Measurement of the semileptonic charge asymmetry in B0 meson mixing with the D0 detector V.M. Abazov,32 B. Abbott,68 B. S. Acharya,26 M. Adams,46 T. Adams,44 G. D. Alexeev,32 G. Alkhazov,36 A. Alton,57,* A. Askew,44 S. Atkins,55 K. Augsten,7 C. Avila,5 F. Badaud,10 L. Bagby,45 B. Baldin,45 D.V. Bandurin,44 S. Banerjee,26 E. Barberis,56 P. Baringer,53 J. F. Bartlett,45 U. Bassler,15 V. Bazterra,46 A. Bean,53 M. Begalli,2 L. Bellantoni,45 S. B. Beri,24 G. Bernardi,14 R. Bernhard,19 I. Bertram,39 M. Besançon,15 R. Beuselinck,40 P. C. Bhat,45 S. Bhatia,59 V. Bhatnagar,24 G. Blazey,47 S. Blessing,44 K. Bloom,60 A. Boehnlein,45 D. Boline,65 E. E. Boos,34 G. Borissov,39 A. Brandt,71 O. Brandt,20 R. Brock,58 A. Bross,45 D. Brown,14 J. Brown,14 X. B. Bu,45 M. Buehler,45 V. Buescher,21 V. Bunichev,34 S. Burdin,39,† C. P. Buszello,38 E. Camacho-Pérez,29 B. C. K. Casey,45 H. Castilla-Valdez,29 S. Caughron,58 S. Chakrabarti,65 D. Chakraborty,47 K.M. Chan,51 A. Chandra,73 E. Chapon,15 G. Chen,53 S. Chevalier-Théry,15 S.W. Cho,28 S. Choi,28 B. Choudhary,25 S. Cihangir,45 D. Claes,60 J. Clutter,53 M. Cooke,45 W. E. Cooper,45 M. Corcoran,73 F. Couderc,15 M.-C. Cousinou,12 A. Croc,15 D. Cutts,70 A. Das,42 G. Davies,40 S. J. de Jong,30,31 E. De La Cruz-Burelo,29 F. Déliot,15 R. Demina,64 D. Denisov,45 S. P. Denisov,35 S. Desai,45 C. Deterre,15 K. DeVaughan,60 H. T. Diehl,45 M. Diesburg,45 P. F. Ding,41 A. Dominguez,60 A. Dubey,25 L. V. Dudko,34 D. Duggan,61 A. Duperrin,12 S. Dutt,24 A. Dyshkant,47 M. Eads,60 D. Edmunds,58 J. Ellison,43 V.D. Elvira,45 Y. Enari,14 H. Evans,49 A. Evdokimov,66 V.N. Evdokimov,35 G. Facini,56 L. Feng,47 T. Ferbel,64 F. Fiedler,21 F. Filthaut,30,31 W. Fisher,58 H. E. Fisk,45 M. Fortner,47 H. Fox,39 S. Fuess,45 A. Garcia-Bellido,64 J. A. Garcı́a-González,29 G.A. Garcı́a-Guerra,29,‡ V. Gavrilov,33 P. Gay,10 W. Geng,12,58 D. Gerbaudo,62 C. E. Gerber,46 Y. Gershtein,61 G. Ginther,45,64 G. Golovanov,32 A. Goussiou,75 P. D. Grannis,65 S. Greder,16 H. Greenlee,45 G. Grenier,17 Ph. Gris,10 J.-F. Grivaz,13 A. Grohsjean,15,§ S. Grünendahl,45 M.W. Grünewald,27 T. Guillemin,13 G. Gutierrez,45 P. Gutierrez,68 J. Haley,56 L. Han,4 K. Harder,41 A. Harel,64 J.M. Hauptman,52 J. Hays,40 T. Head,41 T. Hebbeker,18 D. Hedin,47 H. Hegab,69 A. P. Heinson,43 U. Heintz,70 C. Hensel,20 I. Heredia-De La Cruz,29 K. Herner,57 G. Hesketh,41,{ M.D. Hildreth,51 R. Hirosky,74 T. Hoang,44 J. D. Hobbs,65 B. Hoeneisen,9 J. Hogan,73 M. Hohlfeld,21 I. Howley,71 Z. Hubacek,7,15 V. Hynek,7 I. Iashvili,63 Y. Ilchenko,72 R. Illingworth,45 A. S. Ito,45 S. Jabeen,70 M. Jaffré,13 A. Jayasinghe,68 M. S. Jeong,28 R. Jesik,40 P. Jiang,4 K. Johns,42 E. Johnson,58 M. Johnson,45 A. Jonckheere,45 P. Jonsson,40 J. Joshi,43 A.W. Jung,45 A. Juste,37 E. Kajfasz,12 D. Karmanov,34 P. A. Kasper,45 I. Katsanos,60 R. Kehoe,72 S. Kermiche,12 N. Khalatyan,45 A. Khanov,69 A. Kharchilava,63 Y. N. Kharzheev,32 I. Kiselevich,33 J.M. Kohli,24 A.V. Kozelov,35 J. Kraus,59 A. Kumar,63 A. Kupco,8 T. Kurča,17 V. A. Kuzmin,34 S. Lammers,49 G. Landsberg,70 P. Lebrun,17 H. S. Lee,28 S.W. Lee,52 W.M. Lee,45 X. Lei,42 J. Lellouch,14 D. Li,14 H. Li,11 L. Li,43 Q. Z. Li,45 J. K. Lim,28 D. Lincoln,45 J. Linnemann,58 V.V. Lipaev,35 R. Lipton,45 H. Liu,72 Y. Liu,4 A. Lobodenko,36 M. Lokajicek,8 R. Lopes de Sa,65 H. J. Lubatti,75 R. Luna-Garcia,29,** A. L. Lyon,45 A.K. A. Maciel,1 R. Madar,19 R. Magaña-Villalba,29 S. Malik,60 V. L. Malyshev,32 Y. Maravin,54 J. Martı́nez-Ortega,29 R. McCarthy,65 C. L. McGivern,41 M.M. Meijer,30,31 A. Melnitchouk,45 D. Menezes,47 P. G. Mercadante,3 M. Merkin,34 A. Meyer,18 J. Meyer,20 F. Miconi,16 N.K. Mondal,26 M. Mulhearn,74 E. Nagy,12 M. Naimuddin,25 M. Narain,70 R. Nayyar,42 H. A. Neal,57 J. P. Negret,5 P. Neustroev,36 H. T. Nguyen,74 T. Nunnemann,22 J. Orduna,73 N. Osman,12 J. Osta,51 M. Padilla,43 A. Pal,71 N. Parashar,50 V. Parihar,70 S. K. Park,28 R. Partridge,70,k N. Parua,49 A. Patwa,66 B. Penning,45 M. Perfilov,34 Y. Peters,20 K. Petridis,41 G. Petrillo,64 P. Pétroff,13 M.-A. Pleier,66 P. L.M. Podesta-Lerma,29,†† V.M. Podstavkov,45 A.V. Popov,35 M. Prewitt,73 D. Price,49 N. Prokopenko,35 J. Qian,57 A. Quadt,20 B. Quinn,59 M. S. Rangel,1 K. Ranjan,25 P. N. Ratoff,39 I. Razumov,35 P. Renkel,72 I. Ripp-Baudot,16 F. Rizatdinova,69 M. Rominsky,45 A. Ross,39 C. Royon,15 P. Rubinov,45 R. Ruchti,51 G. Sajot,11 P. Salcido,47 A. Sánchez-Hernández,29 M. P. Sanders,22 A. S. Santos,1,‡‡ G. Savage,45 L. Sawyer,55 T. Scanlon,40 R. D. Schamberger,65 Y. Scheglov,36 H. Schellman,48 C. Schwanenberger,41 R. Schwienhorst,58 J. Sekaric,53 H. Severini,68 E. Shabalina,20 V. Shary,15 S. Shaw,58 A.A. Shchukin,35 R.K. Shivpuri,25 V. Simak,7 P. Skubic,68 P. Slattery,64 D. Smirnov,51 K. J. Smith,63 G. R. Snow,60 J. Snow,67 S. Snyder,66 S. Söldner-Rembold,41 L. Sonnenschein,18 K. Soustruznik,6 J. Stark,11 D. A. Stoyanova,35 M. Strauss,68 L. Suter,41 P. Svoisky,68 M. Titov,15 V. V. Tokmenin,32 Y.-T. Tsai,64 K. Tschann-Grimm,65 D. Tsybychev,65 B. Tuchming,15 C. Tully,62 L. Uvarov,36 S. Uvarov,36 S. Uzunyan,47 R. Van Kooten,49 W.M. van Leeuwen,30 N. Varelas,46 E.W. Varnes,42 I. A. Vasilyev,35 P. Verdier,17 A.Y. Verkheev,32 L. S. Vertogradov,32 M. Verzocchi,45 M. Vesterinen,41 D. Vilanova,15 P. Vokac,7 H.D. Wahl,44 M.H. L. S. Wang,45 J. Warchol,51 G. Watts,75 M. Wayne,51 J. Weichert,21 L. Welty-Rieger,48 A. White,71 D. Wicke,23 M.R. J. Williams,39 G.W. Wilson,53 M. Wobisch,55 D. R. Wood,56 T. R. Wyatt,41 Y. Xie,45 R. Yamada,45 S. Yang,4 T. Yasuda,45 Y. A. Yatsunenko,32 W. Ye,65 Z. Ye,45 H. Yin,45 K. Yip,66 S.W. Youn,45 J.M. Yu,57 J. Zennamo,63 T. Zhao,75 T. G. Zhao,41 B. Zhou,57 J. Zhu,57 M. Zielinski,64 D. Zieminska,49 and L. Zivkovic70 PHYSICAL REVIEW D 86, 072009 (2012) 1550-7998=2012=86(7)=072009(20) 072009-1 � 2012 American Physical Society (The D0 Collaboration)* 1LAFEX, Centro Brasileiro de Pesquisas Fı́sicas, Rio de Janeiro, Brazil 2Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil 3Universidade Federal do ABC, Santo André, Brazil 4University of Science and Technology of China, Hefei, People’s Republic of China 5Universidad de los Andes, Bogotá, Colombia 6Charles University, Faculty of Mathematics and Physics, Center for Particle Physics, Prague, Czech Republic 7Czech Technical University in Prague, Prague, Czech Republic 8Center for Particle Physics, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 9Universidad San Francisco de Quito, Quito, Ecuador 10LPC, Université Blaise Pascal, CNRS/IN2P3, Clermont, France 11LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut National Polytechnique de Grenoble, Grenoble, France 12CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 13LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France 14LPNHE, Universités Paris VI and VII, CNRS/IN2P3, Paris, France 15CEA, Irfu, SPP, Saclay, France 16IPHC, Université de Strasbourg, CNRS/IN2P3, Strasbourg, France 17IPNL, Université Lyon 1, CNRS/IN2P3, Villeurbanne, France and Université de Lyon, Lyon, France 18III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany 19Physikalisches Institut, Universität Freiburg, Freiburg, Germany 20II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 21Institut für Physik, Universität Mainz, Mainz, Germany 22Ludwig-Maximilians-Universität München, München, Germany 23Fachbereich Physik, Bergische Universität Wuppertal, Wuppertal, Germany 24Panjab University, Chandigarh, India 25Delhi University, Delhi, India 26Tata Institute of Fundamental Research, Mumbai, India 27University College Dublin, Dublin, Ireland 28Korea Detector Laboratory, Korea University, Seoul, Korea 29CINVESTAV, Mexico City, Mexico 30Nikhef, Science Park, Amsterdam, The Netherlands 31Radboud University Nijmegen, Nijmegen, The Netherlands 32Joint Institute for Nuclear Research, Dubna, Russia 33Institute for Theoretical and Experimental Physics, Moscow, Russia 34Moscow State University, Moscow, Russia 35Institute for High Energy Physics, Protvino, Russia 36Petersburg Nuclear Physics Institute, St. Petersburg, Russia 37Institució Catalana de Recerca i Estudis Avançats (ICREA) and Institut de Fı́sica d’Altes Energies (IFAE), Barcelona, Spain 38Uppsala University, Uppsala, Sweden 39Lancaster University, Lancaster LA1 4YB, United Kingdom 40Imperial College London, London SW7 2AZ, United Kingdom 41The University of Manchester, Manchester M13 9PL, United Kingdom 42University of Arizona, Tucson, Arizona 85721, USA 43University of California Riverside, Riverside, California 92521, USA 44Florida State University, Tallahassee, Florida 32306, USA 45Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA 46University of Illinois at Chicago, Chicago, Illinois 60607, USA 47Northern Illinois University, DeKalb, Illinois 60115, USA 48Northwestern University, Evanston, Illinois 60208, USA 49Indiana University, Bloomington, Indiana 47405, USA 50Purdue University Calumet, Hammond, Indiana 46323, USA 51University of Notre Dame, Notre Dame, Indiana 46556, USA 52Iowa State University, Ames, Iowa 50011, USA 53University of Kansas, Lawrence, Kansas 66045, USA 54Kansas State University, Manhattan, Kansas 66506, USA 55Louisiana Tech University, Ruston, Louisiana 71272, USA V.M. ABAZOV et al. PHYSICAL REVIEW D 86, 072009 (2012) 072009-2 56Northeastern University, Boston, Massachusetts 02115, USA 57University of Michigan, Ann Arbor, Michigan 48109, USA 58Michigan State University, East Lansing, Michigan 48824, USA 59University of Mississippi, University, Mississippi 38677, USA 60University of Nebraska, Lincoln, Nebraska 68588, USA 61Rutgers University, Piscataway, New Jersey 08855, USA 62Princeton University, Princeton, New Jersey 08544, USA 63State University of New York, Buffalo, New York 14260, USA 64University of Rochester, Rochester, New York 14627, USA 65State University of New York, Stony Brook, New York 11794, USA 66Brookhaven National Laboratory, Upton, New York 11973, USA 67Langston University, Langston, Oklahoma 73050, USA 68University of Oklahoma, Norman, Oklahoma 73019, USA 69Oklahoma State University, Stillwater, Oklahoma 74078, USA 70Brown University, Providence, Rhode Island 02912, USA 71University of Texas, Arlington, Texas 76019, USA 72Southern Methodist University, Dallas, Texas 75275, USA 73Rice University, Houston, Texas 77005, USA 74University of Virginia, Charlottesville, Virginia 22904, USA 75University of Washington, Seattle, Washington 98195, USA (Received 30 August 2012; published 26 October 2012) We present a measurement of the semileptonic mixing asymmetry for B0 mesons, adsl, using two independent decay channels: B0 ! �þD�X, with D� ! Kþ����; and B0 ! �þD��X, with D�� ! �D0��, �D0 ! Kþ�� (and charge conjugate processes). We use a data sample corresponding to 10:4 fb�1 of p �p collisions at ffiffiffi s p ¼ 1:96 TeV, collected with the D0 experiment at the Fermilab Tevatron collider. We extract the charge asymmetries in these two channels as a function of the visible proper decay length of the B0 meson, correct for detector-related asymmetries using data-driven methods, and account for dilution from charge-symmetric processes using Monte Carlo simulation. The final measurement combines four signal visible proper decay length regions for each channel, yielding adsl ¼ ½0:68� 0:45ðstatÞ � 0:14ðsystÞ�%. This is the single most precise measurement of this parameter, with uncertainties smaller than the current world average of B factory measurements. DOI: 10.1103/PhysRevD.86.072009 PACS numbers: 11.30.Er, 12.15.Ff, 14.40.Nd I. INTRODUCTION Fundamental asymmetries in the interactions of elemen- tary particles influence the large-scale behavior of the Universe. Of particular interest is the process of baryo- genesis, whereby an initially symmetric system of particles and antiparticles produced by the big bang evolved into the observed matter-dominated universe of the present day. Current theoretical models, building on the work of Sakharov [1], require CP-symmetry violating processes in order for baryogenesis to have occurred in the very early universe [2–5]. As such, studies of asymmetries in particle physics experiments have an influence far beyond the scale that they probe directly. CP symmetry implies that physical processes are invari- ant under the combined parity and charge conjugation trans- formations. The standard model (SM) of particle physics is notCP symmetric as it stands, due to a complex phase in the quark mixing matrix of the weak interaction, which has been measured to be nonzero [6]. While such SM processes introduce some degree ofCP violation (CPV), the effects in the quark sector are far too weak to explain the observed matter dominance of the Universe [7]. Consequently, it is important to search for further non-SM sources of CPV. Studies of neutral B meson oscillations, whereby a neutral meson changes into its own antiparticle via a box-diagram-mediated weak interaction [6], can provide a sensitive probe for such CPV processes. The semilep- tonic mixing asymmetry, defined as aqsl ¼ �ð �B0 q ! B0 q ! ‘þXÞ � �ðB0 q ! �B0 q ! ‘�XÞ �ð �B0 q ! B0 q ! ‘þXÞ þ �ðB0 q ! �B0 q ! ‘�XÞ ; (1) *Visitor from Augustana College, Sioux Falls, SD, USA. †Visitor from The University of Liverpool, Liverpool, United Kingdom. ‡Visitor from UPIITA-IPN, Mexico City, Mexico. §Visitor from DESY, Hamburg, Germany. kVisitor from SLAC, Menlo Park, CA, USA. {Visitor from University College London, London, United Kingdom. **Visitor from Centro de Investigacion en Computacion - IPN, Mexico City, Mexico. ††Visitor from ECFM, Universidad Autonoma de Sinaloa, Culiaćan, Mexico. ‡‡Visitor from Universidade Estadual Paulista, São Paulo, Brazil. MEASUREMENT OF THE SEMILEPTONIC CHARGE . . . PHYSICAL REVIEW D 86, 072009 (2012) 072009-3 http://dx.doi.org/10.1103/PhysRevD.86.072009 allows the effects of any CP-violating processes to be directly observed in terms of the resulting asymmetry of the decay products. Here ‘ denotes a charged lepton of any flavor, and q represents the flavor of the non-b valence quark of the meson. In the standard model, the semileptonic mixing asymmetry is related to the properties of the corresponding B meson system, namely, the mass difference �Mq ¼ MðB0 qHÞ �MðB0 qLÞ, the decay-width difference ��q ¼ �ðB0 qLÞ � �ðB0 qHÞ, and the CP-violating phase �q, by aqsl ¼ j�q 12j jMq 12j sin�q ¼ ��q �Mq tan�q: (2) Here the states B0 qH and B0 qL are the heavy and light mass eigenstates of the B meson system, which differ from the flavor eigenstates. Mq 12 and �q 12 are, respectively, the off- diagonal elements of the mass and decay matrices [6]. The standard model predictions [8] for both assl and adsl are very small: adsl ¼ ð�0:041� 0:006Þ%; (3) assl ¼ ð0:0019� 0:0003Þ%: (4) These predictions are effectively negligible compared to the current experimental precision. Hence, the measure- ment of any significant deviation from zero is an unambiguous signal of new physics, which could lead to order-of-magnitude enhancements of jadslj [9]. The B0 semileptonic mixing asymmetry, adsl, has been extensively studied by the B factories operating at the �ð4SÞ resonance, including measurements by the CLEO [10,11], BABAR [12,13], and Belle [14] Collaborations. The current world average of these measurements is [6] adsl ¼ ð�0:05� 0:56Þ%: (5) Additional inclusive measurements from LEP [15–17] and D0 [18] are subject to contamination from B0 s mesons, and the extraction of adsl relies upon assumptions about the contribution from assl. The recent evidence for a nonzero dimuon charge asym- metry by the D0 experiment is sensitive to the linear combination of B0 and B0 s mixing asymmetries, with ap- proximately equal contributions from each source [19]. The measurement constrains a band in the ðadsl; asslÞ plane, which is inconsistent with the SM prediction at the 3.9 standard deviation level. By dividing the sample into two components with different relative contributions from B0 and B0 s , the semileptonic asymmetries are measured to be adslð��Þ ¼ ð�0:12� 0:52Þ%; (6) asslð��Þ ¼ ð�1:81� 1:06Þ%; (7) where the measurements have a correlation coefficient of �0:799. The above extraction assumes that any new source of CPVentering the dimuon asymmetry does so through B mixing. Alternative hypotheses, for example, new sources of dimuons from non-SM processes, cannot be excluded. Recent searches for CPV in B0 s ! J=c� decays from the D0 [20], CDF [21], and LHCb [22] Collaborations find agreement of the CP-violating phase �s with SM predic- tions. Given the current body of experimental evidence, improved measurements of both adsl and assl are required in order to constrain the possible sources of new physics in B meson mixing and decay [23]. This article describes the measurement of the semilep- tonic mixing asymmetry for B0 d mesons, adsl¼ �ð �B0!B0!‘þDð�Þ�XÞ��ðB0! �B0!‘�Dð�ÞþXÞ �ð �B0!B0!‘þDð�Þ�XÞþ�ðB0! �B0!‘�Dð�ÞþXÞ ; (8) without the use of initial-state flavor tagging. The flavor of the B0 meson at the time of decay is determined by the charge of the muon in the semileptonic decay. Two sepa- rate decay channels are used: (1) B0!�þ�D�X, with D�!Kþ���� (plus charge conjugate process); (2) B0!�þ�D��X, withD�� ! �D0��, �D0 ! Kþ�� (plus charge conjugate process). The two channels are treated separately, with each being used to extract adsl before the final measurements are com- bined. For clarity, the two channels are, respectively, de- noted by �D and �D� throughout this paper, with the appropriate combinations of charges implied. Charges are only explicitly shown when required to describe the asym- metry measurement, or to avoid possible ambiguity. II. ANALYSIS OVERVIEW Experimentally, the semileptonic mixing asymmetry is expressed as adsl ¼ A� ABG Fosc B0 : (9) Here, A is the measured raw asymmetry, defined by A ¼ N�þDð�Þ� � N��Dð�Þþ N�þDð�Þ� þ N��Dð�Þþ � Ndiff Nsum ; (10) where N��Dð�Þ� is the number of reconstructed ��Dð�Þ� signal candidates. The sum is extracted by fitting the total mass distribution, and the difference by fitting the differ- ence of two charge-specific mass distributions. The term ABG accounts for inherent detector-related background (BG) asymmetries, for example, due to the different re- construction efficiencies for positively and negatively charged kaons. The denominator Fosc B0 is defined as the fraction of all �Dð�Þ signal events that arise from decays of B0 mesons after they have oscillated. It is required to account for Dð�Þ mesons arising from direct B0 decays, V.M. ABAZOV et al. PHYSICAL REVIEW D 86, 072009 (2012) 072009-4 decays of B� and B0 s mesons, or direct hadronization from c �c quarks. All background asymmetries are extracted using data-driven methods, while Monte Carlo (MC) simulation is used to determine the fraction of B0 mesons that have undergone mixing prior to decay. This measurement assumes that the initial production of B0- �B0 is symmetric, and that there is no asymmetry in the decays of unmixed B0 or �B0 mesons (that would imply CPT violation), and no direct CP asymmetry in the semi- leptonic decays to charm states, or the decay of these charm states to the indicated products. With these assump- tions, any observed semileptonic asymmetry would have to arise due to the mixing process. The B0 meson has a mixing frequency �Md ¼ 0:507� 0:004 ps�1, of comparable scale to the lifetime �ðB0Þ ¼ 1:518� 0:007 ps [6]. Hence the fraction of oscillated B0 mesons is a strong function of the measured decay time. The proper decay length ct for a particle is given by ct ¼ L �� ¼ L � cM p ¼ Lxy � cMpT ; (11) where � and � are the usual relativistic kinematic quanti- ties; p, M and L are, respectively, the particle momentum, mass and decay length in the detector reference frame. The best precision is obtained by using the transverse quantities Lxy and pT , due to finer instrumentation for tracking in this plane. The transverse decay length Lxy is the projection of the vector pointing from the production to the decay vertex of the B meson onto the B meson transverse momentum direction. It can be negative due to the limited spatial resolution of the detector. For semileptonic decays, the missing energy due to the undetected neutrino results in the measured transverse momentum being underestimated with respect to the actual value. Hence the measured variable is actually the visible proper decay length (VPDL): VPDL ðBÞ ¼ LxyðBÞ � cMðBÞ pTð�DÞ : (12) The dilution Fosc B0 is a very strong function of this variable, increasing monotonically with VPDL. To exploit this be- havior, the measurements of all asymmetries are performed separately in bins of VPDLðB0Þ. These measurements are then combined for each channel to obtain the final mea- surement. The selected VPDLðB0Þ bins are defined by the edges f�0:10; 0:00; 0:02; 0:05; 0:10; 0:20; 0:60g cm. The �Dð�Þ signal contributions outside of this range are found to be negligible. The first two bins in VPDL have negli- gible contributions from oscillated B0 mesons, and are not included in the final adsl measurement. They represent a control region in which the measured raw asymmetry should be dominated by the background contribution, i.e., A� ABG � 0. There can be significant ( 1%) asymmetries due to detector effects. In particular, the material and detector elements that a particle traverses are different for positively and negatively charged particles, as a result of the specific orientation of magnetic fields in the central tracking and muon detectors. In this analysis, such effects are removed to first order by reweighting all events, such that the total weight of events collected in each of the four (solenoid, toroid) magnet polarity configurations is the same (see Sec. III). Remaining asymmetries are of order 0.1%, and are corrected using data-driven methods. To avoid possible experimental bias, the central values of the raw asymmetries were hidden until all analysis methods were finalized. Initially this was achieved by randomly assigning all candidate charges; later, to allow the background asymmetries to be examined, the true charges were used, but unknown offsets were added to the raw charge asymmetries. The D0 detector is briefly described in Sec. III, highlight- ing those features most relevant for this measurement. The event selection and raw asymmetry extraction are described in Secs. IV, V, and VI. The determination of background asymmetries is described in Sec. VII, while Sec. VIII covers the extraction of the oscillated B0 fraction. The results and conclusions are presented in Secs. IX, X, XI, and XII. III. THE D0 DETECTOR The D0 detector has been described in detail elsewhere [24]. The most important detector components for this measurement are the central tracking system, the muon detectors, and the magnets. The central tracking system comprises a silicon micro- strip tracker (SMT) and a central fiber tracker (CFT), both located within a 2 T superconducting solenoidal magnet. The SMT has � 800 000 individual strips, with typical pitch of 50–80 �m, and a design optimized for tracking and vertexing capability at pseudorapidities of j�j< 2:5, where � ¼ � ln½tanð =2Þ� and is the polar angle with respect to the beam axis. The system has a six-barrel longitudinal structure, each with a set of four layers ar- ranged axially around the beam pipe, and interspersed with 16 radial disks. In the spring of 2006, a ‘‘Layer 0’’ barrel detector with 12 288 additional strips was installed [25], and two radial disks were removed. This upgrade defines the chronological boundary between the two running peri- ods, denoted Run IIa and Run IIb. The sensors of Layer 0 are located at a radius of 17 mm from the colliding beams. The CFT has eight thin coaxial barrels, each supporting two doublets of overlapping scintillating fibers of 0.835-mm diameter, one doublet being parallel to the collision axis, and the other alternating by �3 relative to the axis. Light signals are transferred via clear fibers to solid-state photon counters that have � 80% quantum efficiency. A muon system resides beyond the calorimeter, and consists of a layer of tracking detectors and scintillation trigger counters before a 1.8-T toroidal magnet, followed by two similar layers after the toroid. Tracking at j�j< 1 relies on 10-cm wide drift tubes, while 1-cm minidrift tubes are used at 1< j�j< 2. MEASUREMENT OF THE SEMILEPTONIC CHARGE . . . PHYSICAL REVIEW D 86, 072009 (2012) 072009-5 The polarities of both the solenoidal and toroidal mag- nets were regularly reversed during data acquisition, ap- proximately every two weeks, resulting in almost equal beam exposure in each of the four polarity configurations. This feature of the D0 detector is crucial in reducing detector-related asymmetries, for example, due to the dif- ferent trajectories of positive and negative muons as they traverse the magnetic fields in the detector. IV. EVENT SELECTION This analysis uses data collected by the D0 detector from 2002 to 2011, corresponding to approximately 10:4 fb�1 of integrated luminosity, and representing the full Tevatron Run II sample of p �p collisions at center-of-mass energyffiffiffi s p ¼ 1:96 TeV. Signal candidates are collected using single and dimuon triggers, which may also impose addi- tional criteria. To avoid lifetime-dependent trigger efficien- cies, which are difficult to model in simulation, events that exclusively satisfy muon triggers with track impact- parameter requirements are removed. For both channels, events are considered for selection if they contain a muon candidate with reconstructed track segments both inside and outside the toroid magnet. The muon candidate must be matched to a track in the central tracking system, with at least three hits in both the SMT and CFT. In addition, it must have transverse momentum pT > 2 GeV=c, and total momentum p > 3 GeV=c. For events fulfilling these requirements, Dð�Þ� candi- dates are constructed by combining three other tracks associated with the same initial p �p interaction. Each track must satisfy pT > 0:7 GeV=c, and have at least two hits in both the SMT and CFT. The tracks must have a summed charge of magnitude jqj ¼ 1, with an opposite sign to the muon charge. Each of the tracks comprising the like- charge pair is assigned the charged pion mass [6]. The third track, which has the same charge as the muon, is assigned the charged kaon mass [6]. A. �D channel For the D� ! Kþ���� decay (and charge conjugate process), the three hadron tracks must be consistent with originating at a single common vertex, with a vertex fit to the three tracks satisfying 2ðvertexÞ< 16. These tracks are combined to construct a D� candidate. The resulting D� trajectory must be consistent with forming a common vertex with the muon to reconstruct a B0 candidate. The cosine of the angle DT between the momentum and trajec- tory vectors of the D� meson in the transverse plane must satisfy cosð DT Þ> 0:0; i.e., the two vectors must point to the same hemisphere. The invariant masses must satisfy 1:6< MðD�Þ< 2:1 GeV=c2 and 2:0 0:7 GeV=c and j�ð �D0Þj< 2:0. The invariant mass must lie in the range 1:7 3; (13) where �TðLÞ and �TðLÞ represent the distance and corre- sponding uncertainty of the transverse (longitudinal) dis- placement between the two vertices. The D�� candidate is then combined with the muon, to form a B0 candidate. The muon, �D0, and �D� trajectories must be consistent with arising from a common vertex, and the invariant mass of the B0 must satisfy 2:0 0; (ii) j�ðKÞj< 0:7 and j�ðKÞj> 0:7; (iii) pðKÞ< 3:2 GeV=c and pðKÞ> 3:2 GeV=c; (iv) a chronological division corresponding to early and late data collection; (v) �ðVPDLÞ< 40 �m and �ðVPDLÞ> 40 �m. The results are summarized in Table IX. In all cases, the measured values of adsl are statistically consistent with each other, despite some samples having significantly different background corrections. ) (cm)0VPDL(B -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 (% ) sld a -6 -4 -2 0 2 4 6 -1D0 Run II, 10.4 fb sl da Mean value ) (cm)0VPDL(B -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 (% ) sld a -6 -4 -2 0 2 4 6 -1D0 Run II, 10.4 fb sl da Mean value FIG. 7 (color online). Final measurements of the semileptonic asymmetry adsl, in bins of VPDL(B0), for both channels. The cross- hatched bands show the mean values (and their total uncertainties) determined for each channel separately. (a) �D channel; (b) �D� channel. TABLE VIII. Individual measurements of ðA� ABGÞ and adsl in each of the six VPDLðB0Þ bins, for both channels in this analysis. For each entry, the first uncertainty is statistical, the second systematic, with all correlations taken into account. Also shown are the weights wðijÞ used to combine the eight separate measurements, normalized to unity. Bin 1 Bin 2 Bin 3 Bin 4 Bin 5 Bin 6 �0:10–0:00 cm 0:00–0:02 cm 0:02–0:05 cm 0:05–0:10 cm 0:10–0:20 cm 0:20–0:60 cm �D Channel A� ABG (%) 1:48� 1:28� 0:20 �0:20� 0:35� 0:09 �0:07� 0:32� 0:10 0:26� 0:33� 0:09 0:23� 0:41� 0:07 �0:05� 0:89� 0:14 adsl (%) Not used �1:29� 5:68� 1:69 1:25� 1:61� 0:43 0:44� 0:79� 0:14 �0:07� 1:36� 0:21 weight wðijÞ=PijwðijÞ Not used 0.006 0.072 0.309 0.105 �D� Channel A� ABG (%) 0:64� 0:67� 0:14 �0:07� 0:31� 0:07 �0:23� 0:31� 0:08 0:20� 0:34� 0:09 0:93� 0:44� 0:10 �0:63� 0:99� 0:11 adsl (%) Not used �3:79� 5:00� 1:27 0:87� 1:45� 0:39 1:63� 0:78� 0:17 �0:89� 1:39� 0:15 weight wðijÞ=PijwðijÞ Not used 0.007 0.088 0.311 0.102 MEASUREMENT OF THE SEMILEPTONIC CHARGE . . . PHYSICAL REVIEW D 86, 072009 (2012) 072009-17 In addition, the measurement is repeated using only events that satisfy a single muon trigger. This corresponds to approximately 90% of the total sample. The resulting adsl value for these events is consistent with the nominal value, taking into account the correlation between the samples. The fraction of events from mixed B0 decays, Fosc B0 , is a strong function of the visible proper decay length of the reconstructed B0 candidate. Hence any nonzero value of adsl will lead to a VPDL dependence on the background- subtracted asymmetry ðA� ABGÞ [see Eq. (6)]. Figure 8 shows this dependence for both channels, with the Fosc B0 � adsl distribution superimposed on the plot for comparison, us- ing the final adsl measurement from the two channel combi- nation. The two distributions are statistically consistent, indicating that the VPDL dependence of the observed background-subtracted asymmetry is consistent with the hypothesis that it originates from the mixing of B0 mesons. The 2 quantifying this agreement between the ðA� ABGÞ and Fosc B0 � adsl distributions is 2.3 (4.5) for the �Dð�Þ chan- nel, compared to 2.7 (6.9) under the SM assumption for adsl. For this test, the statistical and systematic uncertainties are combined in quadrature. The same data can be used to validate the adsl measure- ment using an alternative method, in which the distribution of ðA� ABGÞ versus VPDLðB0Þ is fitted to the function: FðVPDLÞ ¼ Aconst þ Fosc B0 ðVPDLÞ � adsl; (40) where adsl and Aconst are the two free parameters. The constant asymmetry term allows for a contribution from possible additional background sources of asymmetry that have not been considered in this analysis. For this study we neglect any uncertainties on Fosc B0 . The results are as fol- lows: adsl ¼ ð0:51� 0:86Þ% ð�D channelÞ; (41) adsl ¼ ð1:25� 0:87Þ% ð�D� channelÞ: (42) These values are consistent with those from the full analy- sis method. The uncertainties are larger as a result of the additional parameter in the fit. The constant asymmetry parameter converges to values consistent with zero for both channels: Aconst ¼ ð�0:03� 0:23Þ% ð�D channelÞ; (43) Aconst ¼ ð�0:09� 0:21Þ% ð�D� channelÞ; (44) demonstrating that any possible residual background asymmetries not accounted for are small, as expected. ) (cm)0VPDL(B -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 A sy m m et ry ( % ) -2 -1 0 1 2 3 -1D0 Run II, 10.4 fb BGA - A sl d a×osc 0BF ) (cm)0VPDL(B -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 A sy m m et ry ( % ) -2 -1 0 1 2 3 -1D0 Run II, 10.4 fb BGA - A sl d a×osc 0BF FIG. 8 (color online). Final measurements of the background corrected asymmetry, in bins of VPDLðB0Þ, for both channels. The points show the observed asymmetry, with the solid lines showing Fosc B0 � adsl. Any asymmetry caused by mixing should exhibit a characteristic turn-on shape as the fraction of oscillated B0 mesons increases. (a) �D channel; (b) �D� channel. TABLE IX. Results of the analysis cross-checks, in which the data are divided into pairs of orthogonal and independent sub- sets, and the measurements of adsl repeated for each sample. The uncertainties shown here are the sum in quadrature of the statistical and systematic components. adsl (%) Subsample requirement �D channel �D� channel Comb. Nominal result 0:43� 0:65 0:92� 0:64 0:68� 0:47 �ð�Þ< 0 0:38� 0:88 0:60� 0:88 0:49� 0:63 �ð�Þ> 0 0:53� 0:91 1:21� 0:88 0:88� 0:64 j�ðKÞj< 0:7 0:48� 0:95 �0:39� 1:14 0:04� 0:77 j�ðKÞj> 0:7 0:36� 0:85 1:17� 0:86 0:76� 0:62 pðKÞ< 3:2 GeV=c 0:02� 0:87 �0:30� 1:42 �0:14� 0:85 pðKÞ> 3:2 GeV=c 1:11� 0:92 1:00� 0:79 1:05� 0:62 �ðVPDLÞ< 40 �m 0:22� 0:84 0:18� 0:95 0:20� 0:65 �ðVPDLÞ> 40 �m 0:76� 0:95 0:98� 1:01 0:87� 0:70 First half data 0:82� 0:89 1:39� 0:88 1:11� 0:67 Second half data 0:19� 0:86 �0:30� 1:02 �0:06� 0:68 V.M. ABAZOV et al. PHYSICAL REVIEW D 86, 072009 (2012) 072009-18 XI. COMBINATIONS WITH OTHER MEASUREMENTS This measurement of adsl can be combined with the existing world average from the B factories [6]. We use a simple weighted average, assuming that the two measure- ments are fully independent. The total uncertainty on the result presented in this article is �0:47%, obtained from the addition in quadrature of statistical and systematic uncertainties. The normalized weights are then 0.59 (D0) and 0.41 (WA). We obtain adsl ¼ ð0:38� 0:36Þ%: (45) This number can in turn be combined with the recent assl measurement [31], and the two-dimensional constraints on ðadsl; asslÞ from the D0 measurement of the dimuon charge asymmetry Ab sl [19]. The full two-dimensional fit yields the following values: adslðcombÞ ¼ ð0:07� 0:27Þ%; (46) asslðcombÞ ¼ ð�1:67� 0:54Þ%; (47) where the two parameters have a correlation coefficient of �0:46. The results are shown in Fig. 9(a), with the two- dimensional contours overlaid on the four constraints from the input measurements. The fit returns a 2 of 2.0 for 2 degrees of freedom. The p value of the combination with respect to the SM point is 0.0037, corresponding to an inconsistency at the 2.9 standard deviation level. Using only the D0 measurements of adsl, a s sl, and Ab sl, we obtain the following values: adslðcombÞ ¼ ð0:10� 0:30Þ%; (48) asslðcombÞ ¼ ð�1:70� 0:56Þ%; (49) with a correlation coefficient of�0:50. The 2 of this fit is 2.9, and the standard model p value is 0.0036, correspond- ing to a 2.9 standard deviation effect. Figure 9(b) shows the two-dimensional contours from this combination. XII. CONCLUSIONS We have performed a measurement of the semileptonic mixing asymmetry from B0 decays, adsl, using B0 ! �þDð�Þ�X decays in two independent channels. We obtain adsl ¼ ½0:68� 0:45ðstatÞ � 0:14ðsystÞ�%, which is consis- tent with the SM prediction of ð�0:041� 0:006Þ%. The resulting precision is dominated by limited statistics in the signal channel, and is better than the current world-average precision obtained by combining results from the B facto- ries [Eq. (4)]. The background asymmetries are determined using data-driven methods in dedicated decay channels. The most important background is from differences in the reconstruction efficiencies for positively and negatively charged kaons, which is of order 1%. The use of simulation is limited to measuring the relatively small ð 10%–20%Þ fraction of signal events which do not arise from B0 decay, and modeling the oscillation of B0 mesons. sl da -0.04 -0.02 0 0.02 sls a -0.04 -0.02 0 0.02 sl sD0 a sl dNew WA a ) 68% C.L. >120 (IPsl bA ) 68% C.L. <120 (IPsl bA Combination Standard Model sl da -0.04 -0.02 0 0.02 sls a -0.04 -0.02 0 0.02 sl sD0 a sl dD0 a ) 68% C.L. >120 (IPsl bA ) 68% C.L. <120 (IPsl bA Combination Standard Model FIG. 9 (color online). Combination of measurements of adsl (D0 and existing world average from B factories [6]), assl (D0 [31]), and the two impact-parameter-binned constraints from the same-charge dimuon asymmetry Ab sl (D0 [19]). The bands represent the �1 standard deviation uncertainties on each measurement. The ellipses represent the 1, 2, 3, and 4 standard deviation two-dimensional confidence level regions of the combination. (a) Using a combination of D0 and B factory average for adsl; (b) Using the D0 value for adsl. MEASUREMENT OF THE SEMILEPTONIC CHARGE . . . PHYSICAL REVIEW D 86, 072009 (2012) 072009-19 ACKNOWLEDGMENTS We thank the staffs at Fermilab and collaborating insti- tutions, and acknowledge support from the DOE and NSF (USA); CEA and CNRS/IN2P3 (France); MON, Rosatom, and RFBR (Russia); CNPq, FAPERJ, FAPESP, and FUNDUNESP (Brazil); DAE and DST (India); Colciencias (Colombia); CONACyT (Mexico); NRF (Korea); FOM (The Netherlands); STFC and the Royal Society (United Kingdom); MSMT and GACR (Czech Republic); BMBF and DFG (Germany) ; SFI (Ireland); The Swedish Research Council (Sweden); and CAS and CNSF (China). [1] A. D. Sakharov, Pis’ma Zh. Eksp. Teor. Fiz. 5, 32 (1967) [Sov. Phys. Usp. 34, 392 (1991)]. [2] M. S. Carena, J.M. Moreno, M. Quiros, M. Seco, and C. E.M. Wagner, Nucl. Phys. B599, 158 (2001). [3] W. S. Hou, Chin. J. Phys. (Taipei) 47, 134 (2009). [4] S. Tulin and P. Winslow, Phys. Rev. D 84, 034013 (2011). [5] J.M. Cline, K. Kainulainen, and M. Trott, J. High Energy Phys. 11 (2011) 089. [6] J. Beringer et al. (Particle Data Group), Phys. Rev. D 86, 010001 (2012); http://www.slac.stanford.edu/xorg/hfag/ osc/spring_2012/. [7] P. Huet and E. Sather, Phys. Rev. D 51, 379 (1995). [8] A. Lenz and U. Nierste, J. High Energy Phys. 06 (2007) 072; Recent update arXiv:1102.4274. [9] A. Lenz, U. Nierste, J. Charles, S. Descotes-Genon, A. Jantsch, C. Kaufhold, H. Lacker, S. Monteil, V. Niess, and S. T’Jampens, Phys. Rev. D 83, 036004 (2011). [10] B. H. Behrens et al. (CLEO Collaboration), Phys. Lett. B 490, 36 (2000). [11] D. E. Jaffe et al. (CLEO Collaboration), Phys. Rev. Lett. 86, 5000 (2001). [12] B. Aubert et al. (BABAR Collaboration), Phys. Rev. Lett. 92, 181801 (2004). [13] B. Aubert et al. (BABAR Collaboration), Phys. Rev. Lett. 96, 251802 (2006). [14] E. Nakano et al. (Belle Collaboration), Phys. Rev. D 73, 112002 (2006). [15] K. Ackerstaff et al. (OPAL Collaboration), Z. Phys. C 76, 401 (1997). [16] R. Barate et al. (ALEPH Collaboration), Eur. Phys. J. C 20, 431 (2001). [17] G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 12, 609 (2000). [18] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. D 74, 092001 (2006). [19] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. D 84, 052007 (2011). [20] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. D 85, 032006 (2012). [21] T. Aaltonen et al. (CDF Collaboration), Phys. Rev. D 85, 072002 (2012); arXiv:1208.2967 [Phys. Rev. Lett. (to be published)]. [22] R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 108, 101803 (2012). [23] A. Lenz, U. Nierste, J. Charles, S. Descotes-Genon, H. Lacker, S. Monteil, V. Niess, and S. T’Jampens, Phys. Rev. D 86, 033008 (2012). [24] V.M. Abazov et al. (D0 Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 565, 463 (2006). [25] R. Angstadt et al. (D0 Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 622, 298 (2010). [26] G. Borisov, Nucl. Instrum. Methods Phys. Res., Sect. A 417, 384 (1998). [27] T. Sjöstrand, S. Mrenna, and P. Z. Skands, J. High Energy Phys. 05 (2006) 026. [28] D. J. Lange, Nucl. Instrum. Methods Phys. Res., Sect. A 462, 152 (2001). [29] A. Hoecker et al., Proc. Sci., ACAT2007 (2007) 040. [30] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. D 82, 032001 (2010). [31] V.M. Abazov et al. (D0 Collaboration), arXiv:1207.1769v1. V.M. ABAZOV et al. PHYSICAL REVIEW D 86, 072009 (2012) 072009-20 http://dx.doi.org/10.1070/PU1991v034n05ABEH002497 http://dx.doi.org/10.1016/S0550-3213(01)00032-3 http://dx.doi.org/10.1103/PhysRevD.84.034013 http://dx.doi.org/10.1007/JHEP11(2011)089 http://dx.doi.org/10.1007/JHEP11(2011)089 http://dx.doi.org/10.1103/PhysRevD.86.010001 http://dx.doi.org/10.1103/PhysRevD.86.010001 http://www.slac.stanford.edu/xorg/hfag/osc/spring_2012/ http://www.slac.stanford.edu/xorg/hfag/osc/spring_2012/ http://dx.doi.org/10.1103/PhysRevD.51.379 http://dx.doi.org/10.1088/1126-6708/2007/06/072 http://dx.doi.org/10.1088/1126-6708/2007/06/072 http://arXiv.org/abs/1102.4274 http://dx.doi.org/10.1103/PhysRevD.83.036004 http://dx.doi.org/10.1016/S0370-2693(00)00990-4 http://dx.doi.org/10.1016/S0370-2693(00)00990-4 http://dx.doi.org/10.1103/PhysRevLett.86.5000 http://dx.doi.org/10.1103/PhysRevLett.86.5000 http://dx.doi.org/10.1103/PhysRevLett.92.181801 http://dx.doi.org/10.1103/PhysRevLett.92.181801 http://dx.doi.org/10.1103/PhysRevLett.96.251802 http://dx.doi.org/10.1103/PhysRevLett.96.251802 http://dx.doi.org/10.1103/PhysRevD.73.112002 http://dx.doi.org/10.1103/PhysRevD.73.112002 http://dx.doi.org/10.1007/s002880050564 http://dx.doi.org/10.1007/s002880050564 http://dx.doi.org/10.1007/s100520100644 http://dx.doi.org/10.1007/s100520100644 http://dx.doi.org/10.1103/PhysRevD.74.092001 http://dx.doi.org/10.1103/PhysRevD.74.092001 http://dx.doi.org/10.1103/PhysRevD.84.052007 http://dx.doi.org/10.1103/PhysRevD.84.052007 http://dx.doi.org/10.1103/PhysRevD.85.032006 http://dx.doi.org/10.1103/PhysRevD.85.032006 http://dx.doi.org/10.1103/PhysRevD.85.072002 http://dx.doi.org/10.1103/PhysRevD.85.072002 http://arXiv.org/abs/1208.2967 http://dx.doi.org/10.1103/PhysRevLett.108.101803 http://dx.doi.org/10.1103/PhysRevLett.108.101803 http://dx.doi.org/10.1103/PhysRevD.86.033008 http://dx.doi.org/10.1103/PhysRevD.86.033008 http://dx.doi.org/10.1016/j.nima.2006.05.248 http://dx.doi.org/10.1016/j.nima.2006.05.248 http://dx.doi.org/10.1016/j.nima.2010.04.148 http://dx.doi.org/10.1016/j.nima.2010.04.148 http://dx.doi.org/10.1016/S0168-9002(98)00777-3 http://dx.doi.org/10.1016/S0168-9002(98)00777-3 http://dx.doi.org/10.1088/1126-6708/2006/05/026 http://dx.doi.org/10.1088/1126-6708/2006/05/026 http://dx.doi.org/10.1016/S0168-9002(01)00089-4 http://dx.doi.org/10.1016/S0168-9002(01)00089-4 http://dx.doi.org/10.1103/PhysRevD.82.032001 http://dx.doi.org/10.1103/PhysRevD.82.032001 http://arXiv.org/abs/1207.1769v1