uncertainty on the track finding efficiency atlow momenta to be about 1.0%. For all other tracks, thedifference between data and MC in tracking efficiency isestimated to be about 0.5% per track. The systematicuncertainty on the ratio ∆Ru/sl is calculated as described

above, and shown in Tables VI and VII.

Similarly, for single photons, we estimate the system-atic uncertainty by randomly eliminating showers thatare not matched to the π0

soft used to veto B → D∗ℓνdecays, with a probability of 1.8% per shower.

We estimate the systematic uncertainty due to π0 de-tection by randomly eliminating neutral pions that areused in the B → D∗ℓν veto, with a probability of 3% perπ0.

Uncertainties on charged particle identification effi-ciencies have been assessed to be 2.0% for electrons and3.0% for muons. The uncertainty on the correspondingmisidentification rates are estimated to be 15%. System-atic uncertainties on the kaon identification efficiency andmisidentification rate are 2% and 15%, respectively.

In this analysis, no effort was made to identify K0L. On

the other hand, K0Lmesons interacting in the detector

deposit only a fraction of their energy in the EMC, thusthey impact Pmiss and other kinematic variables used inthis analysis. Based on detailed studies of data controlsamples of D0 → K0π+π− decays, corrections to the K0

L

efficiency and energy deposition have been derived andapplied to the simulation as a function of the K0

L momen-tum and angles. We take the difference compared to theresults obtained without this correction applied to thesimulation as an estimate of the systematic uncertainty.

Differences in bothK0LandK0

Sproduction rates of data

and MC are taken into account by adjusting the inclusiveD → K0X and Ds → K0X branching fractions. The

17

2000

4000

6000 (a)E

ntrie

s/0.

5 G

eV2

0

4000

8000(d)

-4 0 4 8 12Dat

a/M

CE

ntrie

s/0.

5 G

eV2

Dat

a/M

C

0.51

0

0.51

MM2 (GeV2)

-4 0 4 8 12MM2 (GeV2) Missing Energy (GeV)

0.5 1.5 2.5 3.5 4.5

Missing Energy (GeV)0.5 1.5 2.5 3.5 4.5

2000

4000

6000

(c)

(f)

2000

4000

6000

Ent

ries/

0.25

GeV

Dat

a/M

C 0

0.51

0

0.51

Ent

ries/

0.25

GeV

Dat

a/M

C

2000

0

4000

6000

8000

Missing Momentum (GeV)

Missing Momentum (GeV)

0.5 1.5 2.5

0.5 1.5 2.5

2000

0

4000

6000

8000

0.51

(b)

(e)E

ntrie

s/0.

2 G

eVD

ata/

MC

Ent

ries/

0.2

GeV

Dat

a/M

C

0.51

FIG. 7: Comparison of data (points with statistical uncertainties) and MC (histograms) simulated distributions of (a,d) themissing mass squared, (b,e) the missing momentum, and (c,f) the missing energy for B → Xuℓν enhanced (top row) anddepleted (bottom row) event samples.

associated systematic uncertainty is assessed by varyingthese branching fractions within their uncertainties.

B. Signal and background simulation

1. Signal simulation

Knowledge of the details of inclusive B → Xuℓν decaysis crucial to several aspects of the analysis: the fractionof events within the selected kinematic region depends onthe signal kinematics over the full phase space. Specif-ically, the efficiencies ǫu and ǫkin rely on accurate MCsimulation, because the particle multiplicities, momenta,and angles depend on the hadronization model for thehadronic states Xu.To simulate the signal B → Xuℓν decays we have cho-

sen the prescription by De Fazio and Neubert [36]. Differ-ent choices of the parameterization for the Fermi motionof the b quark inside the B meson (Section IID) lead todifferent spectra of the hadron mass MX and lepton mo-mentum p∗ℓ . We estimate the impact of these choices byrepeating the analysis with shape function parameters setto values of λSF

1 and ΛSF corresponding to the contour

of the ∆χ2 = 1 error ellipse [53]. To assess the impact ofthe choice of the SF ansatz, we repeat this procedure fora different SF ansatz [36].

Since the simulation of B → Xuℓν decays is a hybridof exclusive decays to low-mass charmless mesons andinclusive decays to higher-mass states Xu, the relativecontributions of the various decays impact the overallkinematics and thereby the efficiencies. We evalute theimpact of varying the branching fractions of the exclu-sive charmless semileptonic B decays by one standarddeviation.

The signal losses caused by the kaon veto depend onthe production rate of kaons in these decays. In the MCsimulation, the number of K+ and K0

S in the signal de-cays is set by the probability of producing ss quark pairsfrom the vacuum. The fraction of ss events is about12.0% for the nonresonant component of the signal andis fixed by the parameter γs in the fragmentation byjetset [37]. This parameter has been measured by twoexperiments at center of mass energies between 12 and36 GeV as γs = 0.35 ± 0.05 [54], γs = 0.27 ± 0.06 [55].We adopt the value γs = 0.3 and estimate the systematicuncertainty by varying the fraction of ss events by ±30%.

The theoretical uncertainty due to the lower limit

18

2000

4000

6000

2000

6000

10000

1 3 5 7 90.5

1

(a)

(d)

# charged tracks

1 3 5 7 9# charged tracks

Ent

ries/

bin

Dat

a/M

C

0

0.51

0

Ent

ries/

bin

Dat

a/M

C

400

1200

2000

1000

3000

5000

0.51

Ent

ries/

bin

Dat

a/M

C 0

2 6 10 14# neutral clusters

2 6 10 14# neutral clusters

(b)

(e)

0

0.51

Ent

ries/

bin

Dat

a/M

C

4000

8000

12000

6000

12000

18000

24000

0.51

Ent

ries/

bin

Dat

a/M

C 0

Total Charge

-3 -1 1 3Total Charge

(c)

(f)

Ent

ries/

bin

Dat

a/M

C 0

0.51

-3 -1 1 3

FIG. 8: Comparison of data (points with statistical uncertainties) and MC (histograms) simulated distributions of (a,d) thecharged track multiplicity, (b,e) the photon multiplicity, (c,f) and the total charge per event for B → Xuℓν enhanced (top row)and depleted (bottom row) event samples.

on the lepton spectrum is largely accounted for by thereweighting of events for the assessment of the theoreti-cal uncertainty related to the Fermi motion.

2. Branching fractions for B and D decays

The exclusive semileptonic branching fractions forB → Xcℓν decays and the hadronic mass spectra forthese decays are crucial for the determination of the yieldof the inclusive normalization sample and the B → Xcℓνbackground. Exclusive B andD branching fractions usedin the MC simulation differ slightly from the world av-erages [38]; this difference is corrected by reweightingevents in the simulation. The branching fraction forthe sum of semileptonic decays to nonresonant D(∗)πor broad D∗∗ states is taken as the difference betweenthe total semileptonic rate and the other well measuredbranching fractions, and amounts to about 1.7%.Similarly, branching fractions and decay distributions

for hadronic and semileptonic D meson decays affect themeasurement of ∆Ru/sl. The effect is different for neutral

and charged B mesons, because B0 decays mostly intocharged D mesons while B− decays almost always into

neutral charm mesons.Likewise, uncertainties on the form factors for B →

D(∗)ℓν decays are taken into account by repeating theanalysis with changes of the form factor values by theirexperimental uncertainties [45]. For B → D∗∗ℓν decays,the uncertainties on the form factor have not been spec-ified. Thus, we perform the fits with the ISGW2 [56] pa-rameterization of the form factors and take the differencewith respect to the default fits as systematic uncertainty.The uncertainty related to the λD∗∗ parameter intro-

duced in Eq. (8) has been estimated by varying it withinits uncertainty, and taking the difference with respect tothe default fits as systematic uncertainty.

3. Combinatorial background subtraction and normalization

For the fits to the mES distributions in individual binsof a given kinematic variable, all parameters other thanevent yields and the ARGUS shape are fixed to valuesdetermined from distributions obtained from the full sig-nal sample. To estimate the systematic uncertainty duethis choice of parameters, their values are varied withintheir statistical uncertainty, taking correlations into ac-

19

TABLE VI: Statistical and systematic uncertainties (in percent) on measurements of the partial branching fraction in sevenselected kinematic regions. The total systematic uncertainty is the sum in quadrature of the MC statistical uncertainty and allthe other single contibutions from detector effects, signal and background simulation, background subtraction and normalization.The total uncertainty is the sum in quadrature of the data statistical and total systematic uncertainties.

Phase space restrictionMX < 1.55 MX < 1.70 P+ < 0.66 MX < 1.70GeV,

MX – q2p∗ℓ > 1.0 p∗ℓ > 1.3

GeV GeV GeV q2 > 8 GeV2 GeV GeVData statistical uncertainty 7.1 8.9 8.9 8.0 7.1 9.4 8.8MC statistical uncertainty 1.3 1.3 1.3 1.6 1.1 1.1 1.2

Detector effectsTrack efficiency 0.4 1.0 1.1 1.7 0.7 1.2 1.0Photon efficiency 1.3 2.1 4.0 0.7 1.0 0.9 0.9π0 efficiency 1.2 0.9 1.1 0.9 0.9 2.9 1.1Particle identification 1.9 2.4 3.3 2.9 2.3 2.9 2.2KL production/detection 0.9 1.3 1.1 2.1 1.6 1.3 0.6KS production/detection 0.8 1.4 1.7 2.1 1.2 1.3 0.3

Signal simulationShape function parameters 2.0 1.3 1.2 0.7 5.4 6.4 6.6Shape function form 1.2 1.6 2.6 1.2 1.5 1.1 1.1Exclusive B → Xuℓν 0.6 1.3 1.6 0.7 1.9 5.3 3.4ss production 1.2 1.6 1.1 1.0 2.7 3.1 2.4

Background simulationB semileptonic branching ratio 0.9 1.4 1.5 1.4 1.0 0.8 0.7D decays 1.1 0.6 1.1 0.6 1.1 1.6 1.5B → Dℓν form factor 0.5 0.5 1.3 0.4 0.4 0.1 0.2B → D∗ℓν form factor 0.7 0.7 0.9 0.7 0.7 0.7 0.7B → D∗∗ℓν form factor 0.8 0.9 1.3 0.4 0.9 1.0 0.3B → D∗∗ reweighting 0.5 1.4 1.5 1.0 1.9 0.4 1.5

mES background subtractionmES background subtraction 2.0 2.7 1.9 2.6 1.9 2.0 2.5combinatorial backg. 1.8 1.8 2.6 1.8 1.0 2.1 0.5

NormalizationTotal semileptonic BF 1.4 1.4 1.4 1.4 1.4 1.4 1.4Total systematic uncertainty 5.5 6.7 8.3 6.6 8.4 11.0 9.3Total experimental uncertainty 9.0 11.1 12.2 10.4 11.0 14.4 12.8

count. To estimate the effect of the uncertainty on theARGUS shape parameter ξ we repeat the fits to the fulldata sample using the value of ξ obtained from a MCsample where combinatorial events are identified usingthe Monte Carlo truth and are removed. The differencesrelative to the default fit are taken as systematic uncer-tainties.

Finally, the uncertainty on the knowledge of the totalsemileptonic branching fraction adds 1.4% to the assess-ment of our systematic uncertainty.

In summary, the smallest statistical and systematic un-certainties are achieved for the MX < 1.55 GeV region,which has an acceptance that is reduced by 40% with re-spect to the region defined by p∗ℓ > 1.0 GeV, but has thebest separation of signal and background. The dominantsystematic uncertainty for samples with no phase spacerestrictions, except for p∗ℓ > 1.0 GeV, is due to the un-certainty on the shape function parameters which impactthe differential q2 and p∗ℓ distributions.

VI. EXTRACTION OF |Vub|

A. QCD corrections

We extract |Vub| from the measurements of the partialbranching fractions ∆B(B → Xuℓν) by relying on QCDpredictions. In principle, the total rate for B → Xuℓν de-cays can be calculated based on heavy quark expansions(HQE) in powers of 1/mb with uncertainties at the levelof 5%, in a similar way as for B → Xcℓν decays. Unfor-tunately, the restrictions imposed on the phase space toreduce the large background from Cabibbo-favored de-cays spoil the HQE convergence. Perturbative and non-perturbative corrections are drastically enhanced and therate becomes sensitive to the Fermi motion of the b quarkinside the B meson, introducing terms that are not sup-pressed by powers of 1/mb. In practice, nonperturbativeSFs are introduced. The form of the SFs cannot be calcu-lated from first principles. Thus, knowledge of these SFsrelies on global fits performed by several collaborationsto moments of the lepton energy and hadronic invari-

20

TABLE VII: Statistical and systematic uncertainties (in percent) on the partial branching fraction for neutral and charged Bmesons for the five selected kinematic regions. The total systematic uncertainty is the sum in quadrature of the MC statisticaluncertainty and all the other single contibutions from detector effects, signal and background simulation, background subtractionand normalization. The total uncertainty is the sum in quadrature of the the data statistical and total systematic uncertainties.

Phase space restrictionMX < 1.55 MX < 1.70 P+ < 0.66 MX < 1.70GeV,

GeV GeV GeV q2 > 8 GeV2 MX – q2

B0 B− B0 B− B0 B− B0 B− B0 B−

Data statistical uncertainty 10.4 9.6 14.4 11.0 12.0 12.5 14.6 10.1 13.0 9.2MC statistical uncertainty 2.5 1.6 2.5 1.6 2.4 1.8 2.8 2.0 1.9 1.3Detector effects 4.5 4.9 5.0 6.3 5.9 7.2 5.3 6.3 5.6 4.7Signal simulation 6.6 5.4 5.2 4.8 4.8 5.9 3.7 5.4 8.7 7.6Background simulation 4.4 4.2 5.6 4.5 5.9 5.4 4.9 4.4 4.4 5.0mES background subtraction 4.1 5.4 5.2 5.0 2.9 5.3 5.2 5.1 3.8 4.1Total semileptonic BF 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4Total systematic uncertainty 10.4 10.2 10.9 10.6 10.5 12.2 10.1 11.0 12.1 11.2Total experimental uncertainty 14.7 14.0 18.1 15.3 15.9 17.5 17.8 14.9 17.8 14.5

ant mass in semileptonic B decays, and of the photonenergy in radiative B → Xsγ inclusive decays [57–59].We adopt results of the global fits to published measure-ments of moments, performed in the kinetic renormaliza-tion scheme, specifically the b quark massmkin

b = (4.59±0.03) GeV and the mean value of the b quark momen-

tum operator µ2(kin)π = (0.45± 0.04) GeV2 [44, 53]. Due

to confinement and nonperturbative effects the quanti-tative values of the quark mass and other HQE param-eters are specific to the theoretical framework in whichit is defined. Thus the results of the global fits need tobe translated to other schemes, depending on the QCDcalculation used to extract |Vub|. In the following, we de-termine |Vub| based on four different QCD calculations.The numerical calculations are based on computer codekindly provided by the authors.

The measured partial branching fractions ∆B(B →Xuℓν) are related to |Vub| via the following equation,

|Vub| =√

∆B(B → Xuℓν)

τB ∆Γtheory, (9)

where ∆Γtheory, the theoretically predicted B → Xuℓνrate for the selected phase space region, is based on dif-ferent QCD calculations. We adopt the uncertainties on∆Γtheory as assessed by the authors. It should be notedthat the systematic uncertainty on the branching fractionthat is related to the uncertainties on the SF parameteri-zation are fully correlated to the theoretical uncertaintiesdiscussed here.

The calculated decay rates ∆Γtheory and the resulting|Vub| values are shown for the various kinematic regionsin Tables VIII and IX, separately for the four differentQCD calculations.

1. BLNP calculation

The theoretical uncertainties [18–20] arise from the un-certainty on mb, µ

2π and other nonperturbative correc-

tions, the functional form of the leading and the sub-leading SFs, the variation of the matching scales, andthe uncertainty on the estimated contribution from weakannihilation processes. The dominant contributions aredue to the uncertainties on mb, and µ2

π. These param-eters need to be translated to the shape function renor-

malization scheme, for which m(SF)b = (4.62± 0.04) GeV

and µ2(SF)π = (0.29 ± 0.07) GeV2. The stated errors in-

clude the uncertainties due to higher order terms whichare neglected in the translation from one scheme to an-other.

A recent calculation at NNLO [60] indicates that thedifferences with respect to NLO calculations are ratherlarge. They would increase the value of |Vub| by about8%, suggesting that the current uncertainties are under-estimated. Similar effects might also be present for otherQCD calculations, but estimates are not yet available.

2. DGE calculation

The theoretical uncertainties [21, 22] arise from the un-certainty on αs, the uncertainty on mb, and other non-perturbative corrections, for instance, the variation of thematching scales, and the uncertainty on the weak annihi-lation. The dominant error is the uncertainty on mb forwhich the MS renormalization scheme is used. There-fore the results of the global fit had to be translated to

the MS scheme, mMSb = (4.22 ± 0.05) GeV, where the

uncertainty includes the uncertainty on the translation.

21

3. GGOU calculation

The theoretical uncertainties [25] in the determinationsof the widths and |Vub| from the GGOU calculations arisefrom the uncertainty on αs, mb, and µ2

π , plus variousnonperturbative corrections: the modeling of the q2 tailand choice of the scale q2∗ , the functional form of thedistribution functions, and the uncertainty on the weakannihilation rate. The dominant error originates from theuncertainties on mb and µ2

π . Since GGOU calculationsare based on the kinetic renormalization scheme, there isno need for translation.

4. ADFR calculation

The ADFR calculation [23, 24] relates ∆B(B → Xuℓν)to |Vub| in a way that is different from the other threecalculations discussed above. In the framework of ADFR,the partial branching ratio is expressed in terms of Rc/u,

∆B(B → Xuℓν) =B(B → Xℓν)

1 +Rc/uW, (10)

where W = ∆Γ(B → Xuℓν)/Γ(B → Xuℓν) is the frac-tion of the charmless branching fraction in a selectedkinematic region and B(B → Xℓν) is the total semilep-tonic branching fraction. Rc/u is related to |Vub| as

Rc/u =|Vcb|2|Vub|2

I(ρ)G(αs, ρ). (11)

The function I(ρ) accounts for the suppression of phasespace due to mc and I(ρ) = 1−8ρ+12ρ2 log(1/ρ)+8ρ2−ρ4, with ρ ≡ m2

c/m2b ≈ 0.1. The factor G(αs, ρ) contains

corrections suppressed by powers of αs and powers of ρ,

G(αs, ρ) = 1 +

∞∑

n=1

Gn(ρ)αns , (12)

with Gn(0) = 0. The errors of the ADFR calculationsarise from the uncertainty in αs, |Vcb|, the quark massesmb and mc, and the uncertainty on B(B → Xℓν). Thedominant uncertainty is due to the uncertainty on themass mc.

B. |Vub| extraction

We present the results for |Vub| with statistical, sys-tematic and theoretical uncertainties in Table VIII. Val-ues of |Vub| extracted from partial branching fractionsfor samples with the lower limit on the lepton momen-tum p∗ℓ varying from 1.0 GeV to 2.4 GeV are tabulatedin Table IX. The different values of |Vub| are consis-tent within one standard deviation and equally consistentwith the previous BABAR measurements of |Vub| on inclu-sive charmless semileptonic B decays [11, 15, 16] as wellas a similar measurement by the Belle Collaboration [17].

Our result on the study of the lepton spectrum above2 GeV can be compared to what BABAR [15, 16], Belle [14]and CLEO [13] have published on the analysis of the lep-ton endpoint spectrum in untagged B decays. Experi-mental uncertainties are comparable, as well as theoret-ical uncertainties, which are quite large in this region ofphase space. The values of |Vub| obtained with such dif-ferent techniques agree very well.We have evaluated the correlations of the measure-

ments of |Vub| in selected regions of phase space tak-ing into account the experimental and theoretical pro-cedures, as presented in Table IV. The theoretical cor-relations have been obtained for the BLNP calculationsby taking several values of the heavy quark parameterswithin their uncertainties and computing the correlationof the acceptance for pairs of phase space regions. Theresulting correlation coefficients are in all cases greaterthan 97%. It is assumed that the correlations are alsoclose to 100% for the other three theory calculations.We choose to quote the |Vub| value corresponding to the

most inclusive measurement, namely the one based onthe two-dimensional fit of the MX – q2 distribution withno phase space restrictions, except for p∗ℓ > 1.0 GeV.We calculate the arithmetic average of the values anduncertainties obtained with the different theoretical cal-culations shown above and find

|Vub| = (4.31± 0.25± 0.16)× 10−3, (13)

where the first uncertainty is experimental and the sec-ond theoretical.

C. Limits on weak annihilation

The measurements of ∆B(B → Xuℓν), separately forneutral and charged B mesons, are summarized in Ta-ble V for the various kinematic selections. These resultsare used to test isospin invariance, based on the ratio

R =∆Γ−

∆Γ0=τ0

τ−∆B(B− → Xuℓν)

∆B(B0 → Xuℓν), (14)

where τ−/τ0 = 1.071± 0.009 [38] is the ratio of the life-times for B− and B0. For the MX < 1.55 GeV selection,we obtain R − 1 = 0.03 ± 0.15 ± 0.18, where the firstuncertainty is statistical and the second is systematic.This result is consistent with zero; similar results, withlarger uncertainties, are obtained for the other regions ofphase space listed in Table V. Thus, we have no evidencefor a difference between partial decay rates for B− andB0. If we define the possible contribution of the weakannihilation as ∆ΓWA = ∆Γ− − ∆Γ0, its relative con-tribution to the partial decay width ∆Γ for B → Xuℓνdecays is ∆ΓWA/∆Γ = R − 1. With fWA defined asthe fraction of weak annihilation contribution for a spe-cific kinematic region and fu defined as the fraction ofB → Xuℓν events predicted for that region, we can write

22

TABLE VIII: Results for |Vub| obtained for the four different QCD calculations. The sources of the quoted uncertainties areexperimental statistical, experimental systematic and theory, respectively. The theoretical B → Xℓν widths, ∆Γtheory in ps−1,for the various phase space regions examined, as determined from the BLNP, DGE and GGOU calculations, are also shown.The ADFR calculation uses another methodology (see text), therefore the values for ∆Γtheory have been obtained by invertingEq. 9. The p∗ℓ > 1GeV requirement is implicitly assumed in the definitions of phase space regions, unless otherwise noted.

QCD Calculation Phase Space Region ∆Γtheory (ps−1) |Vub|(10−3)

MX ≤ 1.55 GeV 42.0+6.2−5.1 4.03 ± 0.15 ± 0.11+0.28

−0.26

MX ≤ 1.70 GeV 47.3+6.6−5.3 3.91 ± 0.17 ± 0.12+0.25

−0.23

P+ ≤ 0.66 GeV 40.9+6.3−5.1 3.90 ± 0.18 ± 0.16+0.28

−0.26

BLNP MX ≤ 1.70 GeV, q2 ≥ 8 GeV2 24.3+3.7−3.0 4.22 ± 0.19 ± 0.12+0.30

−0.28

MX – q2, p∗ℓ > 1.0 GeV 62.7+7.0−5.7 4.27 ± 0.15 ± 0.18+0.23

−0.20

p∗ℓ > 1.0 GeV 62.7+7.0−5.7 4.26 ± 0.19 ± 0.23+0.23

−0.20

p∗ℓ > 1.3 GeV 53.4+6.2−5.0 4.25 ± 0.19 ± 0.19+0.23

−0.21

MX ≤ 1.55 GeV 38.3+3.8−3.7 4.23 ± 0.16 ± 0.12+0.22

−0.19

MX ≤ 1.70 GeV 44.8+5.6−5.3 4.02 ± 0.18 ± 0.12+0.26

−0.23

P+ ≤ 0.66 GeV 40.2+6.5−6.4 3.93 ± 0.18 ± 0.16+0.36

−0.29

DGE MX ≤ 1.70 GeV, q2 ≥ 8 GeV2 25.6+2.9−2.6 4.10 ± 0.18 ± 0.12+0.23

−0.22

MX – q2, p∗ℓ > 1.0 GeV 60.7+4.3−3.9 4.34 ± 0.16 ± 0.18+0.15

−0.15

p∗ℓ > 1.0 GeV 60.7+4.3−3.9 4.28 ± 0.19 ± 0.23+0.15

−0.15

p∗ℓ > 1.3 GeV 53.7+4.0−3.7 4.24 ± 0.19 ± 0.19+0.16

−0.16

MX ≤ 1.55 GeV 43.7+6.5−4.8 3.96 ± 0.15 ± 0.11+0.24

−0.27

MX ≤ 1.70 GeV 49.4+5.5−4.1 3.97 ± 0.16 ± 0.11+0.17

−0.20

P+ ≤ 0.66GeV 47.0+8.7−7.0 3.64 ± 0.17 ± 0.15+0.30

−0.30

GGOU MX ≤ 1.70 GeV, q2 ≥ 8 GeV2 26.0+4.6−2.8 4.07 ± 0.18 ± 0.12+0.24

−0.32

MX – q2, p∗ℓ > 1.0 GeV 62.1+4.4−3.1 4.29 ± 0.15 ± 0.18+0.11

−0.14

p∗ℓ > 1.0 GeV 62.1+4.4−3.1 4.24 ± 0.20 ± 0.23+0.11

−0.14

p∗ℓ > 1.3 GeV 53.6+4.2−2.8 4.23 ± 0.19 ± 0.19+0.12

−0.16

MX ≤ 1.55 GeV 46.0+6.6−5.3 3.84 ± 0.14 ± 0.11+0.24

−0.25

MX ≤ 1.70 GeV 52.0+6.7−5.7 3.96 ± 0.17 ± 0.14+0.23

−0.24

P+ ≤ 0.66 GeV 47.8+7.0−5.6 3.59 ± 0.17 ± 0.15+0.23

−0.24

ADFR MX ≤ 1.70 GeV, q2 ≥ 8 GeV2 30.1+4.0−3.3 3.77 ± 0.17 ± 0.12+0.23

−0.23

MX – q2, p∗ℓ > 1.0 GeV 60.2+7.8−6.6 4.35 ± 0.19 ± 0.20+0.26

−0.26

p∗ℓ > 1.0 GeV 60.2+7.8−6.6 4.28 ± 0.20 ± 0.23+0.24

−0.28

p∗ℓ > 1.3 GeV 52.0+6.7−5.7 4.30 ± 0.19 ± 0.20+0.24

−0.28

∆ΓWA = fWAΓWA and ∆Γ = fuΓ, where Γ is the to-tal decay width of B → Xuℓν decays. Thus the relativecontribution of the weak annihilation is

ΓWA

Γ=

fufWA

(R− 1). (15)

Since the weak annihilation is expected to be confined tothe high q2 region, it is reasonable to assume fWA = 1.0for all the kinematic selections. We adopt the predic-tion for fu by De Fazio-Neubert (see Section IID) andplace limits on ΓWA/Γ. The most stringent limit isobtained for the selection MX < 1.55 GeV, namely−0.17 ≤ (ΓWA/Γ) < 0.19 at 90% confidence level (C.L.).This model-independent limit on WA is consistent, butweaker than the limit derived by the CLEO collabora-tion [61] on the basis of an assumed q2 distribution. Bothlimits are larger than the theoretically estimated value of3% [26, 27], derived from the measured leptonic Ds decayrate.

VII. CONCLUSIONS

In summary, we have measured the branching fractionsfor inclusive charmless semileptonic B decays B → Xuℓν,in various overlapping regions of phase space, based onthe full BABAR data sample. The results are presentedfor the full sample, and also separately for charged andneutral B mesons.

We have extracted the magnitude of the CKM ele-ment |Vub| based on four sets of theoretical calculations.Measurements in different phase space regions are consis-tent for all sets of calculations, within their uncertainties.Correlations between |Vub|measurements, including bothexperimental and theoretical uncertainties are presented.They are close to 100% for the theoretical input.

We have obtained the most precise results from theanalysis based on the two-dimensional fit to MX– q2,with no restriction other than p∗ℓ > 1.0 GeV. The totaluncertainty is about 6.9%, comparable in precision to theresult recently presented by the Belle Collaboration [17]

23

TABLE IX: Summary of the fitted number of events Nu, the efficiencies, the partial branching fractions ∆B(B → Xuℓν) and |Vub| (10−3) based on four different QCD

calculations of the hadronic matrix element as a function of the lower limit on the lepton momentum p∗ℓ . The uncertainties on ∆B(B → Xuℓν) are statistical andsystematic, those for |Vub| are statistical, systematic and theoretical. The uncertainties on all other parameters are statistical. |Vub| values for BLNP and GGOU arenot provided above 2.2 GeV due to large uncertainties.

p∗ℓmin ∆B(B → Xuℓν) |Vub| BLNP |Vub| GGOU |Vub| DGE |Vub| ADFR

(GeV)Nu ǫuselǫ

ukin

ǫslℓ ǫsltag

ǫuℓǫutag (10−3) (10−3) (10−3) (10−3) (10−3)

1.0 1470± 130 0.342 ± 0.002 1.18 ± 0.03 1.80± 0.16 ± 0.19 4.26 ± 0.19± 0.23+0.23−0.20 4.24± 0.20 ± 0.23+0.11

−0.14 4.28± 0.19± 0.23+0.15−0.15 4.28 ± 0.20± 0.23+0.24

−0.28

1.1 1440± 127 0.345 ± 0.002 1.18 ± 0.19 1.74± 0.15 ± 0.18 4.28 ± 0.18± 0.22+0.24−0.19 4.22± 0.19 ± 0.21+0.13

−0.21 4.30± 0.18± 0.22+0.13−0.13 4.37 ± 0.19± 0.23+0.25

−0.29

1.2 1421± 124 0.353 ± 0.002 1.18 ± 0.05 1.68± 0.14 ± 0.18 4.32 ± 0.18± 0.23+0.25−0.20 4.20± 0.19 ± 0.23+0.13

−0.21 4.33± 0.18± 0.23+0.13−0.14 4.39 ± 0.18± 0.24+0.27

−0.31

1.3 1329± 121 0.363 ± 0.002 1.18 ± 0.09 1.52± 0.13 ± 0.14 4.25 ± 0.19± 0.19+0.23−0.21 4.23± 0.19 ± 0.19+0.12

−0.16 4.24± 0.19± 0.19+0.16−0.16 4.30 ± 0.19± 0.20+0.24

−0.28

1.4 1381± 114 0.368 ± 0.002 1.18 ± 0.04 1.57± 0.13 ± 0.14 4.48 ± 0.18± 0.21+0.26−0.21 4.33± 0.18 ± 0.20+0.14

−0.24 4.47± 0.18± 0.20+0.15−0.16 4.51 ± 0.18± 0.20+0.27

−0.31

1.5 1383± 107 0.378 ± 0.003 1.19 ± 0.02 1.51± 0.12 ± 0.14 4.61 ± 0.18± 0.21+0.28−0.23 4.48± 0.18 ± 0.20+0.15

−0.26 4.58± 0.17± 0.21+0.16−0.17 4.62 ± 0.18± 0.21+0.26

−0.31

1.6 1248± 99 0.390 ± 0.003 1.17 ± 0.03 1.34± 0.10 ± 0.13 4.59 ± 0.18± 0.22+0.28−0.23 4.41± 0.18 ± 0.22+0.15

−0.28 4.53± 0.18± 0.22+0.17−0.18 4.55 ± 0.18± 0.22+0.27

−0.31

1.7 1158± 90 0.404 ± 0.003 1.16 ± 0.03 1.21± 0.09 ± 0.12 4.66 ± 0.18± 0.23+0.30−0.24 4.45± 0.18 ± 0.22+0.16

−0.31 4.57± 0.17± 0.23+0.18−0.19 4.56 ± 0.17± 0.23+0.27

−0.32

1.8 1043± 80 0.418 ± 0.003 1.16 ± 0.04 1.06± 0.08 ± 0.10 4.71 ± 0.18± 0.23+0.31−0.26 4.49± 0.18 ± 0.22+0.18

−0.35 4.58± 0.17± 0.23+0.20−0.21 4.55 ± 0.17± 0.22+0.26

−0.31

1.9 845± 69 0.430 ± 0.004 1.14 ± 0.06 0.84± 0.07 ± 0.10 4.66 ± 0.19± 0.27+0.33−0.27 4.41± 0.19 ± 0.25+0.19

−0.40 4.47± 0.18± 0.26+0.21−0.24 4.39 ± 0.18± 0.25+0.25

−0.30

2.0 567± 56 0.457 ± 0.004 1.11 ± 0.04 0.55± 0.05 ± 0.06 4.28 ± 0.20± 0.22+0.33−0.28 4.01± 0.20 ± 0.21+0.20

−0.44 4.01± 0.19± 0.21+0.22−0.25 3.89 ± 0.19± 0.20+0.21

−0.25

2.1 432± 44 0.474 ± 0.005 1.07 ± 0.03 0.42± 0.04 ± 0.05 4.46 ± 0.22± 0.25+0.42−0.37 4.12± 0.22 ± 0.23+0.25

−0.59 4.05± 0.20± 0.23+0.28−0.30 3.85 ± 0.19± 0.22+0.23

−0.27

2.2 339± 29 0.499 ± 0.007 1.02 ± 0.04 0.33± 0.03 ± 0.03 5.05 ± 0.22± 0.23+0.66−0.61 4.80± 0.20 ± 0.21+0.48

−1.07 4.36± 0.19± 0.20+0.42−0.43 4.03 ± 0.17± 0.19+0.25

−0.29

2.3 227± 19 0.521 ± 0.009 1.00 ± 0.04 0.22± 0.02 ± 0.02 − − 4.73± 0.19± 0.25+0.68−0.68 4.20 ± 0.17± 0.22+0.27

−0.33

2.4 82± 9 0.539 ± 0.013 1.00 ± 0.08 0.07± 0.01 ± 0.01 − − 4.55± 0.24± 0.31+1.07−1.28 3.69 ± 0.20± 0.26+0.27

−0.31

24

which uses a multivariate discriminant to reduce the com-binatorial background. The results presented here su-persede earlier BABAR measurements based on a smallertagged sample of events [11].We have found no evidence for isospin violation; the

difference between the partial branching fractions for B0

and B− is consistent with zero. Based on this measure-ment, we place a limit on a potential contribution fromWeak Annihilation of 19% of the total charmless semilep-tonic branching faction at 90% C.L., which is still largerthan the theoretical expectation of 3% [26, 27].Improvements in these measurements will require

larger tagged data samples recorded with improved de-tectors and much improved understanding of the simula-tion of semileptonic B decays, both background decaysinvolving charm mesons as well as exclusive and inclusivedecays contributing to the signal. Reductions in the theo-retical uncertainties are expected to come from improvedQCD calculations for b → uℓν and b → sγ transitions,combined with improved information on the b quark massand measurements of radiative B decays.

VIII. ACKNOWLEDGEMENTS

We thank Matthias Neubert, Gil Paz, Einan Gardi,Paolo Gambino, Paolo Giordano, Ugo Aglietti, GiancarloFerrera, and Giulia Ricciardi for useful discussions and

for providing the software tools and code which enabledus to compute |Vub| values from measured branching frac-tions.

We are grateful for the extraordinary contributions ofour PEP-II colleagues in achieving the excellent luminos-ity and machine conditions that have made this work pos-sible. The success of this project also relies critically onthe expertise and dedication of the computing organiza-tions that support BABAR. The collaborating institutionswish to thank SLAC for its support and the kind hospital-ity extended to them. This work is supported by the USDepartment of Energy and National Science Foundation,the Natural Sciences and Engineering Research Council(Canada), the Commissariat a l’Energie Atomique andInstitut National de Physique Nucleaire et de Physiquedes Particules (France), the Bundesministerium fur Bil-dung und Forschung and Deutsche Forschungsgemein-schaft (Germany), the Istituto Nazionale di Fisica Nu-cleare (Italy), the Foundation for Fundamental Researchon Matter (The Netherlands), the Research Council ofNorway, the Ministry of Education and Science of theRussian Federation, Ministerio de Ciencia e Innovacion(Spain), and the Science and Technology Facilities Coun-cil (United Kingdom). Individuals have received supportfrom the Marie-Curie IEF program (European Union),the A. P. Sloan Foundation (USA) and the BinationalScience Foundation (USA-Israel).

[1] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963).[2] M. Kobayashi and T. Maskawa, Prog. Theor. Phys.

49,652 (1973).[3] J. D. Bjorken, Theoretical Topics in B Physics, Lectures

at 18th Annual SLAC Summer Inst. on Particle Physics,Stanford, CA, Jul 16-27, 1990, published in SLAC Report378, p. 167 (1990).

[4] R. Kowalewski and T. Mannel, J. Phys. G 37, 075021(2010).

[5] M. Antonelli et al., Phys. Rept. 494, 197 (2010).[6] UTfit Collaboration, A. Bevan et al., e-Print:

arXiv:1010.5089 [hep-ph].[7] CKMfitter Collaboration, J. Charles et al., Eur. Phys. J.

C 41, 1-131 (2005).[8] A. V. Manohar and M. B. Wise, Phys. Rev. D 49, 1310

(1994), e-Print: arXiv:hep-ph/9308246.[9] I. I. Y. Bigi, B. Blok, M. A. Shifman, and A. I. Vainshtein,

Phys. Lett. B 323, 408 (1994), e-Print: arXiv:hep-ph/9311339.

[10] Charge-conjugate modes are implied throughout this pa-per, unless explicitly stated.

[11] BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett.100, 171802 (2008), e-Print: arXiv:0708.3702 [hep-ex].

[12] CLEO Collaboration, J. E. Bartelt et al., Phys. Rev.Lett. 71, 4111 (1993).

[13] CLEO Collaboration, A. Bornheim et al., Phys. Rev.Lett. 88, 231803 (2002).

[14] Belle Collaboration, A. Limosani et al., Phys. Lett. B621, 28 (2005).

[15] BABAR Collaboration, B. Aubert et al., Phys. Rev. D 73,012006 (2006).

[16] BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett.95, 111801 (2005) [Erratum-ibid. 97, 019903 (2006)], e-Print: arXiv:hep-ex/0506036.

[17] Belle Collaboration, P. Urquijo et al., Phys. Rev. Lett.104, 021801 (2010), e-Print: arXiv:0907.0379 [hep-ex].

[18] B. O. Lange, M. Neubert, and G. Paz, Phys. Rev. D 72,073006 (2005), e-Print: arXiv:hep-ph/0504071.

[19] S. W. Bosch, B. O. Lange, M. Neubert, and G. Paz, Nucl.Phys. B 699, 335 (2004), e-Print: arXiv:hep-ph/0402094.

[20] S. W. Bosch, M. Neubert, and G. Paz, JHEP 11, 073(2004), e-Print: arXiv:hep-ph/0409115.

[21] J. R. Andersen and E. Gardi, JHEP 0601, 097 (2006),e-Print: arXiv:hep-ph/0509360.

[22] E. Gardi, e-Print: arXiv:0806.4524 [hep-ph].[23] U. Aglietti, F. Di Lodovico, G. Ferrera and G. Ricciardi,

Eur. Phys. J. C 59, 831 (2009), e-Print: arXiv:0711.0860[hep-ph].

[24] U. Aglietti, G. Ferrera, and G. Ricciardi, Nucl. Phys.B 768, 85 (2007), e-Print: arXiv:hep-ph/0608047, andreferences therein.

[25] P. Gambino, P. Giordano, G. Ossola, and N. Uraltsev,JHEP 0710, 058 (2007).

[26] I. I. Bigi and N. Uraltsev, Nucl. Phys. B 423, 33 (1994).[27] M. B. Voloshin, Phys. Lett. B 515, 74 (2001).[28] BABAR Collaboration, B. Aubert et al., Nucl. Instrum.

Meth. A 479, 1 (2002).[29] BABAR Collaboration, B. Aubert et al., Phys. Rev. D 66,

25

032003 (2002), e-Print: arXiv:hep-ex/0201020.[30] GEANT4 Collaboration, S. Agostinelli et al., Nucl. In-

strum. Meth. A 506, 250 (2003).[31] D. J. Lange, Nucl. Instr. and Methods A 462, 152 (2001).[32] D. Becirevic and A. B. Kaidalov, Phys. Lett. B 478, 417

(2000).[33] BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett.

98, 091801 (2007).[34] P. Ball and R. Zwicky, Phys. Rev. D 71, 014015 (2005).[35] P. Ball and R. Zwicky, Phys. Rev. D 71, 014029 (2005).[36] F. De Fazio and M. Neubert, JHEP 9906, 017 (1999),

e-Print: arXiv:hep-ph/9905351.[37] T. Sjœstrand, Comput. Phys. Commun. 82, 74 (1994).[38] Particle Data Group, K. Nakamura et al., J. Phys. G 37,

075021 (2010).[39] I. Caprini, L. Lellouch, and M. Neubert, Nucl. Phys. B

530, 153 (1998), e-Print: arXiv:hep-ph/9712417.[40] B. Grinstein, Nucl. Phys. B 339, 253 (1990).[41] E. Eichten and B. R. Hill, Phys. Lett. B 234, 511 (1990).[42] H. Georgi, Phys. Lett. B 240, 447 (1990).[43] A. F. Falk, H. Georgi, B. Grinstein, and M. B. Wise,

Nucl. Phys. B 343, 1 (1990).[44] Heavy Flavour Averaging Group, D. Asner et al., e-Print:

arXiv:1010.1589 (2010).[45] BABAR Collaboration, B. Aubert et al., Phys. Rev. D 79,

012002 (2009), e-Print: arXiv:0809.0828 [hep-ex].[46] BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett.

104, 011802 (2010), e-Print: arXiv:0904.4063 [hep-ex].[47] BABAR Collaboration, B. Aubert et al., Phys. Rev. D 77,

032002 (2008), e-Print: arXiv:0705.4008 [hep-ex].

[48] A. K. Leibovich, Z. Ligeti, I. W. Stewart, and M. B. Wise,Phys. Rev. D 57, 308 (1998), e-Print: arXiv:hep-ph/9705467.

[49] J. L. Goity and W. Roberts, Phys. Rev. D 51, 3459(1995), e-Print: arXiv:hep-ph/9406236.

[50] ARGUS Collaboration, H. Albrecht et al., Z. Phys. C 48,543 (1990).

[51] Crystal Ball Collaboration, T. Skwarnicki et al., DESYInternal Report, F31-86-02 (1986).

[52] BABAR Collaboration, B. Aubert et al., Phys. Rev. D 74,091105 (2006), e-Print: arXiv:hep-ex/0607111.

[53] Belle Collaboration, C. Schwanda et al., Phys. Rev. D78, 032016 (2008), e-Print: arXiv:0803.2158v2 [hep-ex].

[54] TASSO Collaboration, M. Althoff et al., Z. Phys. C 27,27 (1985).

[55] JADE Collaboration, W. Bartel et al., Z. Phys. C 20,187 (1983).

[56] N. Isgur and D. Scora, Phys. Rev. D 52, 2783 (1995).[57] P. Gambino and N. Uraltsev, Eur. Phys. J. C 34, 181-189

(2004), e-Print: arXiv:hep-ph/0401063v1.[58] C. W. Bauer, Z. Ligeti, M. Luke, A. V. Manohar, and

M. Trott, Phys. Rev. D 70, 094017 (2004), e-Print:arXiv:hep-ph/0408002v3.

[59] D. Benson, I. I. Bigi, and N. Uraltsev, Nucl. Phys. B 710,371-401 (2005), e-Print: arXiv:hep-ph/0410080v2

[60] C. Greub, M. Neubert and B.D. Pecjak, Eur. Phys. J. C65, 501 (2010).

[61] JADE Collaboration, J. L. Rosner et al., Phys. Rev. Lett.96, 121801 (2006), e-Print: arXiv:hep-ex/0601027.