BABAR-PUB-13/015SLAC-PUB-15947

Measurements of Direct CP Asymmetries in B → Xsγ decaysusing Sum of Exclusive Decays

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

E. GraugesUniversitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain

A. Palanoab

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, M. J. Lee, and G. LynchLawrence 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

C. Hearty, T. S. Mattison, J. A. McKenna, and R. Y. SoUniversity of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1

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

V. E. Blinovac, A. R. Buzykaeva, V. P. Druzhininab, V. B. Golubevab, E. A. Kravchenkoab, A. P. Onuchinac,

S. I. Serednyakovab, Yu. I. Skovpenab, E. P. Solodovab, K. Yu. Todyshevab, and A. N. Yushkova

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090a,Novosibirsk State University, Novosibirsk 630090b,

Novosibirsk State Technical University, Novosibirsk 630092c, Russia

D. Kirkby, A. J. Lankford, and M. MandelkernUniversity of California at Irvine, Irvine, California 92697, USA

B. Dey, J. W. Gary, and O. LongUniversity of California at Riverside, Riverside, California 92521, USA

C. Campagnari, M. Franco Sevilla, 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, W. S. Lockman, B. A. Schumm, and A. SeidenUniversity of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA

D. S. Chao, C. H. Cheng, B. Echenard, K. T. Flood, D. G. Hitlin, P. Ongmongkolkul, and F. C. PorterCalifornia Institute of Technology, Pasadena, California 91125, USA

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

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

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R. Ayad∗ and W. H. TokiColorado State University, Fort Collins, Colorado 80523, USA

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

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

S. PlayferUniversity of Edinburgh, Edinburgh EH9 3JZ, United Kingdom

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

I. Garziaab, E. Luppiab, L. Piemontesea, and V. Santoroa

INFN Sezione di Ferraraa; Dipartimento di Fisica e Scienze della Terra, Universita di Ferrarab, I-44122 Ferrara, Italy

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

S. Martellotti, 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

M. MoriiHarvard University, Cambridge, Massachusetts 02138, USA

A. Adametz and U. UwerUniversitat Heidelberg, Physikalisches Institut, D-69120 Heidelberg, Germany

H. M. LackerHumboldt-Universitat zu Berlin, Institut fur Physik, D-12489 Berlin, Germany

P. D. DaunceyImperial College London, London, SW7 2AZ, United Kingdom

U. MallikUniversity of Iowa, Iowa City, Iowa 52242, USA

C. Chen, J. Cochran, W. T. Meyer, and S. PrellIowa State University, Ames, Iowa 50011-3160, USA

H. Ahmed and H. AhmedJazan University, Jazan 22822, Kingdom of Saudi Arabia

A. V. GritsanJohns Hopkins University, Baltimore, Maryland 21218, USA

N. Arnaud, M. Davier, D. Derkach, G. Grosdidier, F. Le Diberder,

A. M. Lutz, B. Malaescu,‡ P. Roudeau, A. Stocchi, and G. WormserLaboratoire de l’Accelerateur Lineaire, IN2P3/CNRS et Universite Paris-Sud 11,

Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France

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D. J. Lange and D. M. WrightLawrence Livermore National Laboratory, Livermore, California 94550, USA

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, and R. SaccoQueen 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

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

A. G. Denig, M. Fritsch, W. Gradl, K. Griessinger, A. Hafner, E. Prencipe, and K. R. SchubertJohannes Gutenberg-Universitat Mainz, Institut fur Kernphysik, D-55099 Mainz, Germany

R. J. Barlow§ and G. D. LaffertyUniversity of Manchester, Manchester M13 9PL, United Kingdom

E. Behn, R. Cenci, B. Hamilton, A. Jawahery, and D. A. RobertsUniversity of Maryland, College Park, Maryland 20742, USA

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

R. Cheaib, P. M. Patel,¶ and S. H. RobertsonMcGill University, Montreal, Quebec, Canada H3A 2T8

P. Biassoniab, N. Neria, and F. Palomboab

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

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

M. Simard 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

M. Martinelli and G. RavenNIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands

C. P. Jessop and J. M. LoSeccoUniversity 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, M. Margoniab, M. Morandina, M. Posoccoa, M. Rotondoa, G. Simia, F. Simonettoab, and R. Stroiliab

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

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

G. Calderini, J. Chauveau, 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. Manonia, S. Pacettiab, and A. Rossia

INFN Sezione di Perugiaa; Dipartimento di Fisica, Universita di Perugiab, I-06123 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, J. Olsen, and A. J. S. SmithPrinceton University, Princeton, New Jersey 08544, USA

R. Facciniab, F. Ferrarottoa, F. Ferroniab, M. Gasperoab, L. Li Gioia, 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, C. Voß, 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

F. Anulli,‡‡ D. Aston, D. J. Bard, J. F. Benitez, C. Cartaro, M. R. Convery, J. Dorfan, G. P. Dubois-Felsmann,

W. Dunwoodie, M. Ebert, R. C. Field, B. G. Fulsom, A. M. Gabareen, M. T. Graham, C. Hast,

W. R. Innes, P. Kim, M. L. Kocian, D. W. G. S. Leith, P. Lewis, D. Lindemann, B. Lindquist, S. Luitz,

V. Luth, H. L. Lynch, D. B. MacFarlane, D. R. Muller, H. Neal, S. Nelson, 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, W. F. Wang, W. J. Wisniewski, M. Wittgen, D. H. Wright, H. W. Wulsin, 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, P. R. Burchat, T. S. Miyashita, and E. M. T. PuccioStanford 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

S. M. SpanierUniversity of Tennessee, Knoxville, Tennessee 37996, USA

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

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

F. Bianchiab, F. De Moriab, A. Filippia, D. Gambaab, and S. Zambitoab

INFN Sezione di Torinoa; Dipartimento di Fisica, 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

F. Martinez-Vidal, A. Oyanguren, and P. Villanueva-PerezIFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain

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

M. J. Lewczuk, T. Lueck, 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, and T. E. LathamDepartment 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 measure the direct CP violation asymmetry, ACP , in B → Xsγ and the isospin difference of theasymmetry, ∆ACP , using 429 fb−1 of data collected at Υ (4S) resonance with the BABAR detectorat the PEP-II asymmetric-energy e+e− storage rings operating at the SLAC National AcceleratorLaboratory. B mesons are reconstructed from 10 charged B final states and 6 neutral B final states.We find ACP = +(1.7 ± 1.9 ± 1.0)%, which is in agreement with the Standard Model predictionand provides an improvement on the world average. Moreover, we report the first measurement ofthe difference between ACP for charged and neutral decay modes, ∆ACP = +(5.0 ± 3.9 ± 1.5)%.Using the value of ∆ACP , we also provide 68% and 90% confidence intervals on the imaginarypart of the ratio of the Wilson coefficients corresponding to the chromo-magnetic dipole and theelectromagnetic dipole transitions.

PACS numbers: 13.20.-v,13.25.Hw

I. INTRODUCTION

The flavor-changing neutral current decay B → Xsγ,whereXs represents any hadronic system with one unit ofstrangeness, is highly suppressed in the standard model(SM), as is the direct CP asymmetry,

ACP =ΓB0/B−→Xsγ − ΓB0/B+→Xsγ

ΓB0/B−→Xsγ + ΓB0/B+→Xsγ, (1)

∗Now at the University of Tabuk, Tabuk 71491, Saudi Arabia†Also with Universita di Perugia, Dipartimento di Fisica, Perugia,Italy‡Now at Laboratoire de Physique Nuclaire et de Hautes Energies,IN2P3/CNRS, Paris, France§Now at the University of Huddersfield, Huddersfield HD1 3DH,UK¶Deceased∗∗Now at University of South Alabama, Mobile, Alabama 36688,USA††Also with Universita di Sassari, Sassari, Italy‡‡Also with INFN Sezione di Roma, Roma, Italy§§Now at Universidad Tecnica Federico Santa Maria, Valparaiso,Chile 2390123

due to the combination of CKM and GIM suppres-sions [1]. New physics effects could enhance the asym-metry to a level as large as 15% [2][3][4]. The currentworld average of ACP based on the results from BABAR [5],Belle [6] and CLEO [7] is −(0.8± 2.9)%[8]. The SM pre-diction for the asymmetry was found in a recent studyto be long-distance-dominated [9] and to be in the range−0.6% < ASMCP < 2.8%.

Benzke et al. [9] predict a difference in direct CP asym-metry for charged and neutral B mesons:

∆AXsγ = AB±→Xsγ −AB0/B0→Xsγ , (2)

which suggests a new test of the SM. The difference,∆AXsγ , arises from an interference term in ACP thatdepends on the charge of the spectator quark. The mag-nitude of ∆AXsγ is proportional to Im (C8g/C7γ) whereC7γ and C8g are Wilson coefficients corresponding to theelectromagnetic dipole and the chromo-magnetic dipoletransitions, respectively. The two coefficients are real inthe SM; therefore ∆AXsγ=0. New physics contributionsfrom the enhancement of the CP -violating phase or of themagnitude of the two Wilson coefficients [1][10], or theintroduction of new operators [11] could enhance ∆AXsγto be as large as 10% [9]. Unlike C7γ , C8g currently does

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not have a strong experimental constraint [12]. Thus ameasurement of ∆AXsγ together with the existing con-straints on C7γ can provide a constraint on C8g.

Experimental studies of B → Xsγ are approached inone of two ways. The inclusive approach relies entirelyon observation of the high-energy photon from these de-cays without reconstruction of the hadronic system Xs.By ignoring the Xs system, this approach is sensitive tothe full b → sγ decay rate and is robust against finalstate fragmentation effects. The semi-inclusive approachreconstructs the Xs system in as many specific final stateconfigurations as practical. This approach provides ad-ditional information, but since not all Xs final states canbe reconstructed without excessive background, fragmen-tation model-dependence is introduced if semi-inclusivemeasurements are extrapolated to the complete ensem-ble of B → Xsγ decays. BABAR has recently publishedresults on the B → Xsγ branching fraction and photonspectrum for both approaches [13][14]. The inclusive ap-proach has also been used to search for direct CP viola-tion, but since the inclusive method does not distinguishhadronic final states, decays due to b → dγ transitionsare included.

We report herein a measurement of ACP and thefirst measurement of ∆AXsγ using the semi-inclusive ap-proach with the full BABAR data set. We reconstruct 38exclusive B-decay modes, listed in Table I, but for usein this analysis a subset of 16 modes (marked with anasterisk in Table I) is chosen for which high statisticalsignificance is achieved. Also, for this analysis, modesmust be flavor self-tagging (i.e., the bottomness can bedetermined from the reconstructed final state). The 16modes include ten charged B and six neutral B decays.After all event selection criteria are applied, the massof the hadronic Xs system (mXs) in this measurementcovers the range of about 0.6 to 2.0 GeV/c2. The up-per edge of this range approximately corresponds to aminimum photon energy in the B rest frame of 2.3 GeV.For B → Xsγ decays with 0.6 < mXs < 2.0 GeV/c2, the10 charged B modes used account for about 52% of allB+ → Xsγ decays and the six neutral modes account forabout 34% of all neutral B0 → Xsγ decays [15]. In thisanalysis it is assumed that ACP and ∆AXsγ are indepen-dent of final state fragmentation. That is, it is assumedthat ACP and ∆AXsγ are independent of the specific Xs

final states used for this analysis and independent of themXs distribution of the selected events.

II. ANALYSIS OVERVIEW

With data from the BABAR detector (Section III), wereconstructedB candidates from various final states (Sec-tion IV). We then trained two multivariate classifiers(Section V): one to separate correctly reconstructed Bdecays from mis-reconstructed events and the other toreject the continuum background, e+e− → qq, whereq = u, d, s, c. The output of the first classifier is used

TABLE I: The 38 final states we reconstruct in this analysis.Charge conjugation is implied. The 16 final states used in theCP measurement are marked with an asterisk.

# Final State # Final State

1* B+ → KSπ+γ 20 B0 → KSπ

+π−π+π−γ2* B+ → K+π0γ 21 B0 → K+π+π−π−π0γ3* B0 → K+π−γ 22 B0 → KSπ

+π−π0π0γ4 B0 → KSπ

0γ 23* B+ → K+ηγ5* B+ → K+π+π−γ 24 B0 → KSηγ6* B+ → KSπ

+π0γ 25 B+ → KSηπ+γ

7* B+ → K+π0π0γ 26 B+ → K+ηπ0γ8 B0 → KSπ

+π−γ 27* B0 → K+ηπ−γ9* B0 → K+π−π0γ 28 B0 → KSηπ

0γ10 B0 → KSπ

0π0γ 29 B+ → K+ηπ+π−γ11* B+ → KSπ

+π−π+γ 30 B+ → KSηπ+π0γ

12* B+ → K+π+π−π0γ 31 B0 → KSηπ+π−γ

13* B+ → KSπ+π0π0γ 32 B0 → K+ηπ−π0γ

14* B0 → K+π+π−π−γ 33* B+ → K+K−K+γ15 B0 → KSπ

0π+π−γ 34 B0 → K+K−KSγ16* B0 → K+π−π0π0γ 35 B+ → K+K−KSπ

+γ17 B+ → K+π+π−π+π−γ 36 B+ → K+K−K+π0γ18 B+ → KSπ

+π−π+π0γ 37* B0 → K+K−K+π−γ19 B+ → K+π+π−π0π0γ 38 B0 → K+K−KSπ

0γ

to select the best B candidate for each event. Then,the outputs from both classifiers are used to reject back-grounds. We use the remaining events to determine theasymmetries.

We use identical procedures to extract three asymme-tries: the asymmetries of charged and neutral B mesons,and of the combined sample, and the difference, ∆AXsγ .The bottomness of the B meson is determined by thecharge of the kaon for B0 and B0, and by the total chargeof the reconstructed B meson for B+ and B−.

We can decompose ACP into three components:

ACP = Apeak −Adet +D (3)

where Apeak is the fitted asymmetry of the events in thepeak of the mES distribution (Section VI), Adet is thedetector asymmetry due to the difference in K+ and K−

efficiency (Section VII), and D is the bias due to peakingbackground contamination (Section VIII). In this anal-ysis we establish upper bounds on the magnitude of D,and then treat those as systematic errors.

III. DETECTOR AND DATA

We use a data sample of 429 fb−1 [16] collected at theΥ (4S) resonance,

√s = 10.58 GeV/c2, with the BABAR

detector at the PEP-II asymetric-energy B factory atthe SLAC National Accelerator Laboratory. The datacorresponds to 471× 106 produced BB pairs.

The BABAR detector and its operation are describedin detail elsewhere [17][18]. The charges and momenta

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of charged particles are measured by a five-layer double-sided silicon strip detector (SVT) and a 40-layer driftchamber (DCH) operated in a 1.5 T solenoidal field.Charged K/π separation is achieved using dE/dx infor-mation from the trackers and by a detector of internallyreflected Cherenkov light (DIRC), which measures theangle of the Cherenkov radiation cone. An electromag-netic calorimeter (EMC) consisting of an array of CsI(Tl)crystals measures the energy of photons and electrons.

We use a Monte Carlo (MC) simulation based on Evt-Gen [19] to optimize the event selection criteria. Wemodel the background as e+e− → qq, e+e− → τ+τ−

and BB. We generate signal B → Xsγ with a uniformphoton spectrum and then weight signal MC events sothat the photon spectrum matches the kinematic-schememodel [20] with parameter values consistent with the pre-vious BABAR B → Xsγ photon spectrum analysis (mb =4.65 GeV/c2 and µ2

π = 0.20 GeV2) [21]. We use JET-SET [22] as the fragmentation model and GEANT4 [23]to simulate the detector response.

IV. B RECONSTRUCTION

We reconstructed B meson candidates from 38 finalstates listed in Table I. The 16 modes marked with anasterisk (*) in Table I are used in the CP measurement.The other final states are either not flavor-specific finalstates or are low in yield. We reconstruct the unusedmodes in order to veto them after selecting the best can-didate. In total, we use 10 charged B final states and 6neutral B final states in the ACP measurement. These fi-nal states are the same as those used in a previous BABARanalysis [5].

Charged kaons and pions are selected from tracksclassified with an error-correcting output code algo-rithm [18][25]. The classification uses SVT, DIRC, DCH,and EMC information. The kaon particle identification(PID) algorithm has approximately 90% efficiency anda pion-as-kaon misidentification rate of about 1%. Pionidentification is roughly 99% efficient with a 15% kaon-as-pion misidentification rate.

Neutral kaons are reconstructed from the decay K0S →

π+π−. The invariant mass of the two oppositely chargedtracks is required to be between 489 and 507 MeV. Theflight distance of the K0

S must be greater than 0.2 cmfrom the interaction point. The flight significance (de-fined as the flight distance divided by the uncertainty inthe flight distance) of the K0

S must be greater than three.K0L and K0

S → π0π0 decays are not reconstructed for thisanalysis.

The neutral π0 and η mesons are reconstructed fromtwo photons. We require each photon to have energy ofat least 30 MeV for π0 and at least 50 MeV for η. Theinvariant mass of the two photons must be in the rangeof [115,150] MeV for π0 candidates and in the range of[470,620] MeV for η candidates. Only π0 and η candi-dates with momentum greater than 200 MeV are used.

We do not reconstruct η → π+π−π0 decays explicitly, butsome are included in final states that contain π+π−π0.

Each event is required to have at least one photon withenergy 1.6 < E∗γ < 3.0 GeV, where the asterisk denotesvariables measured in the Υ (4S) center-of-mass (CM)frame. These photons are used as the primary photonin reconstructing B mesons. Such a photon must have alateral moment [26] less than 0.8 and the nearest EMCcluster must be at least 15 cm away. The angle of thephoton momentum with respect to the beam axis mustsatisfy −0.74 < cos θ < 0.93.

The invariant mass of Xs(all daughters of the B can-didate excluding the primary photon) must satisfy 0.6 <mXs < 3.2 GeV/c2. The Xs candidate is then com-bined with the primary photon to form a B candidate,which is required to have an energy-substituted mass

mES =√s/4− p∗B

2, where p∗B is the momentum of B

in the CM frame, greater than 5.24 GeV/c2. We alsorequire the difference between half of the beam totalenergy and the energy of the reconstructed B in theCM frame, |∆E| = |E∗beam/2 − E∗B |, to be less than0.15 GeV. The angle between the thrust axis of the restof the event(ROE) and the primary photon must satisfy| cos θ∗Tγ | < 0.85.

V. EVENT AND CANDIDATE SELECTION

There are three main sources of background. Thedominant source is continuum background, e+e− → qq.These events are more jet-like than the e+e− → Υ (4S)→BB. Thus, event shape variables provide discrimination.The continuum mES distribution does not peak at the Bmeson mass. The second background source is BB de-cays to final states other than Xsγ; hereafter we refer tothese as generic BB decays. The third source is cross-feed background which comes from actual B → Xsγ de-cays in which we fail to reconstruct the B in the correctfinal state. The e+e− → τ+τ− contribution is negligiblysmall.

We first place a preliminary selection on the ratio ofangular moments [27][28], L12/L10 < 0.46 to reduce thenumber of the continuum background events. This ratiomeasures the jettiness of the event. Since the mass ofthe B meson is close to half the mass of the Υ (4S), thekinetic energy that the B meson can have is less thanthat available to e+e− → light quark pairs. Therefore,the signal peaks at a lower value of L12/L10 than doesthe continuum background.

The B meson reconstruction typically yields multipleB candidates per event. To select the best candidate,we train a random forest classifier [29] based on ∆E/σE ,where σE is the uncertainty on the B candidate energy,the thrust of the reconstructed B candidate [30], π0 mo-mentum, the invariant mass of the Xs system, and thezeroth and fifth Fox-Wolfram moments [31]. This SignalSelecting Classifier (SSC) is trained on a large MC event

8

sample to separate correctly reconstructed B → Xsγ de-cays from mis-reconstructed ones. For each event, thecandidate with the maximum classifier output is chosenas the best candidate. This is the main difference froma previous BABAR analysis [5] which chose the event withthe smallest |∆E| as the best candidate. This methodincreases the efficiency by a factor of approximately twofor the same misidentification rate.

It should be emphasized that the best candidate selec-tion procedure also selects final states in which the bot-tomness of the B cannot be deduced from the final decayproducts (flavor-ambiguous final states). After selectingthe best candidate, we keep only events in which the bestcandidate is reconstructed with the final states markedwith an asterisk in Table I. This removes events which areflavor-ambiguous final states from the ACP measurement.Furthermore, because of the way the SSC was trainedto discriminate against mis-reconstructed B candidates,SSC also provides good discriminating power against thegeneric BB background.

To further reduce the continuum background we buildanother random forest classifier, the Background Reject-ing Classifier (BRC), using the following variables:

• π0 score: the output from a random forest classi-fier using the invariant mass of the primary pho-ton with all other photons in the event and the en-ergy of the other photons, which is trained to rejecthigh-energy photons that come from the π0 → γγdecays.

• Momentum flow [32] in 10◦ increments about thereconstructed B direction.

• Zeroth, first and second order angular momentsalong the primary photon axis computed in the CMframe of the ROE.

• The ratio of the second and the zeroth angular mo-ments described above.

• | cos θ∗B |: the cosine of the angle between the Bflight direction and the beam axis in the CM frame.

• | cos θ∗T |: the cosine of the angle between the thrustaxis of the B candidate and the thrust axis of theROE in the CM frame.

• | cos θ∗Tγ |: the cosine of the angle between the pri-mary photon momentum and the thrust axis of theROE in the CM frame.

To obtain the best sensitivity, we simultaneously op-timize, using MC samples, the SSC and BRC selectionsin four Xs mass ranges ([0.6-1.1], [1.1-2.0], [2.0-2.4], and[2.4-2.8] GeV/c2), maximizing S/

√S +B, where S is the

number of expected signal events and B is the numberof expected background events with mES > 5.27 GeV/c2.The optimized selection values are the same for both Band B.

VI. FITTED ASYMMETRY

For each B flavor, we describe the mES distributionwith a sum of an ARGUS distribution [33][34] and a two-piece normal distribution (G) [35]:

PDFb(mES) =Tcont

2(1 +Acont)ARGUS(mES; cb, χb, pb)+

Tpeak2

(1 +Apeak)G(mES;µb, σbL, σbR), (4)

PDFb(mES) =Tcont

2(1−Acont)ARGUS(mES; cb, χb, pb)+

Tpeak2

(1−Apeak)G(mES;µb, σbL, σbR) (5)

where

Tcont = nbcont + nbcont, (6)

Tpeak = nbpeak + nbpeak (7)

are the total number of events of both flavors describedby the ARGUS distribution and the two-piece normaldistribution and

Acont =nbcont − nbcontnbcont + nbcont

, (8)

Apeak =nbpeak − nbpeaknbpeak + nbpeak

(9)

are the flavor asymmetries of events described by the AR-GUS distribution and the two-piece normal distribution,respectively. The superscript b and b indicate whetherthe parameter belongs to the b-quark containing B me-son (B0 and B−) distribution or the b-quark containingB meson distribution (B0 and B+), respectively. In par-

ticular, nbpeak and nbpeak are the numbers of events in the

peaking (Gaussian) part of the distribution. Similarly,

nbcont and nbcont are the numbers of events in the contin-uum (ARGUS) part of the distribution. The shape pa-rameters for ARGUS distributions are the curvatures (χb

and χb), the powers (pb and pb), and the endpoint ener-

gies (cb and cb). The shape parameters for two-piece nor-

mal distribution are the peak locations (µb and µb), the

left-side widths (σbL and σbL), and the right-side widths

(σbR and σbR).It should be noted that Apeak is related to ACP de-

fined in Eq. 1 by the relation shown in Eq. 3. To obtainApeak, we perform a simultaneous binned likelihood fit for

both B flavors. The ARGUS endpoint energies cb and cb

are fixed at 5.29 GeV/c2. All other shape parameters forthe ARGUS distributions and the two-piece normal dis-tributions are allowed to float separately. Fig. 1 showsthe mES distributions, along with fitted shapes. Table IIsummarizes the results for Apeak.

9

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FIG. 1: The mES distributions along with fitted probability density functions, for: B0 and B− sample (top left), B0 and B+

sample (top right), B− sample (middle left), B+ sample (middle right), B0 sample (bottom left), and B0 sample (bottom right).Data are shown as points with error bars. The ARGUS distribution component, two-piece normal distribution component andthe total probability density function are shown with dotted lines, dashed lines, and solid lines, respectively.

VII. DETECTOR ASYMMETRY

Part of the difference between Apeak and ACP comesfrom the difference in K+ and K− efficiencies. The K+

PID efficiency is slightly higher than the K− PID effi-ciency; the difference also varies with the track momen-tum. The cause of this difference is the fact that thecross-section for K−-hadron interactions is higher thanthat for K+-hadron interactions. This translates to theK− having a greater probability of interacting before itreaches the DIRC, thereby lowering the quality of theK− Cherenkov cone angle measurement, which affectsthe PID performance.

The first order correction to ACP from K+/K− effi-

ciency differences is given by

Adet =νb − νbνb + νb

(10)

where νb and νb are the number of events for each flavorafter all selections, assuming the underlying physics hasno flavor asymmetry.

We use a sideband region (mES < 5.27 GeV/c2) whichconsists mostly of e+e− → qq events to measure Adet.We do not expect a flavor asymmetry in the underlyingphysics in this region. We count the number of eventsin the sideband region for each flavor and use Eq. 10 todetermine Asideband

det .However, since the difference in K− and K+ hadron

cross section depends on K momentum and the Kmomentum distributions of the side band region and

10

the peaking region (mES > 5.27 GeV/c2) slightly differ,Asideband

det and Adet need not be identical. The variation ofAdet for any K momentum distribution can be boundedby the maximum and minimum value of the ratio betweenK+ and K− efficiencies (εK+/εK−) in the K momentumrange of interest:

1

2

(minpK

εK+

εK−− 1

)≤ Adet ≤

1

2

(maxpK

εK+

εK−− 1

). (11)

The final states with no charged K can be consideredas having a special value of pK where εK+ and εK− areidentical.

We use highly pure samples of charged kaons from thedecay D∗+ → D0π+, followed by D0 → K−π+, and itscharge conjugate, to measure the ratio of efficiencies forK+ and K−. We find that the deviation from unity ofεK+/εK− varies from 0 to 2.5% depending on the trackmomentum.

The bound given in Eq. 11 implies that the distributionof the differences between any two detector asymmetrieschosen uniformly within the bound is a triangle distribu-tion with the base width of 2.5%.

The standard deviation of such a distribution is2.5%/

√24 = 0.5%. We use Asideband

det as the central valuefor Adet and this standard deviation as the systematic un-certainty associated with detector asymmetry. Table IIlists the results of Adet.

VIII. PEAKING BACKGROUNDCONTAMINATION

Our fitting procedure does not explicitly separate thecross-feed and generic BB backgrounds from the signal.Both backgrounds have small peaking components, asshown in Figure 2, so the yield for each flavor used incalculating Apeak contains both signal and these peakingbackgrounds. We quantify the effect and include it as asource of systematic uncertainty.

Let the number of signal events for b-quark contain-ing B mesons and b-quark containing B mesons be nband nb and the number of contaminating peaking back-ground events misreconstructed as b-quark containing Bmesons and b-quark containing B mesons be βb and βb.The difference between Apeak and ACP due to peakingbackground contamination is given by:

D = R× δA, (12)

where R is the ratio of the number of peaking backgroundevents to the total number of events in the peaking re-gion, given by

R =βb + βb

nb + nb + βb + βb, (13)

and δA is the difference between the true signal asym-metry and the peaking background asymmetry, given by

δA =nb − nbnb + nb

−βb − βbβb + βb

. (14)

We estimate R using the MC sample. We use the sumof the expected number of cross-feed background eventsand expected number of generic BB events with mES >5.27 GeV/c2 for each flavor as βb and βb. We obtain nband nb from the total number of expected signal eventsfor each flavor.

Since the peaking background events are from mis-reconstructed B mesons, the mES distribution of thepeaking background has a very long tail. It resemblesthe sum of an ARGUS distribution and a small peakingpart. The fit to the total mES distribution is the sum ofa two-piece normal distribution and an ARGUS distri-bution. A significant portion of peaking background isabsorbed into the ARGUS distribution causing our esti-mate of R to be overestimated.

We bound the difference in asymmetry, δA, us-ing the range of values predicted by the SM:−0.6 % < ASMCP < 2.8 %. This gives |δA| < 3.4%.This value is also very conservative, since the amountof cross-feed background in the signal region is approxi-mately five times the amount of generic BB background,and we expect the flavor asymmetry of the cross-feedevents to be similar to that of the signal.

We validate our estimates by extracting Apeak frompseudo MC experiments with varying amounts of cross-feed background asymmetry and observe the shift fromthe true value of the signal asymmetry. The shift is abouthalf the value estimated using the method described; weuse the more conservative estimate as our systematic un-certainty. For ACP of the charged and neutral B, thisestimate is conservative enough to cover a large possi-ble range of |∆AXsγ | < 15% that could shift the value

of Apeak via the cross-feed of the type B0 → Xsγ mis-

reconstructed as B− → Xsγ (B0 ⇒ B−) and B− → Xsγmisreconstructed as B0 → Xsγ (B− ⇒ B0). Table IIIlists the values of R, δA and D.

IX. RESULTS

Following Eq. 3, we subtract Adet from Apeak to obtainACP . The statistical uncertainties are added in quadra-ture. Systematic uncertainties from peaking backgroundcontamination and from detector asymmetry are addedin quadrature to obtain the total systematic uncertainty.We find

ACP = +(1.7± 1.9± 1.0)% (15)

where the uncertainties are statistical and systematic, re-spectively. Compared to the current world average, thestatistical uncertainty is smaller by approximately 1/3due to the improved rejection of peaking background de-scribed above.

The measurement of ACP is based on the ratio of thenumber of events, but ACP is defined as the ratio ofwidths. In order to make the two definitions of ACPequivalent, we make two assumptions. First, we assume

11

TABLE II: Summary of ACP results along with Adet and systematic uncertainties due to peaking background contamination(D) for each B sample. The ACP ’s in the last column are calculated using Eq. 3. The first error is statistical, the second (ifpresent) is systematics.

B Sample Apeak D Adet ACP

All B +(0.33± 1.87)% ±0.88% −(1.40± 0.49± 0.51)% +(1.73± 1.93± 1.02)%Charged B +(3.14± 2.86)% ±0.80% −(1.09± 0.67± 0.51)% +(4.23± 2.93± 0.95)%Neutral B −(2.48± 2.47)% ±0.97% −(1.74± 0.72± 0.51)% −(0.74± 2.57± 1.10)%

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FIG. 2: The contributions to the total mES distributions (gray lines with triangle markers) from the signal B → Xsγ (graylines with circle markers), the continuum background (gray lines with x markers), the cross-feed background (gray lines withno marker), and the generic BB background (solid black lines) according to the MC sample for: B0 and B− sample (top left),B0 and B+ sample (top right), B− sample (middle left), B+ sample (middle right), B0 sample (bottom left), and B0 sample(bottom right).

that there are as many decaying B0 mesons as decay-ing B0 mesons, i.e. there is no CP violation in mixing.This has been measured to be at most a few 10−3 forB mesons [8]. Second, since the ratio of the number ofevents is essentially the ratio of the branching fractions

under the first assumption, we assume that the lifetimeof b- and b-containing B mesons are identical so that theratio of the branching fractions is equal to the ratio ofthe decay widths. This is guaranteed if we assume CPTinvariance. The isospin asymmetry has negligible effect

12

TABLE III: Values of R, δA and D.

B Sample R |δA| D

All B 0.26 3.4% ±0.88%Charged B 0.28 3.4% ±0.80%Neutral B 0.24 3.4% ±0.97%

on ACP : The effect from the difference of B0 and B+

lifetime and from ∆AXsγ is suppressed by a factor ofisospin efficiency asymmetry [36], which we find to be onthe order of 2%. The total effect is thus on the order of10−4, which is below our sensitivity.

Using the values of ACP for charged B and neutral Bin Table II, we find

∆AXsγ = +(5.0± 3.9± 1.5)%, (16)

where the uncertainties are statistical and systematic, re-spectively. The statistical and systematic uncertaintieson ∆AXsγ are obtained by summing in quadrature theuncertainties on the charged and neutral ACP measure-ments. The systematic uncertainty for ∆AXsγ is alsovalidated with an alternative method of estimating themultiplicative effects from the peaking background con-tamination on ∆AXsγ taking into account each compo-nent of cross-feed. In particular, the cross-feed of thetype B0 ⇒ B−, B− ⇒ B0 and generic BB produceshifts that are proportional to ∆AXsγ . We use a con-servative value for the peaking background compositionof 2:2:1 (B0 ⇒ B0 : B− ⇒ B0 : Generic BB)and the value of cross-feed contamination ratio R ∼ 1/4.We find the total effect to be conservatively at most14∆AXsγ = 1.3%. The estimate is in agreement withthe quadrature sum of the peaking background contami-nation systematics for charged and neutral B asymmetry,which is

√1.0%2 + 0.8%2 = 1.3%.

In the calculation of ∆AXsγ , we also assume that thefragmentation does not create an additional asymmetry.This is generally assumed in this type of analysis. This isparticularly important for the ∆AXsγ measurement sincethe final states are not all isospin counterparts. With thisassumption, we can use ACP for 10 charged B final statesand ACP for 6 neutral B final states as ACP for chargedB and neutral B, respectively.

Using the formula,

∆AXsγ ' 0.12× Λ78

100 MeVIm (C8g/C7γ) , (17)

given in [9], we can use the measured value of ∆AXsγto determine the 68% and 90% confidence limits (CL) on

Im (C8g/C7γ). The interference amplitude, Λ78, in Eq. 17is only known as a range of possible values,

17 MeV < Λ78 < 190 MeV. (18)

We calculate a quantity called minimum χ2 defined by

minimum χ2 =

minΛ78

[(∆ATh −∆AExp)2

]σ2

, (19)

where ∆ATh is the theoretical prediction of ∆AXsγ for

given Im (C8g/C7γ) and Λ78 using Eq. 17, ∆AExp is themeasured value, σ is uncertainty on the measured value,and the minimum is taken over the range of Λ78 givenin Eq. 18. Figure 3 shows the plot of minimum χ2 ver-sus Im (C8g/C7γ). It has two notable features. First,there is a plateau of minimum χ2 = 0. This is the re-gion of Im (C8g/C7γ) where we can always find a value of

Λ78 within the possible range (Eq. 18) such that ∆ATh

matches exactly ∆AExp. Second, the discontuinity atIm (C8g/C7γ) = 0 comes from the fact that the value

of Λ78 that gives the minimum value is different. WhenIm (C8g/C7γ) is small and positive, we need a large posi-

tive Λ78 to be as close as possible to the measured value,while when Im (C8g/C7γ) is negative, we need a small

positive value of Λ78 to not be too far from the measuredvalue.

2 1 0 1 2 3 4 5 6 7

ImC8g

C7γ

0

1

2

3

4

5

6M

inim

um

χ2

Minimum χ2

68% CL.

90% CL

FIG. 3: The minimum χ2 for given ImC8g

C7γfrom all possible

values of Λ78. 68% and 90% confidence intervals are shownin dark gray and light gray, respectively.

The 68% and 90% confidence limits are then obtainedfrom the ranges of Im (C8g/C7γ), which yield the mini-mum χ2 less than 1 and 4, respectively. We find

0.07 ≤ ImC8g

C7γ≤ 4.48, 68% CL, (20)

−1.64 ≤ ImC8g

C7γ≤ 6.52, 90% CL. (21)

The dependence of minimum χ2 on Im (C8g/C7γ) asshown in Figure 3 is not parabolic, which would be ex-pected from a Gaussian probability. Care must be taken

13

when combining it with other constraints. Since the con-fidence intervals obtained are dominated by the possiblevalues Λ78 at the low end, improvement of limits on Λ78

will narrow the confidence interval. We therefore alsoprovide confidence interval for Im (C8g/C7γ) as the func-

tion of Λ78 in Figure 4.

2 1 0 1 2 3 4 5 6 7

ImC8g

C7γ

17

25

50

75

100

125

150

175

190

Λ78

(MeV

)

68% CL

90% CL

FIG. 4: The 68% and 90% confidence intervals for ImC8g

C7γand

Λ78.

X. SUMMARY

In conclusion, we present a measurement of the di-rect CP violation asymmetry, ACP , in B → Xsγ andthe isospin difference of the asymmetry, ∆AXsγ with 429

fb−1 of data collected at the Υ (4S) resonance with the

BABAR detector. B meson candidates are reconstructedfrom 10 charged B final states and 6 neutral B finalstates. We find ACP = +(1.7±1.9±1.0)%, in agreementwith the SM prediction and with the uncertainty smallerthan that of the current world average. We also reportthe first measurement of ∆AXsγ = +(5.0 ± 3.9 ± 1.5)%,consistent with the SM prediction. Using the value of∆AXsγ , we calculate the 68% and 90% confidence in-tervals for Im (C8g/C7γ) shown in Eqs. 20 and Eq. 21,respectively. The confidence interval can be combinedwith existing constraints on C7γ to provide a constrainton C8g.

XI. ACKNOWLEDGEMENTS

We would like to thank Gil Paz for very useful dis-cussions. We are grateful for the extraordinary con-tributions of our PEP-II colleagues in achieving theexcellent luminosity and machine conditions that havemade this work possible. The success of this projectalso relies critically on the expertise and dedication ofthe computing organizations that support BABAR. Thecollaborating institutions wish to thank SLAC for itssupport and the kind hospitality extended to them.This work is supported by the US Department of En-ergy and National Science Foundation, the Natural Sci-ences and Engineering Research Council (Canada), theCommissariat a l’Energie Atomique and Institut Na-tional de Physique Nucleaire et de Physique des Partic-ules (France), the Bundesministerium fur Bildung undForschung and Deutsche Forschungsgemeinschaft (Ger-many), the Istituto Nazionale di Fisica Nucleare (Italy),the Foundation for Fundamental Research on Matter(The Netherlands), the Research Council of Norway,the Ministry of Education and Science of the RussianFederation, Ministerio de Economıa y Competitividad(Spain), the Science and Technology Facilities Council(United Kingdom), and the Binational Science Founda-tion (U.S.-Israel). Individuals have received support fromthe Marie-Curie IEF program (European Union) and theA. P. Sloan Foundation (USA).

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[30]

Thrust = maxA

N∑i=1

|A · pi|

N∑i=1

√pi · pi

where A is a unit vector, pi are three momenta of thedecay particles of the B candidate.

[31] G. Fox and S. Wolfram, Phys. Rev. Lett. 41, 1581 (1978)[32] The scalar sum of all momenta within a cone of a given

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241, 278 (1990).[34]

ARGUS(x; c, χ, p) =2−pχ2(p+1)

Γ(p+ 1)− Γ(p+ 1, 12χ2)×

x

c2

(1− x2

c2

)pexp

{− 1

2χ2(

1− x2

c2

)}[35]

G(x;µ, σL, σR) =N ×

exp{

(x−µ)2

2σ2L

}if x < µ

exp{

(x−µ)2

2σ2R

}if x ≥ µ

where N is the normalization.[36] The ratio of the difference between charged and neutral

B efficiency to the sum of the two.