Angular Distributions in the Decays B -> K* l+l-
aa r X i v : . [ h e p - e x ] J a n B A B AR -PUB-08/022SLAC-PUB-13133arXiv:0804.4412 [hep-ex] Angular Distributions in the Decays B → K ∗ ℓ + ℓ − B. Aubert, M. Bona, Y. Karyotakis, J. P. Lees, V. Poireau, X. Prudent, V. Tisserand, A. Zghiche, J. Garra Tico, E. Grauges, L. Lopez, A. Palano, M. Pappagallo, G. Eigen, B. Stugu, L. Sun, G. S. Abrams, M. Battaglia, D. N. Brown, J. Button-Shafer, R. N. Cahn, R. G. Jacobsen, J. A. Kadyk, L. T. Kerth, Yu. G. Kolomensky, G. Kukartsev, G. Lynch, I. L. Osipenkov, M. T. Ronan, ∗ K. Tackmann, T. Tanabe, W. A. Wenzel, C. M. Hawkes, N. Soni, A. T. Watson, H. Koch, T. Schroeder, D. Walker, D. J. Asgeirsson, T. Cuhadar-Donszelmann, B. G. Fulsom, C. Hearty, T. S. Mattison, J. A. McKenna, M. Barrett, A. Khan, M. Saleem, L. Teodorescu, V. E. Blinov, A. D. Bukin, A. R. Buzykaev, V. P. Druzhinin, V. B. Golubev, A. P. Onuchin, S. I. Serednyakov, Yu. I. Skovpen, E. P. Solodov, K. Yu. Todyshev, M. Bondioli, S. Curry, I. Eschrich, D. Kirkby, A. J. Lankford, P. Lund, M. Mandelkern, E. C. Martin, D. P. Stoker, S. Abachi, C. Buchanan, J. W. Gary, F. Liu, O. Long, B. C. Shen, ∗ G. M. Vitug, Z. Yasin, L. Zhang, V. Sharma, C. Campagnari, T. M. Hong, D. Kovalskyi, M. A. Mazur, J. D. Richman, T. W. Beck, A. M. Eisner, C. J. Flacco, C. A. Heusch, J. Kroseberg, W. S. Lockman, T. Schalk, B. A. Schumm, A. Seiden, L. Wang, M. G. Wilson, L. O. Winstrom, C. H. Cheng, D. A. Doll, B. Echenard, F. Fang, D. G. Hitlin, I. Narsky, T. Piatenko, F. C. Porter, R. Andreassen, G. Mancinelli, B. T. Meadows, K. Mishra, M. D. Sokoloff, F. Blanc, P. C. Bloom, W. T. Ford, J. F. Hirschauer, A. Kreisel, M. Nagel, U. Nauenberg, A. Olivas, J. G. Smith, K. A. Ulmer, S. R. Wagner, R. Ayad, † A. M. Gabareen, A. Soffer, ‡ W. H. Toki, R. J. Wilson, D. D. Altenburg, E. Feltresi, A. Hauke, H. Jasper, M. Karbach, J. Merkel, A. Petzold, B. Spaan, K. Wacker, V. Klose, M. J. Kobel, H. M. Lacker, W. F. Mader, R. Nogowski, J. Schubert, K. R. Schubert, R. Schwierz, J. E. Sundermann, A. Volk, D. Bernard, G. R. Bonneaud, E. Latour, Ch. Thiebaux, M. Verderi, P. J. Clark, W. Gradl, S. Playfer, A. I. Robertson, J. E. Watson, M. Andreotti, D. Bettoni, C. Bozzi, R. Calabrese, A. Cecchi, G. Cibinetto, P. Franchini, E. Luppi, M. Negrini, A. Petrella, L. Piemontese, E. Prencipe, V. Santoro, F. Anulli, R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, G. Finocchiaro, S. Pacetti, P. Patteri, I. M. Peruzzi, § M. Piccolo, M. Rama, A. Zallo, A. Buzzo, R. Contri, M. Lo Vetere, M. M. Macri, M. R. Monge, S. Passaggio, C. Patrignani, E. Robutti, A. Santroni, S. Tosi, K. S. Chaisanguanthum, M. Morii, R. S. Dubitzky, J. Marks, S. Schenk, U. Uwer, D. J. Bard, P. D. Dauncey, J. A. Nash, W. Panduro Vazquez, M. Tibbetts, P. K. Behera, X. Chai, M. J. Charles, U. Mallik, J. Cochran, H. B. Crawley, L. Dong, W. T. Meyer, S. Prell, E. I. Rosenberg, A. E. Rubin, Y. Y. Gao, A. V. Gritsan, Z. J. Guo, C. K. Lae, A. G. Denig, M. Fritsch, G. Schott, N. Arnaud, J. B´equilleux, A. D’Orazio, M. Davier, J. Firmino daCosta, G. Grosdidier, A. H¨ocker, V. Lepeltier, F. Le Diberder, A. M. Lutz, S. Pruvot, P. Roudeau, M. H. Schune, J. Serrano, V. Sordini, A. Stocchi, W. F. Wang, G. Wormser, D. J. Lange, D. M. Wright, I. Bingham, J. P. Burke, C. A. Chavez, J. R. Fry, E. Gabathuler, R. Gamet, D. E. Hutchcroft, D. J. Payne, C. Touramanis, A. J. Bevan, K. A. George, F. Di Lodovico, R. Sacco, M. Sigamani, G. Cowan, H. U. Flaecher, D. A. Hopkins, S. Paramesvaran, F. Salvatore, A. C. Wren, D. N. Brown, C. L. Davis, K. E. Alwyn, N. R. Barlow, R. J. Barlow, Y. M. Chia, C. L. Edgar, G. D. Lafferty, T. J. West, J. I. Yi, J. Anderson, C. Chen, A. Jawahery, D. A. Roberts, G. Simi, J. M. Tuggle, C. Dallapiccola, S. S. Hertzbach, X. Li, E. Salvati, S. Saremi, R. Cowan, D. Dujmic, P. H. Fisher, K. Koeneke, G. Sciolla, M. Spitznagel, F. Taylor, R. K. Yamamoto, M. Zhao, S. E. Mclachlin, ∗ P. M. Patel, S. H. Robertson, A. Lazzaro, V. Lombardo, F. Palombo, J. M. Bauer, L. Cremaldi, V. Eschenburg, R. Godang, R. Kroeger, D. A. Sanders, D. J. Summers, H. W. Zhao, S. Brunet, D. Cˆot´e, M. Simard, P. Taras, F. B. Viaud, H. Nicholson, G. De Nardo, L. Lista, D. Monorchio, C. Sciacca, M. A. Baak, G. Raven, H. L. Snoek, C. P. Jessop, K. J. Knoepfel, J. M. LoSecco, G. Benelli, L. A. Corwin, K. Honscheid, H. Kagan, R. Kass, J. P. Morris, A. M. Rahimi, J. J. Regensburger, S. J. Sekula, Q. K. Wong, N. L. Blount, J. Brau, R. Frey, . Igonkina, J. A. Kolb, M. Lu, R. Rahmat, N. B. Sinev, D. Strom, J. Strube, E. Torrence, G. Castelli, N. Gagliardi, A. Gaz, M. Margoni, M. Morandin, M. Posocco, M. Rotondo, F. Simonetto, R. Stroili, C. Voci, P. del Amo Sanchez, E. Ben-Haim, H. Briand, G. Calderini, J. Chauveau, P. David, L. Del Buono, O. Hamon, Ph. Leruste, J. Ocariz, A. Perez, J. Prendki, L. Gladney, M. Biasini, R. Covarelli, E. Manoni, C. Angelini, G. Batignani, S. Bettarini, M. Carpinelli, ¶ A. Cervelli, F. Forti, M. A. Giorgi, A. Lusiani, G. Marchiori, M. Morganti, N. Neri, E. Paoloni, G. Rizzo, J. J. Walsh, J. Biesiada, Y. P. Lau, D. Lopes Pegna, C. Lu, J. Olsen, A. J. S. Smith, A. V. Telnov, E. Baracchini, G. Cavoto, D. del Re, E. Di Marco, R. Faccini, F. Ferrarotto, F. Ferroni, M. Gaspero, P. D. Jackson, L. Li Gioi, M. A. Mazzoni, S. Morganti, G. Piredda, F. Polci, F. Renga, C. Voena, M. Ebert, T. Hartmann, H. Schr¨oder, R. Waldi, T. Adye, B. Franek, E. O. Olaiya, W. Roethel, F. F. Wilson, S. Emery, M. Escalier, L. Esteve, A. Gaidot, S. F. Ganzhur, G. Hamel de Monchenault, W. Kozanecki, G. Vasseur, Ch. Y`eche, M. Zito, X. R. Chen, H. Liu, W. Park, M. V. Purohit, R. M. White, J. R. Wilson, M. T. Allen, D. Aston, R. Bartoldus, P. Bechtle, J. F. Benitez, R. Cenci, J. P. Coleman, M. R. Convery, J. C. Dingfelder, J. Dorfan, G. P. Dubois-Felsmann, W. Dunwoodie, R. C. Field, S. J. Gowdy, M. T. Graham, P. Grenier, C. Hast, W. R. Innes, J. Kaminski, M. H. Kelsey, H. Kim, P. Kim, M. L. Kocian, D. W. G. S. Leith, S. Li, B. Lindquist, S. Luitz, V. Luth, H. L. Lynch, D. B. MacFarlane, H. Marsiske, R. Messner, D. R. Muller, H. Neal, S. Nelson, C. P. O’Grady, I. Ofte, A. Perazzo, M. Perl, B. N. Ratcliff, A. Roodman, A. A. Salnikov, R. H. Schindler, J. Schwiening, A. Snyder, D. Su, M. K. Sullivan, K. Suzuki, S. K. Swain, J. M. Thompson, J. Va’vra, A. P. Wagner, M. Weaver, C. A. West, W. J. Wisniewski, M. Wittgen, D. H. Wright, H. W. Wulsin, A. K. Yarritu, K. Yi, C. C. Young, V. Ziegler, P. R. Burchat, A. J. Edwards, S. A. Majewski, T. S. Miyashita, B. A. Petersen, L. Wilden, S. Ahmed, M. S. Alam, R. Bula, J. A. Ernst, B. Pan, M. A. Saeed, S. B. Zain, S. M. Spanier, B. J. Wogsland, R. Eckmann, J. L. Ritchie, A. M. Ruland, C. J. Schilling, R. F. Schwitters, B. W. Drummond, J. M. Izen, X. C. Lou, S. Ye, F. Bianchi, D. Gamba, M. Pelliccioni, M. Bomben, L. Bosisio, C. Cartaro, G. Della Ricca, L. Lanceri, L. Vitale, V. Azzolini, N. Lopez-March, F. Martinez-Vidal, D. A. Milanes, A. Oyanguren, J. Albert, Sw. Banerjee, B. Bhuyan, H. H. F. Choi, K. Hamano, R. Kowalewski, M. J. Lewczuk, I. M. Nugent, J. M. Roney, R. J. Sobie, T. J. Gershon, P. F. Harrison, J. Ilic, T. E. Latham, G. B. Mohanty, H. R. Band, X. Chen, S. Dasu, K. T. Flood, Y. Pan, M. Pierini, R. Prepost, C. O. Vuosalo, and S. L. Wu (The B A B AR Collaboration) Laboratoire de Physique des Particules, IN2P3/CNRS et Universit´e de Savoie, F-74941 Annecy-Le-Vieux, France Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain Universit`a di Bari, Dipartimento di Fisica and INFN, I-70126 Bari, Italy University of Bergen, Institute of Physics, N-5007 Bergen, Norway Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA University of Birmingham, Birmingham, B15 2TT, United Kingdom Ruhr Universit¨at Bochum, Institut f¨ur Experimentalphysik 1, D-44780 Bochum, Germany University of Bristol, Bristol BS8 1TL, United Kingdom University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1 Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia University of California at Irvine, Irvine, California 92697, USA University of California at Los Angeles, Los Angeles, California 90024, USA University of California at Riverside, Riverside, California 92521, USA University of California at San Diego, La Jolla, California 92093, USA University of California at Santa Barbara, Santa Barbara, California 93106, USA University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA California Institute of Technology, Pasadena, California 91125, USA University of Cincinnati, Cincinnati, Ohio 45221, USA University of Colorado, Boulder, Colorado 80309, USA Colorado State University, Fort Collins, Colorado 80523, USA Universit¨at Dortmund, Institut f¨ur Physik, D-44221 Dortmund, Germany Technische Universit¨at Dresden, Institut f¨ur Kern- und Teilchenphysik, D-01062 Dresden, Germany Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom Universit`a di Ferrara, Dipartimento di Fisica and INFN, I-44100 Ferrara, Italy Laboratori Nazionali di Frascati dell’INFN, I-00044 Frascati, Italy Universit`a di Genova, Dipartimento di Fisica and INFN, I-16146 Genova, Italy Harvard University, Cambridge, Massachusetts 02138, USA Universit¨at Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany Imperial College London, London, SW7 2AZ, United Kingdom University of Iowa, Iowa City, Iowa 52242, USA Iowa State University, Ames, Iowa 50011-3160, USA Johns Hopkins University, Baltimore, Maryland 21218, USA Universit¨at Karlsruhe, Institut f¨ur Experimentelle Kernphysik, D-76021 Karlsruhe, Germany Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3/CNRS et Universit´e Paris-Sud 11,Centre Scientifique d’Orsay, B. P. 34, F-91898 ORSAY Cedex, France Lawrence Livermore National Laboratory, Livermore, California 94550, USA University of Liverpool, Liverpool L69 7ZE, United Kingdom Queen Mary, University of London, E1 4NS, United Kingdom University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom University of Louisville, Louisville, Kentucky 40292, USA University of Manchester, Manchester M13 9PL, United Kingdom University of Maryland, College Park, Maryland 20742, USA University of Massachusetts, Amherst, Massachusetts 01003, USA Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8 Universit`a di Milano, Dipartimento di Fisica and INFN, I-20133 Milano, Italy University of Mississippi, University, Mississippi 38677, USA Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7 Mount Holyoke College, South Hadley, Massachusetts 01075, USA Universit`a di Napoli Federico II, Dipartimento di Scienze Fisiche and INFN, I-80126, Napoli, Italy NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands University of Notre Dame, Notre Dame, Indiana 46556, USA Ohio State University, Columbus, Ohio 43210, USA University of Oregon, Eugene, Oregon 97403, USA Universit`a di Padova, Dipartimento di Fisica and INFN, I-35131 Padova, Italy Laboratoire de Physique Nucl´eaire et de Hautes Energies,IN2P3/CNRS, Universit´e Pierre et Marie Curie-Paris6,Universit´e Denis Diderot-Paris7, F-75252 Paris, France University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Universit`a di Perugia, Dipartimento di Fisica and INFN, I-06100 Perugia, Italy Universit`a di Pisa, Dipartimento di Fisica, Scuola Normale Superiore and INFN, I-56127 Pisa, Italy Princeton University, Princeton, New Jersey 08544, USA Universit`a di Roma La Sapienza, Dipartimento di Fisica and INFN, I-00185 Roma, Italy Universit¨at Rostock, D-18051 Rostock, Germany Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom DSM/Dapnia, CEA/Saclay, F-91191 Gif-sur-Yvette, France University of South Carolina, Columbia, South Carolina 29208, USA Stanford Linear Accelerator Center, Stanford, California 94309, USA Stanford University, Stanford, California 94305-4060, USA State University of New York, Albany, New York 12222, USA University of Tennessee, Knoxville, Tennessee 37996, USA University of Texas at Austin, Austin, Texas 78712, USA University of Texas at Dallas, Richardson, Texas 75083, USA Universit`a di Torino, Dipartimento di Fisica Sperimentale and INFN, I-10125 Torino, Italy Universit`a di Trieste, Dipartimento di Fisica and INFN, I-34127 Trieste, Italy IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain University of Victoria, Victoria, British Columbia, Canada V8W 3P6 Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom University of Wisconsin, Madison, Wisconsin 53706, USA
We use a sample of 384 million BB events collected with the B A B AR detector at the PEP-II e + e − collider to study angular distributions in the rare decays B → K ∗ ℓ + ℓ − , where ℓ + ℓ − is either e + e − or µ + µ − . For low dilepton invariant masses, m ℓℓ < . /c , we measure a lepton forward-backwardasymmetry A F B = 0 . +0 . − . ± .
05 and K ∗ longitudinal polarization F L = 0 . ± . ± .
04. For m ℓℓ > . /c , we measure A F B = 0 . +0 . − . ± .
07 and F L = 0 . +0 . − . ± . PACS numbers: 13.20.He he decays B → K ∗ ℓ + ℓ − , where K ∗ → Kπ and ℓ + ℓ − is either an e + e − or µ + µ − pair, arise from flavor-changing neutral currents (FCNC), which are forbiddenat tree level in the Standard Model (SM). The lowest-order SM processes contributing to these decays are thephoton or Z penguin and the W + W − box diagramsshown in Fig. 1. The amplitudes can be expressed interms of effective Wilson coefficients for the electromag-netic penguin, C eff , and the vector and axial-vector elec-troweak contributions, C eff and C eff respectively, arisingfrom the interference of the Z penguin and W + W − boxdiagrams [1]. The angular distributions in these decaysas a function of dilepton mass squared q = m ℓ + ℓ − aresensitive to many possible new physics contributions [2].We describe measurements of the distribution of theangle θ K between the K and the B directions in the K ∗ rest frame. A fit to cos θ K of the form [3]32 F L cos θ K + 34 (1 − F L )(1 − cos θ K ) (1)determines F L , the K ∗ longitudinal polarization fraction.We also describe measurements of the distribution of theangle θ ℓ between the ℓ + ( ℓ − ) and the B ( B ) direction inthe ℓ + ℓ − rest frame. A fit to cos θ ℓ of the form [3]34 F L (1 − cos θ ℓ )+ 38 (1 − F L )(1+cos θ ℓ )+ A F B cos θ ℓ (2)determines A F B , the lepton forward-backward asymme-try. These measurements are done in a low q region0 . < q < .
25 GeV /c , and in a high q region above10 .
24 GeV /c . We remove the J/ψ and ψ (2 S ) resonancesby vetoing events in the regions q = 6 . .
24 GeV /c and q = 12 . .
06 GeV /c respectively.The SM predicts a distinctive variation of A F B arisingfrom the interference between the different amplitudes.The expected SM dependence of A F B and F L on q alongwith variations due to opposite-sign Wilson coefficientsare shown in Fig. 3. At low q , where C eff dominates, A F B is expected to be small with a zero-crossing pointat q ∼ /c [4, 5, 6]. There is an experimental con-straint on the magnitude of C eff coming from the branch-ing fraction for b → sγ [6, 7], which corresponds to thelimit q →
0. However, a reversal of the sign of C eff is q q b st,c,uW − γ , Z l + l − q qb st,c,u W + W − ν l − l + FIG. 1: Lowest-order Feynman diagrams for b → sℓ + ℓ − . allowed. At high q , the product of C eff and C eff is ex-pected to give a large positive asymmetry. Right-handedweak currents have an opposite-sign C eff C eff which wouldgive a negative A F B at high q . Contributions from non-SM processes can change the magnitudes and relativesigns of C eff , C eff and C eff , and may introduce complexphases between them [3, 8]. An experimental determi-nation of F L is required to obtain a model-independent A F B result, and thus avoid drawing possibly incorrectinferences about new physics from our observations.We reconstruct signal events in six separate flavor-specific final states containing an e + e − or µ + µ − pair,and a K ∗ (892) candidate reconstructed as K + π − , K + π or K S π + (or their charge conjugates). To understandcombinatorial backgrounds we also reconstruct samplescontaining the same hadronic final states and e ± µ ∓ pairs,where no signal is expected because of lepton flavor con-servation. To understand backgrounds from hadrons ( h )misidentified as muons, we similarly reconstruct samplescontaining h ± µ ∓ pairs with no particle identification re-quirement for the h ± .We use a dataset of 384 million BB pairs collectedat the Υ (4 S ) resonance with the B A B AR detector [9] atthe PEP-II asymmetric-energy e + e − collider. Track-ing is provided by a five-layer silicon vertex trackerand a 40-layer drift chamber in a 1.5 T magnetic field.We identify electrons with a CsI(Tl) electromagneticcalorimeter, muons with an instrumented magnetic fluxreturn, and K + using a detector of internally reflectedCherenkov light as well as ionization energy loss infor-mation. Charged tracks other than identified e , µ and K candidates are treated as pions. Electrons (muons)are required to have momenta p > . .
7) GeV /c in thelaboratory frame. We add photons to electrons whenthey are consistent with bremsstrahlung, and do not useelectrons that arise from photon conversions to low-mass e + e − pairs. Neutral K S → π + π − candidates are requiredto have an invariant mass consistent with the nominal K mass [10], and a flight distance from the e + e − interac-tion point which is more than three times its uncertainty.Neutral pion candidates are formed from two photonswith E γ >
50 MeV, and an invariant mass between 115and 155 MeV /c . We require K ∗ (892) candidates to havean invariant mass 0 . < M ( Kπ ) < .
97 GeV /c . B → K ∗ ℓ + ℓ − decays are characterized by the kine-matic variables m ES = p s/ − p ∗ B and ∆ E = E ∗ B −√ s/
2, where p ∗ B and E ∗ B are the reconstructed B mo-mentum and energy in the center-of-mass (CM) frame,and √ s is the total CM energy. We define a fit re-gion m ES > . /c , with − . < ∆ E < . − . < ∆ E < .
04) GeV for e + e − ( µ + µ − ) finalstates in the low q region, and − . < ∆ E < . − . < ∆ E < .
05) GeV for high q . We use thewider (narrower) ∆ E windows to select the e ± µ ∓ ( h ± µ ∓ )background samples.The most significant background arises from random4ombinations of leptons from semileptonic B and D de-cays. In BB events the leptons are kinematically corre-lated if they come from B → D ( ∗ ) ℓν , D → K ( ∗ ) ℓν . Un-correlated backgrounds combine leptons from separate B decays or from continuum e + e − → c ¯ c events. We sup-press these types of combinatorial background throughthe use of neural networks (NN). For each final state weuse four separate NN designed to suppress either con-tinuum or BB backgrounds in either the low or high q regions, and different selections of NN inputs are useddepending on q bin (low, high), the identity of the lep-tons in the final state ( e , µ ), and the type of background( BB , continuum). Inputs include: • event thrust; • ratio of second-to-zeroth Fox-Wolfram mo-ments [11]; • m ES and ∆ E of the rest of the event (ROE), com-prising all charged tracks and neutral energy de-posits not used to reconstruct the signal candidate; • the magnitude of the total event transverse momen-tum, which is correlated with missing energy due tounreconstructed neutrinos in background semilep-tonic decays; • di-lepton system’s distance of closest approachalong the z-axis, and separately in the xy-plane,to the primary interaction point; • vertex probability of the signal candidate and, sep-arately, of the di-lepton system; • the cosines in the CM frame of the angle betweenthe B candidate’s momentum and the z axis, theangle between the event thrust axis and the z axis( θ thrust ), the angle between the ROE thrust axisand the z axis ( θ ROEthrust ), and the angle between θ ROEthrust and θ thrust .There is also a background contribution in the signalregion from B → D ( K ∗ π ) π decays, where both pionsare misidentified. The misidentification rates for muonsand electrons are ∼
2% and ∼ . µ + µ − final states.These events are vetoed if the invariant mass of the K ∗ π system is in the range 1 . .
90 GeV /c .We optimize the NN and ∆ E selections for each finalstate in each q bin to give the best combined statisti-cal signal significance in the m ES signal region m ES > .
27 GeV /c for the sum of all six final states. After allthese selections have been applied, the final reconstruc-tion efficiencies and expected yields for signal events (cal-culated using world average branching fractions [7]), aswell as expected yields for background events in the sig-nal region, are shown in Table I.For each q region, we combine events from all six finalstates and perform three successive unbinned maximumlikelihood fits. Because of the relatively small numberof signal candidates in each q region, a simultaneous fitover m ES , cos θ K and cos θ ℓ is unlikely to converge and TABLE I: Signal efficiencies (%), and expected signal andbackground yields for m ES > .
27 GeV /c , for low and high q regions. Signal Eff. Signal Yield Bkgd. YieldMode low high low high low high K + π µ + µ − K S π + µ + µ − K + π − µ + µ − K + π e + e − K S π + e + e − K + π − e + e − a sequential fitting procedure is required. We initially fitthe m ES distribution using events with m ES > . /c to obtain the signal and background yields, N S and N B respectively. We use an ARGUS shape [12] with afree shape parameter to describe the combinatorial back-ground in this fit. For the signal, we use a Gaussian shapewith a mean m ES = 5 . ± . /c and σ =2 . ± .
03 MeV /c , which are determined from a fit tothe vetoed charmonium samples. In this and subsequentfits we account for a small contribution from misidentifiedhadrons by subtracting the K ∗ h ± µ ∓ events, weighted bythe probability for the h ± to be misidentified as a muon.We also account in all fits for charmonium events thatescape the veto, and for mis-reconstructed signal events.We estimate contributions from non-resonant Kπ decaysby fitting events outside the K ∗ mass window in the range0 . − . /c . We find no signal-like events that arenot accounted for by the tails of the resonant mass distri-bution, and thus do not expect any significant contribu-tion from non-resonant events within the mass window.The second fit is to the cosine of the helicity an-gle of the K ∗ decay, cos θ K , for events with m ES > .
27 GeV /c . In this fit, the only free parameter is F L ,with the normalizations for signal and combinatorialbackground events taken from the initial m ES fit. Thebackground normalization is obtained by integrating, for m ES > .
27 GeV /c , the ARGUS shape resulting fromthe m ES fit. We model the cos θ K shape of the combina-torial background using e + e − and µ + µ − events, as wellas lepton-flavor violating e + µ − and µ + e − events, in the5 . < m ES < .
27 GeV /c sideband. The signal distri-bution given in equation (1) is folded with the detectoracceptance as a function of cos θ K , which is obtained fromsimulated signal events.The final fit is to the cosine of the lepton helicity angle,cos θ ℓ , for events with m ES > .
27 GeV /c . The only freeparameter in this fit is A F B , with the signal distributiongiven in equation (2) folded with the detector acceptanceas a function of cos θ ℓ . In this fit, the value of F L is fixedfrom the result of the second fit, and normalizations for5 ABLE II: Results for the B → J/ψK ∗ control samples. ∆BFare the differences between the measured branching fractionsand the world average value [10]. The previously measured F L = 0 . ± .
01 [13], and the expected A F B = 0.Mode ∆BF (10 − ) F L A F B K + π µ + µ − +0 . ± .
12 0 . ± . − . ± . K S π + µ + µ − +0 . ± .
11 0 . ± .
02 +0 . ± . K + π − µ + µ − − . ± .
07 0 . ± . − . ± . K + π e + e − +0 . ± .
10 0 . ± .
03 +0 . ± . K S π + e + e − +0 . ± .
10 0 . ± . − . ± . K + π − e + e − +0 . ± .
07 0 . ± .
02 +0 . ± . Kℓ + ℓ − and K ∗ ℓ + ℓ − samples. N S is the number of signal events in the m ES fit.The quoted errors are statistical only.Decay q N S F L A F B Kℓ + ℓ − low 26 . ± . . +0 . − . high 26 . ± . . +0 . − . K ∗ ℓ + ℓ − low 27.2 ± . ± .
16 +0 . +0 . − . high 36.6 ± . +0 . − . +0 . +0 . − . signal and combinatorial background events are identicalto those used in the second fit. We constrain the cos θ ℓ shape of the combinatorial background using the samesideband samples as for the cos θ K fit. The correlatedleptons from B → D ( ∗ ) ℓν , D → K ( ∗ ) ℓν give rise to an m ES -dependent peak in the combinatorial background atcos θ ℓ > .
7, and we consider this correlation in our studyof systematic errors. No such correlation is observed forcos θ K .We test our fits using the large sample of vetoed char-monium events. The branching fractions (BF) and K ∗ polarization for B → J/ψK ∗ are well known [10, 13], and A F B is expected to be zero. The results of the fits to thesix final states are all consistent with expected values (seeTable II). We further test our methodology by perform-ing the m ES and cos θ ℓ fits on a sample of B + → K + ℓ + ℓ − decays. The results are given in Table III and are con-sistent with negligible forward-backward asymmetry, asexpected in the SM and most new physics models [14].We validate the fit model by performing ensembles offits to datasets with events drawn from simulated signaland background event samples. The input SM values of F L and A F B are reproduced with the expected statisticalerrors. A few percent of the fits do not converge due tosmall signal yields. We have also performed fits usingsignal events generated with widely varying values of C eff , C eff and C eff covering the physically allowed regions of F L and A F B , and find minimal bias in our fits.The systematic errors on the fitted values of F L and TABLE IV: Systematic errors on the measurements of F L and A F B in the K ∗ ℓ + ℓ − samples.Source F L A F B of Error low q high q low q high q m ES fit yields 0.001 0.016 0.003 0.002 F L fit error 0.025 0.022Background shape 0.011 0.008 0.017 0.021Signal model 0.036 0.034 0.030 0.038Fit bias 0.012 0.020 0.023 0.052Mis-reconstructed signal 0.010 0.010 0.020 0.020Total 0.041 0.044 0.052 0.074 A F B are summarized in Table IV. The uncertaintiesin the fitted signal yields N S , due to variations in theARGUS shape in the m ES fits, are propagated into theangular fits. The errors on the fitted F L values are prop-agated into the A F B fits. We vary the combinatorialbackground shapes by dividing the sideband sample intotwo disjoint regions in m ES . We vary the signal modelusing simulated events generated with different form fac-tors [5, 15], and with a range of values of C eff , C eff and C eff , to determine an average fit bias. Finally, the mod-eling of mis-reconstructed signal events is constrained bythe fits to the charmonium samples (Table II), where itis the largest systematic uncertainty.The final fits to the K ∗ ℓ + ℓ − samples are shown inFig. 2. The results for F L and A F B are given in Ta-ble III and are shown in Fig. 3. In the low q region,where we expect A F B ∼ − .
03 and F L ∼ .
63 fromthe SM, we measure A F B = 0 . +0 . − . ± .
05 and F L =0 . ± . ± .
04, where the first error is statistical andthe second is systematic. In the high q region, the SMexpectation is A F B ∼ .
38 and F L ∼ .
40, and we mea-sure A F B = 0 . +0 . − . ± .
07 and F L = 0 . +0 . − . ± . . ± . F L and A F B values are gen-erally difficult to characterize in the high q region, andalthough under better control for 1 < q < /c , theextension of our low q region below 1 GeV /c makes es-timates of uncertainties there difficult also. The quotedvalues are obtained using our implementation of thephysics models described in [4, 15], corresponding to theSM curves in Fig. 3.The expected SM value of C eff at next-to-next-to-leading logarithmic (NNLL) order is C eff = − .
43 [16].A more recent NNLL calculation which evaluates con-tributions from the full set of seven form factors gives C eff = − .
13 [17]. The magnitude of possible contri-butions from new physics to C can be constrained if A F B > q . By combining such a constraint on A F B with inclusive b → sℓ + ℓ − branching fraction results,an upper bound of | C NP | < ∼ mES [GeV/c5.2 5.22 5.24 5.26 5.281020 (b)(b) ) K θ cos(-1 -0.5 0 0.5 1 E ve n t s / ( . ) (c)(c) ) K θ cos(-1 -0.5 0 0.5 101020 (d) ) l θ cos(-1 -0.5 0 0.5 15101520 (f) ) l θ cos(-1 -0.5 0 0.5 1 E ve n t s / ( . ) (e) ] mES [GeV/c5.2 5.22 5.24 5.26 5.28 ) E ve n t s / ( . G e V / c (a) FIG. 2: K ∗ ℓ + ℓ − fits: (a) low q m ES , (b) high q m ES , (c)low q cos θ K , (d) high q cos θ K , (e) low q cos θ ℓ , (f) high q cos θ ℓ ; with combinatorial (dots) and peaking (long dash)background, signal (short dash) and total (solid) fit distribu-tions superimposed on the data points. tion results of | C NP | < ∼
10 [18]. Our results are consistentwith measurements by Belle [19], and replace the earlier B A B AR results in which only a lower limit on A F B wasset in the low q region [20].We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues, andfor the substantial dedicated effort from the comput-ing organizations that support B A B AR . The collaborat-ing institutions wish to thank SLAC for its support andkind hospitality. This work is supported by DOE andNSF (USA), NSERC (Canada), CEA and CNRS-IN2P3(France), BMBF and DFG (Germany), INFN (Italy),FOM (The Netherlands), NFR (Norway), MES (Russia),MEC (Spain), and STFC (United Kingdom). Individualshave received support from the Marie Curie EIF (Euro-pean Union) and the A. P. Sloan Foundation. ∗ Deceased † Now at Temple University, Philadelphia, Pennsylvania19122, USA F B A −0.6−0.4−0.200.20.40.60.811.2 (a) ( S ) ψ ψ J/ ] /c [GeV q L F (b) ( S ) ψ ψ J/ FIG. 3: Plots of our results for (a) A F B and (b) F L for thedecay B → K ∗ ℓ + ℓ − showing comparisons with SM (solid); C eff = − C eff (long dash); C eff C eff = − C eff C eff (short dash); C eff = − C eff , C eff C eff = − C eff C eff (dash-dot). Statistical andsystematic errors are added in quadrature. Expected F L val-ues integrated over each q region are also shown. The F L curves with C eff C eff = − C eff C eff are nearly identical to thetwo curves shown. ‡ Now at Tel Aviv University, Tel Aviv, 69978, Israel § Also with Universit`a di Perugia, Dipartimento di Fisica,Perugia, Italy ¶ Also with Universita’ di Sassari, Sassari, Italy[1] G. Buchalla, A. J. Buras and M. E. Lautenbacher, Rev.Mod. Phys. , 1125 (1996).[2] G. Burdman, Phys. Rev. D , 6400 (1995); J. L. Hewettand J. D. Wells, Phys. Rev. D , 5549 (1997); T. Feld-mann and J. Matias, JHEP , 074 (2003); W. J. Li,Y. B. Dai and C. S. Huang, Eur. Phys. J. C , 565(2005); Y. G. Xu, R. M. Wang and Y. D. Yang, Phys.Rev. D , 114019 (2006); P. Colangelo, F. De Fazio,R. Ferrandes and T. N. Pham, Phys. Rev. D , 115006(2006).[3] F. Kruger and J. Matias, Phys. Rev. D , 094009 (2005).[4] A. Ali, P. Ball, L. T. Handoko and G. Hiller, Phys. Rev.D , 074024 (2000).[5] F. Kruger, L. M. Sehgal, N. Sinha and R. Sinha, Phys.Rev. D , 114028 (2000) [Erratum-ibid. D , 019901(2001)]; A. Ali, E. Lunghi, C. Greub and G. Hiller, Phys.Rev. D , 034002 (2002); K. S. M. Lee, Z. Ligeti,I. W. Stewart and F. J. Tackmann, Phys. Rev. D ,034016 (2007).[6] M. Beneke, T. Feldmann and D. Seidel, Nucl. Phys. B , 25 (2001);
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