Measurement of B→Xγ Decays and Determination of | V td / V ts |
aa r X i v : . [ h e p - e x ] A ug B A B AR -PUB-08/035SLAC-PUB-13340 Measurement of B → Xγ Decays and Determination of | V td /V ts | B. Aubert, M. Bona, Y. Karyotakis, J. P. Lees, V. Poireau, E. Prencipe, X. Prudent, V. Tisserand, J. Garra Tico, E. Grauges, L. Lopez ab , A. Palano ab , M. Pappagallo ab , G. Eigen, B. Stugu, L. Sun, G. S. Abrams, M. Battaglia, D. N. Brown, R. N. Cahn, R. G. Jacobsen, L. T. Kerth, Yu. G. Kolomensky, G. Lynch, I. L. Osipenkov, M. T. Ronan, ∗ K. Tackmann, T. Tanabe, C. M. Hawkes, N. Soni, A. T. Watson, H. Koch, T. Schroeder, D. Walker, D. J. Asgeirsson, B. G. Fulsom, C. Hearty, T. S. Mattison, J. A. McKenna, M. Barrett, A. Khan, 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, A. J. Martinez, T. Schalk, B. A. Schumm, A. Seiden, 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, P. C. Bloom, W. T. Ford, A. Gaz, J. F. Hirschauer, M. Nagel, U. Nauenberg, J. G. Smith, K. A. Ulmer, S. R. Wagner, R. Ayad, † 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, M. J. Kobel, W. F. Mader, R. Nogowski, K. R. Schubert, R. Schwierz, A. Volk, D. Bernard, G. R. Bonneaud, E. Latour, M. Verderi, P. J. Clark, S. Playfer, J. E. Watson, M. Andreotti ab , D. Bettoni a , C. Bozzi a , R. Calabrese ab , A. Cecchi ab , G. Cibinetto ab , P. Franchini ab , E. Luppi ab , M. Negrini ab , A. Petrella ab , L. Piemontese a , V. Santoro ab , 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 a , R. Contri ab , M. Lo Vetere ab , M. M. Macri a , M. R. Monge ab , S. Passaggio a , C. Patrignani ab , E. Robutti a , A. Santroni ab , S. Tosi ab , K. S. Chaisanguanthum, M. Morii, A. Adametz, J. Marks, S. Schenk, U. Uwer, V. Klose, H. M. Lacker, D. J. Bard, P. D. Dauncey, J. A. Nash, 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, N. Arnaud, J. B´equilleux, A. D’Orazio, M. Davier, J. Firmino da Costa, 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, 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, C. K. Clarke, 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, A. G. Denig, M. Fritsch, W. Gradl, G. Schott, K. E. Alwyn, D. Bailey, R. J. Barlow, Y. M. Chia, C. L. Edgar, G. Jackson, 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, X. Li, E. Salvati, S. Saremi, R. Cowan, D. Dujmic, P. H. Fisher, G. Sciolla, M. Spitznagel, F. Taylor, R. K. Yamamoto, M. Zhao, P. M. Patel, S. H. Robertson, A. Lazzaro ab , V. Lombardo a , F. Palombo ab , J. M. Bauer, L. Cremaldi, R. Godang, ∗∗ R. Kroeger, D. A. Sanders, D. J. Summers, H. W. Zhao, M. Simard, P. Taras, F. B. Viaud, H. Nicholson, G. De Nardo ab , L. Lista a , D. Monorchio ab , G. Onorato ab , C. Sciacca ab , G. Raven, H. L. Snoek, C. P. Jessop, K. J. Knoepfel, J. M. LoSecco, W. F. Wang, 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, O. Igonkina, J. A. Kolb, M. Lu, R. Rahmat, N. B. Sinev, D. Strom, J. Strube, E. Torrence, G. Castelli ab , N. Gagliardi ab , M. Margoni ab , M. Morandin a , M. Posocco a , M. Rotondo a , F. Simonetto ab , R. Stroili ab , C. Voci ab , 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, S. Sitt, L. Gladney, M. Biasini ab , R. Covarelli ab , E. Manoni ab , C. Angelini ab , G. Batignani ab , S. Bettarini ab , M. Carpinelli ab , †† . Cervelli ab , F. Forti ab , M. A. Giorgi ab , A. Lusiani ac , G. Marchiori ab , M. Morganti ab , N. Neri ab , E. Paoloni ab , G. Rizzo ab , J. J. Walsh a , D. Lopes Pegna, C. Lu, J. Olsen, A. J. S. Smith, A. V. Telnov, F. Anulli a , E. Baracchini ab , G. Cavoto a , D. del Re ab , E. Di Marco ab , R. Faccini ab , F. Ferrarotto a , F. Ferroni ab , M. Gaspero ab , P. D. Jackson a , L. Li Gioi a , M. A. Mazzoni a , S. Morganti a , G. Piredda a , F. Polci ab , F. Renga ab , C. Voena a , M. Ebert, T. Hartmann, H. Schr¨oder, R. Waldi, T. Adye, B. Franek, E. O. Olaiya, F. F. Wilson, S. Emery, M. Escalier, L. Esteve, 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, A. M. Gabareen, 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, 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, F. Bianchi ab , D. Gamba ab , M. Pelliccioni ab , M. Bomben ab , L. Bosisio ab , C. Cartaro ab , G. Della Ricca ab , L. Lanceri ab , L. Vitale ab , 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 INFN Sezione di Bari a ; Dipartmento di Fisica, Universit`a di Bari b , 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 Technische Universit¨at Dortmund, Fakult¨at 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 INFN Sezione di Ferrara a ; Dipartimento di Fisica, Universit`a di Ferrara b , I-44100 Ferrara, Italy INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy INFN Sezione di Genova a ; Dipartimento di Fisica, Universit`a di Genova b , I-16146 Genova, Italy Harvard University, Cambridge, Massachusetts 02138, USA Universit¨at Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany Humboldt-Universit¨at zu Berlin, Institut f¨ur Physik, Newtonstr. 15, D-12489 Berlin, 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 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, 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 Johannes Gutenberg-Universit¨at Mainz, Institut f¨ur Kernphysik, D-55099 Mainz, Germany 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 INFN Sezione di Milano a ; Dipartimento di Fisica, Universit`a di Milano b , 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 INFN Sezione di Napoli a ; Dipartimento di Scienze Fisiche,Universit`a di Napoli Federico II b , 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 INFN Sezione di Padova a ; Dipartimento di Fisica, Universit`a di Padova b , 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 INFN Sezione di Perugia a ; Dipartimento di Fisica, Universit`a di Perugia b , I-06100 Perugia, Italy INFN Sezione di Pisa a ; Dipartimento di Fisica,Universit`a di Pisa b ; Scuola Normale Superiore di Pisa c , I-56127 Pisa, Italy Princeton University, Princeton, New Jersey 08544, USA INFN Sezione di Roma a ; Dipartimento di Fisica,Universit`a di Roma La Sapienza b , I-00185 Roma, Italy Universit¨at Rostock, D-18051 Rostock, Germany Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom CEA, Irfu, SPP, Centre de 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 INFN Sezione di Torino a ; Dipartimento di Fisica Sperimentale, Universit`a di Torino b , I-10125 Torino, Italy INFN Sezione di Trieste a ; Dipartimento di Fisica, Universit`a di Trieste b , 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 (Dated: January 10, 2019)Using a sample of 383 million BB events collected by the B A B AR experiment, we measure sums ofseven exclusive final states B → X d ( s ) γ , where X d ( X s ) is a non-strange (strange) charmless hadronicsystem in the mass range 0 . − . /c . After correcting for unmeasured decay modes in thismass range, we obtain a branching fraction for b → dγ of (7 . ± . stat. ) ± . syst. )) × − .Taking the ratio of X d to X s we find Γ( b → dγ ) / Γ( b → sγ ) = 0 . ± . stat. ) ± . syst. ) , from which we determine | V td /V ts | = 0 . ± . PACS numbers: 13.20.He he decays b → dγ and b → sγ are flavor-changingneutral current processes forbidden at tree level in thestandard model (SM). The leading-order processes areone-loop electroweak penguin diagrams in which the topquark is the dominant virtual particle. In the SM the in-clusive rate for b → dγ is suppressed compared to b → sγ by a factor of | V td /V ts | , where V td and V ts are Cabbibo-Kobayashi-Maskawa matrix elements. Measurements of | V td /V ts | using the exclusive modes B → ( ρ, ω ) γ and B → K ∗ γ [1] have theoretical uncertainties of 7% fromweak annihilation and hadronic form factors [2]. A mea-surement of the inclusive decay b → dγ relative to b → sγ could determine | V td /V ts | with reduced theoretical uncer-tainties compared to the exclusive modes [3]. In theoriesbeyond the SM [4], new virtual particles may appear dif-ferently in the penguin loop diagrams for b → dγ and b → sγ and in the box diagrams responsible for B d and B s mixing [5], leading to measurable differences in | V td /V ts | extracted from these two methods.We present measurements of the rare decays B → X d γ using seven exclusive final states (see Table I) in thehadronic mass range 0 . < M ( X d ) < . /c (whichcontains the ρ and ω resonances), and in the previouslyunmeasured region 1 . < M ( X d ) < . /c . Wecombine our results in the two mass regions and makecorrections for decay modes that are not reconstructedto obtain an inclusive branching fraction for b → dγ in the mass range 0.6-1.8 GeV /c . We perform a par-allel analysis of B → X s γ using the equivalent sevenmodes (Table I), and determine the ratio of inclusiverates Γ( b → dγ ) / Γ( b → sγ ) in the hadronic mass range0 . < M ( X d ) < . /c .These measurements use a sample of 383 × BB TABLE I: The reconstructed decay modes. Charge conjugatestates are implied throughout this paper. B → X d γ B → X s γB → π + π − γ B → K + π − γB + → π + π γ B + → K + π γB + → π + π − π + γ B + → K + π − π + γB → π + π − π γ B → K + π − π γB → π + π − π + π − γ B → K + π − π + π − γB + → π + π − π + π γ B + → K + π − π + π γB + → π + ηγ B + → K + ηγ ∗ Deceased † Now at Temple University, Philadelphia, Pennsylvania 19122,USA ‡ Now at Tel Aviv University, Tel Aviv, 69978, Israel § Also with Universit`a di Perugia, Dipartimento di Fisica, Perugia,Italy ¶ Also with Universit`a di Roma La Sapienza, I-00185 Roma, Italy ∗∗ Now at University of South Alabama, Mobile, Alabama 36688,USA †† Also with Universit`a di Sassari, Sassari, Italy pairs collected at the Υ (4 S ) resonance with the B A B AR detector [6] at the PEP-II B factory. The high-energyphoton is reconstructed from an isolated energy clusterin the CsI(Tl) calorimeter, which has a shape consistentwith a single photon, and an energy 1 . < E ∗ γ < . π ( η ) candidate with another photonof energy greater than 30(250) MeV, if the two-photoninvariant mass is in the range 105 < m γγ <
155 MeV /c (500 < m γγ <
590 MeV /c ).Charged pion and kaon candidates are measured in a1.5 T magnetic field as tracks in a 5-layer silicon vertexdetector and a 40-layer drift chamber, with a minimummomentum in the laboratory frame of 300 MeV /c . To dif-ferentiate pions from kaons we combine information fromthe detector of internally reflected Cherenkov light withthe energy loss measured in the tracking system. At atypical pion energy of 1 GeV, the pion selection efficiencyis 85% and the kaon mis-identification rate is 3%. Kaonsare selected by inverting the pion selection criteria. Wereconstruct π ( η ) candidates with momenta greater than300 MeV /c from pairs of photons of minimum energy 20MeV with an invariant mass 107 < m γγ <
145 MeV /c (470 < m γγ <
620 MeV /c ). The selected charged tracks, π ( η ) candidates, and high-energy photons are combinedto form B meson candidates consistent with one of theseven B → X s γ or B → X d γ decay modes. For B → X s γ decays one charged kaon is required, with all other tracksrequired to be pions. For B → X d γ decays, all tracks arerequired to be identified as pions. The charged particlesare combined to form a common vertex with a vertex fitprobability greater than 2%.Most of the backgrounds in this analysis arise fromcontinuum e + e − → q ¯ q events, q = ( u, d, s, c ), in which ahigh-energy photon comes from either initial state radia-tion or the decay of a π ( η ) meson. We require R < . | cos θ T | < .
8, where R is the ratio of the secondto zeroth Fox-Wolfram moments [7], and θ T is the anglebetween the photon and the thrust axis of the rest of theevent (ROE) in the CM frame. The ROE includes all thecharged tracks and neutral energy in the calorimeter notused to reconstruct the B candidate.The quantity cos θ T and twelve other variables that dis-tinguish between signal and continuum events are com-bined in a neural network (NN). These include the ra-tio R ′ , which is R is calculated in the frame recoilingagainst the photon momentum, the B meson productionangle θ ∗ B in the CM frame with respect to the beam axis,and five Legendre moments of the ROE with respect toboth the thrust axis of the ROE, and the direction ofthe high-energy photon. Differences in lepton and kaonproduction between background and B decays are ex-ploited by including five flavor-tagging variables appliedto the ROE [8]. We optimize the NN configuration formaximal discrimination between signal and continuumbackground, which gives 50% signal efficiency and 0 . E = E ∗ B − E ∗ beam and4 ES = q E ∗ − | ~p ∗ B | , where E ∗ B and ~p ∗ B are the CMenergy and momentum of the B candidate, and E ∗ beam is the CM energy of one beam. Signal events are ex-pected to have a ∆ E distribution centered at zero witha resolution of about 30 MeV, and an m ES distributioncentered at the mass of the B meson with a resolution ofabout 3 MeV /c . We consider candidates in the ranges − . < ∆ E < . m ES > .
22 GeV /c toincorporate sidebands that allow the combinatorial back-ground yields to be extracted from a fit to the data. Onaverage there are 1.75 candidates per event, and in eventswith multiple candidates we select the one with the best π ( η ) mass, or, where there is no π ( η ) we select thecandidate with the best vertex fit probability.The signal yields in the data are determined from two-dimensional unbinned maximum likelihood fits to the ∆ E and m ES distributions of the sums of all seven final stateslisted in Table I. We consider the following contribu-tions: signal, combinatorial backgrounds from continuumprocesses, B → Xπ /η decays, backgrounds from other B decays, and cross-feed from mis-reconstructed signal B → Xγ decays. The fits to the B → X d γ samples con-tain a component from misidentified B → X s γ decays,but we neglect the small B → X d γ background in the B → X s γ samples. The B background yields are deter-mined from a Monte Carlo (MC) simulation, whereas thecontinuum background is allowed to float in the fit.Each background contribution is modeled by a prob-ability density function (PDF) that is determined fromMC. The signal PDFs are the product of one-dimensional m ES and ∆ E distributions determined from fits to the B → K ∗ γ data. For the signal cross-feed component,and the B → X s γ background in the B → X d γ fit,we use two-dimensional histogram PDFs to account forcorrelations. The contributions from B → Xπ /η aremodeled by Gaussian peaks in both ∆ E and m ES , where∆ E is displaced by −
80 MeV due to the missing photon.The B → X s γ background in the B → X d γ sample alsopeaks with ∆ E displaced by −
50 MeV due to the kaonmisidentification. Continuum and other non-peakingbackgrounds are described by an ARGUS shape [9] in m ES and a second-order polynomial in ∆ E .We perform fits separately for B → X d γ and B → X s γ and in the two hadronic mass ranges. The signal and con-tinuum yields and the ARGUS and polynomial contin-uum shape parameters are allowed to vary. We scale thecross-feed contribution proportionally to the fitted signalyield, re-fit, and iterate until the fit converges. The fitsfor B → X s γ and B → X d γ are shown in the low- andhigh-mass regions in Figs. 1 and 2, respectively.The signal yields, average efficiencies and partialbranching fractions for the sums of the seven decay modesare given in Table II. The reconstruction efficiency de-pends on the distribution of the signal yield among thefinal states. For X s we measure the distribution of the fi-nal states in the data, but for X d there is no statisticallyuseful information, so we model the distribution usingthe the phase space fragmentation model implemented FIG. 1: Projections of the fits to data in the hadronic massrange 0.6-1.0 GeV /c . Projection of ∆ E with 5 . < m ES < .
286 GeV /c for (a) B → X s γ and (c) B → X d γ , and m ES with − . < ∆ E < .
05 GeV for (b) B → X s γ and (d) B → X d γ . Data points are compared with the sum of all the fitcontributions (solid line) including the signal (dashed line).FIG. 2: Projections of the fits to data in the hadronic massrange 1.0-1.8 GeV /c . Projection of ∆ E with 5 . < m ES < .
286 GeV /c for (a) B → X s γ and (c) B → X d γ , and m ES with − . < ∆ E < .
05 GeV for (b) B → X s γ and (d) B → X d γ . Data points are compared with the sum of all the fitcontributions (solid line) including the signal (dashed line). in JETSET [10].The branching fractions in Table III are obtained af-ter correcting for missing final states. The low mass B → X s γ measurement is found to be consistent withprevious measurements of the rate for B → K ∗ γ [11],after accounting for the 50% of decays to neutral kaons.For the low mass B → X d γ region, non-reconstructed ρ and ω decays are small and we find a branching fractionof (1 . ± . × − , consistent with previous measure-ments of B ( B → ( ρ, ω ) γ ) [1]. In the high mass region,we correct for missing final states with ≥ π s, using the fragmentation model5 ABLE II: Signal yields ( N S ), average efficiencies ( ǫ ) andpartial branching fractions ( B ) for the measured decay modes.The first error is statistical, the second systematic. M ( X )[ GeV /c ] N S ǫ B ( × − )0 . < M ( X s ) < . ±
46 8.5% 23 . ± . ± . . < M ( X d ) < . ±
26 7.0% 1 . ± . ± . . < M ( X s ) < . ±
75 6.1% 48 . ± . ± . . < M ( X d ) < . ±
47 5.2% 2 . ± . ± . B ( × − ) in the twohadronic mass regions M ( X )[ GeV /c ], after correcting formissing final states, and the ratios of B ( b → dγ ) to B ( b → sγ ).The first errors are statistical, and the second are systematic,including the fragmentation of the hadronic system. M ( X ) B ( b → dγ ) B ( b → sγ ) B ( b → dγ ) / B ( b → sγ )0 . − . . ± . ± . ± ± . ± . ± . . − . . ± . ± . ± ±
33 0 . ± . ± . . − . . ± . ± . ± ±
33 0 . ± . ± . described above.The sources of systematic uncertainties in the measure-ment of the branching fractions are listed in Table IV.These include uncertainties on track reconstruction effi-ciency, γ and π / η reconstruction, the π / η veto, the NNselection, and the number of BB pairs. The 2% uncer-tainty on correct kaon/pion particle identification, andthe 20% uncertainty on kaon misidentification, which isa systematic on the fixed b → sγ background in the B → X d γ fits, do not cancel in the ratio. The system-atic errors associated with the variation of the fit PDFsalso do not cancel because of the very different signal TABLE IV: Systematic errors on the measured partial andtotal branching fractions B . The final column shows system-atic errors that do not cancel in the ratio of rates Γ( b → dγ ) / Γ( b → sγ ).Systematic M ( X s ) M ( X d ) X d /X s Error Source 0.6-1.0 1.0-1.8 0.6-1.0 1.0-1.8 RatioTracking 1.7% 1.7% 1.7% 1.7%High-energy photon 2.5% 2.5% 2.5% 2.5% π /η reconstruction 1.7% 1.7% 1.7% 1.7% π /η veto 1.0% 1.0% 1.0% 1.0% K/π identification 2.0% 2.0% 2.0% 2.0% 2.0%Neural network 5.0% 5.0% 5.0% 5.0% BB pair counting 1.1% 1.1% 1.1% 1.1%Fit PDFs 2.4% 3.6% 7.0% 8.3% 8.7%Backgrounds 0.3% 0.4% 2.4% 6.1% 5.4%Fit bias 0.4% 1.7% 0.4% 3.3% 3.0%Fragmentation 3.6% 7.7% 8.5%Partial B ≥ B to background ratios in the two samples. We vary thesignal PDF parameters within the range allowed by thefit to the B → K ∗ γ data. The normalization of the sig-nal cross-feed is varied by ± B → Xπ /η by ± B backgrounds, including the B → X s γ contribution in the B → X d γ sample, are var-ied by ± X s hadronic system into the seven B → X s γ fi-nal states. The equivalent error for B → X d γ is obtainedfrom the difference between our fragmentation model ap-plied to B → X d γ and the fragmentation observed in B → X s γ data. We assume that these errors are inde-pendent and so do not cancel in the ratio of branchingfractions.Table IV also shows the systematic errors associatedwith correcting the partial branching fractions for themissing final states. There is no information from thedata on the missing fraction of high multiplicity finalstates with ≥ ≥ π or η mesons. We varythese fractions by ±
50% of their values from the defaultphase space fragmentation. We motivate our choice of a ±
50% variation using signal models, for which we mix acombination of resonances as 50% fractions of B → X s γ and B → X d γ in the mass range 1 . − . /c . Thesegive missing fractions close to the lower limits from the ±
50% variations. The missing fraction errors partiallycancel in the ratio when the ±
50% variations are madein the same direction for b → dγ and b → sγ .We take the spectral shape of the high-energyphoton from [12] with the kinetic parameters( m b , µ π ) = (4 .
65 GeV /c , − .
52 GeV ) extractedfrom fits to b → sγ and b → cℓν data [13]. Wevary these shape parameters in a correlated waybetween ( m b , µ π ) = (4 .
60 GeV /c , − .
60 GeV ) and( m b , µ π ) = (4 .
70 GeV /c , − .
45 GeV ). There aresystematic errors on the branching fractions fromthese variations, but they are small and cancel inthe ratio. The fraction of the spectrum in the massrange 0.6-1.8 GeV /c is (51 ± b → dγ and(50 ± b → sγ . We do not extrapolate theratio of branching fractions to M X > . /c , sothese errors, which mostly cancel in the ratio, are notincluded in Table IV. If we make this correction, weobtain B ( b → dγ ) = (1 . ± . ± . ± . × − and B ( b → sγ ) = (4 . ± . ± . ± . × − , where the firsterror is statistical, the second systematic and the thirdaccounts for the uncertainty in extrapolating to the fullmass range. The result for B → X s γ is consistent withthe measured inclusive b → sγ branching fraction of(3 . ± . × − [11].We convert the ratio of branching fractions from thefull mass range 0.6-1.8 GeV /c , Γ( b → dγ ) / Γ( b → sγ ) =6 . ± . ± . | V td /V ts | us-ing Table 1 and Equation (26) of [3]. The result is | V td /V ts | = 0 . ± . ± . ρ and ¯ η , and on1 /m c and 1 /m b corrections, but does not include an un-certainty for the restriction of the measurement of theratio to hadronic masses below 1.8 GeV /c .As a check, we use the low mass region to determine | V td /V ts | using predictions for exclusive B → ( ρ, ω ) γ and B → K ∗ γ from [2]. We find | V td /V ts | = 0 . ± . ± .
028 where the first error is experimental and the secondis theoretical. This is in good agreement with previouslypublished results [1].In summary we have made the first measurement of B → X d γ decays in the hadronic mass range up to 1.8 GeV /c , and have extracted | V td /V ts | from an inclu-sive model with small theoretical uncertainties. Theseresults are consistent with the measurements of | V td /V ts | from the exclusive decays B → ( ρ, ω ) γ [1], and with B s /B d oscillations [5].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. [1] B. Aubert et al. [ B A B AR Collaboration], Phys. Rev Lett. , 151802 (2007); D. Mohapatra et al. [Belle Collabora-tion], Phys. Rev Lett. , 221601 (2006).[2] P. Ball, G. Jones and R. Zwicky, Phys. Rev. D ,054004 (2007).[3] A. Ali, H. Asatrian and C. Greub, Phys. Lett. B ,87 (1998).[4] S. Bertolini, F. Borzumati and A. Masiero, Nucl. Phys.B , 321 (1987); H. Baer and M. Brhlik, Phys. Rev. D , 3201 (1997); J. Hewett and J. Wells, Phys. Rev. D , 5549 (1997); M. Carena et al. , Phys. Lett. B ,141 (2001).[5] W.-M. Yao et al. , J. Phys. G , 1 (2006).[6] B. Aubert et al. [ B A B AR Collaboration], Nucl. Instrum.Methods A , 1 (2002). [7] G. C. Fox and S. Wolfram, Nucl. Phys. B , 413(1979).[8] B. Aubert et al. [ B A B AR Collaboration], Phys. Rev. Lett. , 201802 (2002).[9] H. Albrecht et al. [ARGUS Collaboration], Phys. Lett. B , 218 (1987).[10] T. Sjostrand, hep-ph/9508391; T. Sjostrand, Comput.Phys. Commun. , 74 (1994).[11] E. Barberio et al. [Heavy Flavor Averaging Group],arXiv:0704.3575 (hep-ex) (2007).[12] A. L. Kagan and M. Neubert, Phys. Rev. D , 094012(1998).[13] O. Buchm¨uller and H. Fl¨acher, Phys. Rev. D , 073008(2006)., 073008(2006).