Fermilab-Pub-10/114-E

Evidence for an anomalous like-sign dimuon charge asymmetry

V.M. Abazov,36 B. Abbott,74 M. Abolins,63 B.S. Acharya,29 M. Adams,49 T. Adams,47 E. Aguilo,6 G.D. Alexeev,36

G. Alkhazov,40 A. Altona,62 G. Alverson,61 G.A. Alves,2 L.S. Ancu,35 M. Aoki,48 Y. Arnoud,14 M. Arov,58

A. Askew,47 B. Asman,41 O. Atramentov,66 C. Avila,8 J. BackusMayes,81 F. Badaud,13 L. Bagby,48 B. Baldin,48

D.V. Bandurin,47 S. Banerjee,29 E. Barberis,61 A.-F. Barfuss,15 P. Baringer,56 J. Barreto,2 J.F. Bartlett,48

U. Bassler,18 S. Beale,6 A. Bean,56 M. Begalli,3 M. Begel,72 C. Belanger-Champagne,41 L. Bellantoni,48

J.A. Benitez,63 S.B. Beri,27 G. Bernardi,17 R. Bernhard,22 I. Bertram,42 M. Besancon,18 R. Beuselinck,43

V.A. Bezzubov,39 P.C. Bhat,48 V. Bhatnagar,27 G. Blazey,50 S. Blessing,47 K. Bloom,65 A. Boehnlein,48

D. Boline,71 T.A. Bolton,57 E.E. Boos,38 G. Borissov,42 T. Bose,60 A. Brandt,77 R. Brock,63 G. Brooijmans,69

A. Bross,48 D. Brown,19 X.B. Bu,7 D. Buchholz,51 M. Buehler,80 V. Buescher,24 V. Bunichev,38 S. Burdinb,42

T.H. Burnett,81 C.P. Buszello,43 P. Calfayan,25 B. Calpas,15 S. Calvet,16 E. Camacho-Perez,33 J. Cammin,70

M.A. Carrasco-Lizarraga,33 E. Carrera,47 B.C.K. Casey,48 H. Castilla-Valdez,33 S. Chakrabarti,71 D. Chakraborty,50

K.M. Chan,54 A. Chandra,79 G. Chen,56 S. Chevalier-Thery,18 D.K. Cho,76 S.W. Cho,31 S. Choi,32

B. Choudhary,28 T. Christoudias,43 S. Cihangir,48 D. Claes,65 J. Clutter,56 M. Cooke,48 W.E. Cooper,48

M. Corcoran,79 F. Couderc,18 M.-C. Cousinou,15 A. Croc,18 D. Cutts,76 M. Cwiok,30 A. Das,45 G. Davies,43

K. De,77 S.J. de Jong,35 E. De La Cruz-Burelo,33 F. Deliot,18 M. Demarteau,48 R. Demina,70 D. Denisov,48

S.P. Denisov,39 S. Desai,48 K. DeVaughan,65 H.T. Diehl,48 M. Diesburg,48 A. Dominguez,65 T. Dorland,81

A. Dubey,28 L.V. Dudko,38 D. Duggan,66 A. Duperrin,15 S. Dutt,27 A. Dyshkant,50 M. Eads,65 D. Edmunds,63

J. Ellison,46 V.D. Elvira,48 Y. Enari,17 S. Eno,59 H. Evans,52 A. Evdokimov,72 V.N. Evdokimov,39 G. Facini,61

A.V. Ferapontov,76 T. Ferbel,59, 70 F. Fiedler,24 F. Filthaut,35 W. Fisher,63 H.E. Fisk,48 M. Fortner,50 H. Fox,42

S. Fuess,48 T. Gadfort,72 A. Garcia-Bellido,70 V. Gavrilov,37 P. Gay,13 W. Geist,19 W. Geng,15, 63 D. Gerbaudo,67

C.E. Gerber,49 Y. Gershtein,66 D. Gillberg,6 G. Ginther,48, 70 G. Golovanov,36 A. Goussiou,81 P.D. Grannis,71

S. Greder,19 H. Greenlee,48 Z.D. Greenwood,58 E.M. Gregores,4 G. Grenier,20 Ph. Gris,13 J.-F. Grivaz,16

A. Grohsjean,18 S. Grunendahl,48 M.W. Grunewald,30 F. Guo,71 J. Guo,71 G. Gutierrez,48 P. Gutierrez,74

A. Haasc,69 P. Haefner,25 S. Hagopian,47 J. Haley,61 I. Hall,63 L. Han,7 K. Harder,44 A. Harel,70 J.M. Hauptman,55

J. Hays,43 T. Hebbeker,21 D. Hedin,50 A.P. Heinson,46 U. Heintz,76 C. Hensel,23 I. Heredia-De La Cruz,33

K. Herner,62 G. Hesketh,61 M.D. Hildreth,54 R. Hirosky,80 T. Hoang,47 J.D. Hobbs,71 B. Hoeneisen,12 M. Hohlfeld,24

S. Hossain,74 P. Houben,34 Y. Hu,71 Z. Hubacek,10 N. Huske,17 V. Hynek,10 I. Iashvili,68 R. Illingworth,48 A.S. Ito,48

S. Jabeen,76 M. Jaffre,16 S. Jain,68 D. Jamin,15 R. Jesik,43 K. Johns,45 C. Johnson,69 M. Johnson,48 D. Johnston,65

A. Jonckheere,48 P. Jonsson,43 A. Justed,48 K. Kaadze,57 E. Kajfasz,15 D. Karmanov,38 P.A. Kasper,48

I. Katsanos,65 R. Kehoe,78 S. Kermiche,15 N. Khalatyan,48 A. Khanov,75 A. Kharchilava,68 Y.N. Kharzheev,36

D. Khatidze,76 M.H. Kirby,51 M. Kirsch,21 J.M. Kohli,27 A.V. Kozelov,39 J. Kraus,63 A. Kumar,68 A. Kupco,11

T. Kurca,20 V.A. Kuzmin,38 J. Kvita,9 S. Lammers,52 G. Landsberg,76 P. Lebrun,20 H.S. Lee,31 W.M. Lee,48

J. Lellouch,17 L. Li,46 Q.Z. Li,48 S.M. Lietti,5 J.K. Lim,31 D. Lincoln,48 J. Linnemann,63 V.V. Lipaev,39 R. Lipton,48

Y. Liu,7 Z. Liu,6 A. Lobodenko,40 M. Lokajicek,11 P. Love,42 H.J. Lubatti,81 R. Luna-Garciae,33 A.L. Lyon,48

A.K.A. Maciel,2 D. Mackin,79 R. Madar,18 R. Magana-Villalba,33 P.K. Mal,45 S. Malik,65 V.L. Malyshev,36

Y. Maravin,57 J. Martınez-Ortega,33 R. McCarthy,71 C.L. McGivern,56 M.M. Meijer,35 A. Melnitchouk,64

D. Menezes,50 P.G. Mercadante,4 M. Merkin,38 A. Meyer,21 J. Meyer,23 N.K. Mondal,29 T. Moulik,56

G.S. Muanza,15 M. Mulhearn,80 E. Nagy,15 M. Naimuddin,28 M. Narain,76 R. Nayyar,28 H.A. Neal,62 J.P. Negret,8

P. Neustroev,40 H. Nilsen,22 S.F. Novaes,5 T. Nunnemann,25 G. Obrant,40 D. Onoprienko,57 J. Orduna,33

N. Osman,43 J. Osta,54 G.J. Otero y Garzon,1 M. Owen,44 M. Padilla,46 M. Pangilinan,76 N. Parashar,53

V. Parihar,76 S.-J. Park,23 S.K. Park,31 J. Parsons,69 R. Partridgec,76 N. Parua,52 A. Patwa,72 B. Penning,48

M. Perfilov,38 K. Peters,44 Y. Peters,44 G. Petrillo,70 P. Petroff,16 R. Piegaia,1 J. Piper,63 M.-A. Pleier,72

P.L.M. Podesta-Lermaf ,33 V.M. Podstavkov,48 M.-E. Pol,2 P. Polozov,37 A.V. Popov,39 M. Prewitt,79 D. Price,52

S. Protopopescu,72 J. Qian,62 A. Quadt,23 B. Quinn,64 M.S. Rangel,16 K. Ranjan,28 P.N. Ratoff,42 I. Razumov,39

P. Renkel,78 P. Rich,44 M. Rijssenbeek,71 I. Ripp-Baudot,19 F. Rizatdinova,75 M. Rominsky,48 C. Royon,18

P. Rubinov,48 R. Ruchti,54 G. Safronov,37 G. Sajot,14 A. Sanchez-Hernandez,33 M.P. Sanders,25 B. Sanghi,48

G. Savage,48 L. Sawyer,58 T. Scanlon,43 D. Schaile,25 R.D. Schamberger,71 Y. Scheglov,40 H. Schellman,51

T. Schliephake,26 S. Schlobohm,81 C. Schwanenberger,44 R. Schwienhorst,63 J. Sekaric,56 H. Severini,74

E. Shabalina,23 V. Shary,18 A.A. Shchukin,39 R.K. Shivpuri,28 V. Simak,10 V. Sirotenko,48 P. Skubic,74

2

P. Slattery,70 D. Smirnov,54 G.R. Snow,65 J. Snow,73 S. Snyder,72 S. Soldner-Rembold,44 L. Sonnenschein,21

A. Sopczak,42 M. Sosebee,77 K. Soustruznik,9 B. Spurlock,77 J. Stark,14 V. Stolin,37 D.A. Stoyanova,39

M.A. Strang,68 E. Strauss,71 M. Strauss,74 R. Strohmer,25 D. Strom,49 L. Stutte,48 P. Svoisky,35 M. Takahashi,44

A. Tanasijczuk,1 W. Taylor,6 B. Tiller,25 M. Titov,18 V.V. Tokmenin,36 D. Tsybychev,71 B. Tuchming,18 C. Tully,67

P.M. Tuts,69 R. Unalan,63 L. Uvarov,40 S. Uvarov,40 S. Uzunyan,50 R. Van Kooten,52 W.M. van Leeuwen,34

N. Varelas,49 E.W. Varnes,45 I.A. Vasilyev,39 P. Verdier,20 L.S. Vertogradov,36 M. Verzocchi,48 M. Vesterinen,44

D. Vilanova,18 P. Vint,43 P. Vokac,10 H.D. Wahl,47 M.H.L.S. Wang,70 J. Warchol,54 G. Watts,81 M. Wayne,54

G. Weber,24 M. Weberg,48 M. Wetstein,59 A. White,77 D. Wicke,24 M.R.J. Williams,42 G.W. Wilson,56

S.J. Wimpenny,46 M. Wobisch,58 D.R. Wood,61 T.R. Wyatt,44 Y. Xie,48 C. Xu,62 S. Yacoob,51 R. Yamada,48

W.-C. Yang,44 T. Yasuda,48 Y.A. Yatsunenko,36 Z. Ye,48 H. Yin,7 K. Yip,72 H.D. Yoo,76 S.W. Youn,48

J. Yu,77 S. Zelitch,80 T. Zhao,81 B. Zhou,62 J. Zhu,71 M. Zielinski,70 D. Zieminska,52 and L. Zivkovic69

(The D0 Collaboration∗)1Universidad de Buenos Aires, Buenos Aires, Argentina

2LAFEX, Centro Brasileiro de Pesquisas Fısicas, Rio de Janeiro, Brazil3Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil

4Universidade Federal do ABC, Santo Andre, Brazil5Instituto de Fısica Teorica, Universidade Estadual Paulista, Sao Paulo, Brazil

6Simon Fraser University, Vancouver, British Columbia, and York University, Toronto, Ontario, Canada7University of Science and Technology of China, Hefei, People’s Republic of China

8Universidad de los Andes, Bogota, Colombia9Charles University, Faculty of Mathematics and Physics,

Center for Particle Physics, Prague, Czech Republic10Czech Technical University in Prague, Prague, Czech Republic

11Center for Particle Physics, Institute of Physics,Academy of Sciences of the Czech Republic, Prague, Czech Republic

12Universidad San Francisco de Quito, Quito, Ecuador13LPC, Universite Blaise Pascal, CNRS/IN2P3, Clermont, France

14LPSC, Universite Joseph Fourier Grenoble 1, CNRS/IN2P3,Institut National Polytechnique de Grenoble, Grenoble, France

15CPPM, Aix-Marseille Universite, CNRS/IN2P3, Marseille, France16LAL, Universite Paris-Sud, CNRS/IN2P3, Orsay, France

17LPNHE, Universites Paris VI and VII, CNRS/IN2P3, Paris, France18CEA, Irfu, SPP, Saclay, France

19IPHC, Universite de Strasbourg, CNRS/IN2P3, Strasbourg, France20IPNL, Universite Lyon 1, CNRS/IN2P3, Villeurbanne, France and Universite de Lyon, Lyon, France

21III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany22Physikalisches Institut, Universitat Freiburg, Freiburg, Germany

23II. Physikalisches Institut, Georg-August-Universitat Gottingen, Gottingen, Germany24Institut fur Physik, Universitat Mainz, Mainz, Germany

25Ludwig-Maximilians-Universitat Munchen, Munchen, Germany26Fachbereich Physik, Bergische Universitat Wuppertal, Wuppertal, Germany

27Panjab University, Chandigarh, India28Delhi University, Delhi, India

29Tata Institute of Fundamental Research, Mumbai, India30University College Dublin, Dublin, Ireland

31Korea Detector Laboratory, Korea University, Seoul, Korea32SungKyunKwan University, Suwon, Korea

33CINVESTAV, Mexico City, Mexico34FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands

35Radboud University Nijmegen/NIKHEF, Nijmegen, The Netherlands36Joint Institute for Nuclear Research, Dubna, Russia

37Institute for Theoretical and Experimental Physics, Moscow, Russia38Moscow State University, Moscow, Russia

39Institute for High Energy Physics, Protvino, Russia40Petersburg Nuclear Physics Institute, St. Petersburg, Russia

41Stockholm University, Stockholm and Uppsala University, Uppsala, Sweden42Lancaster University, Lancaster LA1 4YB, United Kingdom

43Imperial College London, London SW7 2AZ, United Kingdom44The University of Manchester, Manchester M13 9PL, United Kingdom

45University of Arizona, Tucson, Arizona 85721, USA46University of California Riverside, Riverside, California 92521, USA

3

47Florida State University, Tallahassee, Florida 32306, USA48Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

49University of Illinois at Chicago, Chicago, Illinois 60607, USA50Northern Illinois University, DeKalb, Illinois 60115, USA

51Northwestern University, Evanston, Illinois 60208, USA52Indiana University, Bloomington, Indiana 47405, USA

53Purdue University Calumet, Hammond, Indiana 46323, USA54University of Notre Dame, Notre Dame, Indiana 46556, USA

55Iowa State University, Ames, Iowa 50011, USA56University of Kansas, Lawrence, Kansas 66045, USA

57Kansas State University, Manhattan, Kansas 66506, USA58Louisiana Tech University, Ruston, Louisiana 71272, USA

59University of Maryland, College Park, Maryland 20742, USA60Boston University, Boston, Massachusetts 02215, USA

61Northeastern University, Boston, Massachusetts 02115, USA62University of Michigan, Ann Arbor, Michigan 48109, USA

63Michigan State University, East Lansing, Michigan 48824, USA64University of Mississippi, University, Mississippi 38677, USA

65University of Nebraska, Lincoln, Nebraska 68588, USA66Rutgers University, Piscataway, New Jersey 08855, USA67Princeton University, Princeton, New Jersey 08544, USA

68State University of New York, Buffalo, New York 14260, USA69Columbia University, New York, New York 10027, USA

70University of Rochester, Rochester, New York 14627, USA71State University of New York, Stony Brook, New York 11794, USA

72Brookhaven National Laboratory, Upton, New York 11973, USA73Langston University, Langston, Oklahoma 73050, USA

74University of Oklahoma, Norman, Oklahoma 73019, USA75Oklahoma State University, Stillwater, Oklahoma 74078, USA

76Brown University, Providence, Rhode Island 02912, USA77University of Texas, Arlington, Texas 76019, USA

78Southern Methodist University, Dallas, Texas 75275, USA79Rice University, Houston, Texas 77005, USA

80University of Virginia, Charlottesville, Virginia 22901, USA81University of Washington, Seattle, Washington 98195, USA

(Dated: May 16, 2010)

We measure the charge asymmetry A of like-sign dimuon events in 6.1 fb−1 of pp collisions recordedwith the D0 detector at a center-of-mass energy

√s = 1.96 TeV at the Fermilab Tevatron collider.

From A, we extract the like-sign dimuon charge asymmetry in semileptonic b-hadron decays: Absl =−0.00957± 0.00251 (stat)± 0.00146 (syst). This result differs by 3.2 standard deviations from thestandard model prediction Absl(SM) = (−2.3+0.5

−0.6) × 10−4 and provides first evidence of anomalousCP-violation in the mixing of neutral B mesons.

PACS numbers: 13.25.Hw; 14.40.Nd

I. INTRODUCTION

Studies of particle production and decay under the re-versal of discrete symmetries (charge, parity and timereversal) have yielded considerable insight on the struc-ture of the theories that describe high energy phenomena.Of particular interest is the observation of CP violation,

∗with visitors from a Augustana College, Sioux Falls, SD, USA, b

The University of Liverpool, Liverpool, UK, c SLAC, Menlo Park,CA, USA, d ICREA/IFAE, Barcelona, Spain, e Centro de Inves-tigacion en Computacion - IPN, Mexico City, Mexico, f ECFM,Universidad Autonoma de Sinaloa, Culiacan, Mexico, g and Uni-versitat Bern, Bern, Switzerland.

a phenomenon well established in the K0 and B0d sys-

tems, but not yet observed for the B0s system, where

all CP violation effects are expected to be small in thestandard model (SM) [1] (See [2] and references thereinfor a review of the experimental results and of the theo-retical framework for describing CP violation in neutralmesons decays). The violation of CP symmetry is a nec-essary condition for baryogenesis, the process thought tobe responsible for the matter-antimatter asymmetry ofthe universe [3]. However, the observed CP violation inthe K0 and B0

d systems, consistent with the standardmodel expectation, is not sufficient to explain this asym-metry, suggesting the presence of additional sources ofCP violation, beyond the standard model.

The D0 experiment at the Fermilab Tevatron proton-antiproton (pp) collider, operating at a center-of-mass

4

energy√s = 1.96 TeV, is in a unique position to study

possible effects of CP violation, in particular through thestudy of charge asymmetries in generic final states, giventhat the initial state is CP -symmetric. The high center-of-mass energy provides access to mass states beyond thereach of the B-factories. The periodic reversal of the D0solenoid and toroid polarities results in a cancellationat the first order of most detector-related asymmetries.In this paper we present a measurement of the like-signdimuon charge asymmetry A, defined as

A ≡ N++ −N−−N++ +N−−

, (1)

where N++ and N−− represent, respectively, the numberof events in which the two muons of highest transversemomentum satisfying the kinematic selections have thesame positive or negative charge. After removing the con-tributions from backgrounds and from residual detectoreffects, we observe a net asymmetry that is significantlydifferent from zero.

We interpret this result assuming that the only sourceof this asymmetry is the mixing of neutral B mesons thatdecay semileptonically, and obtain a measurement of theasymmetry Absl defined as

Absl ≡N++b −N−−b

N++b +N−−b

, (2)

where N++b and N−−b represent the number of events

containing two b hadrons decaying semileptonically andproducing two positive or two negative muons, respec-tively. As shown in Appendix A each neutral B0

q meson(q = d, s) contributes a term to this asymmetry given by:

aqsl =∆Γq∆Mq

tanφq, (3)

where φq is the CP -violating phase, and ∆Mq and ∆Γqare the mass and width differences between the eigen-states of the mass matrices of the neutral B0

q mesons.The SM predicts the values φs = 0.0042 ± 0.0014 andφd = −0.096+0.026

−0.038 [1]. These values set the scale forthe expected asymmetries in the semileptonic decays ofB0q mesons that are negligible compared to the present

experimental sensitivity [1]. In the standard model Abslis

Absl(SM) = (−2.3+0.5−0.6)× 10−4, (4)

where the uncertainty is mainly due to experimental mea-surement of the fraction of B0

q mesons produced in ppcollisions at the Tevatron, and of the parameters control-ling the mixing of neutral B mesons. The B0

d semilep-tonic charge asymmetry, which constrains the phase φd,has been measured at e+e− colliders [2], and the mostprecise results reported by the BaBar and Belle Collab-orations, given in Refs. [4, 5], are in agreement with theSM prediction. Extensions of the SM could produce ad-ditional contributions to the Feynman box diagrams re-sponsible for B0

q mixing and other corrections that can

provide larger values of φq [6–9]. Measurements of Abslor φq that differ significantly from the SM expectationswould indicate the presence of new physics.

The asymmetry Absl is also equal to the charge asym-metry absl of semileptonic decays of b hadrons to muonsof “wrong charge” (i.e. a muon charge opposite to thecharge of the original b quark) induced through B0

q B0q

oscillations [10]:

absl ≡Γ(B → µ+X)− Γ(B → µ−X)

Γ(B → µ+X) + Γ(B → µ−X)= Absl. (5)

We extract Absl from two observables. The first is thelike-sign dimuon charge asymmetry A of Eq. (1), and thesecond observable is the inclusive muon charge asymme-try a defined as

a ≡ n+ − n−n+ + n−

, (6)

where n+ and n− correspond to the number of detectedpositive and negative muons, respectively.

At the Fermilab Tevatron collider, b quarks are pro-duced mainly in bb pairs. The signal for the asymme-try A is composed of like-sign dimuon events, with onemuon arising from direct semileptonic b-hadron decayb→ µ−X [11], and the other muon resulting from B0

q B0q

oscillation, followed by the direct semileptonic B0q me-

son decay B0q → B0

q → µ−X. Consequently the second

muon has the “wrong sign” due to B0q B

0q mixing. For

the asymmetry a, the signal comes from mixing, followedby the semileptonic decay B0

q → B0q → µ−X. The main

backgrounds for these measurements arise from eventswith at least one muon from kaon or pion decay, or fromthe sequential decay of b quarks b → c → µ+X. For theasymmetry a, there is an additional background from di-rect production of c-quarks followed by their semileptonicdecays.

The data used in this analysis were recorded with theD0 detector [12–14] at the Fermilab Tevatron proton-antiproton collider between April 2002 and June 2009and correspond to an integrated luminosity of 6.1 ±0.4 fb−1. The result presented in this Article supersedesour previous measurement [15] based on the initial dataset corresponding to 1 fb−1 of integrated luminosity. Inaddition to the larger data set, the main difference be-tween these two analyses is that almost all quantities inthe present measurement are obtained directly from data,with minimal input from simulation. To avoid any bias,the central value of the asymmetry was extracted fromthe full data set only after all other aspects of the analysisand all systematic uncertainties had been finalized.

The outline of the paper is as follows. In Sec. II, wepresent the strategy of the measurement. The detec-tor and data selections are discussed in Sec. III, and inSec. IV we describe the Monte Carlo simulations usedin this analysis. Sections V-XIII provide further details.Section XIV presents the results, Sec. XV describes con-sistency checks, Sec. XVI compares the obtained result

5

with other existing measurements, and, finally, Sec. XVIIgives the conclusions. Appendices A–E provide addi-tional technical details on aspects of the analysis.

II. MEASUREMENT METHOD

We measure the dimuon charge asymmetry A definedin Eq. (1) and the inclusive muon charge asymmetry a ofEq. (6), starting from a dimuon data sample and an in-clusive muon sample respectively. Background processesand detector asymmetries contribute to these asymme-tries. These contributions are measured directly in dataand used to correct the asymmetries. After applyingthese corrections, the only expected source of residualasymmetry in both the inclusive muon and dimuon sam-ples is from the asymmetry Absl. Simulations are used torelate the residual asymmetries to the asymmetry Absl,and to obtain two independent measurements of Absl.These measurements are combined to take advantage ofthe correlated contributions from backgrounds, and to re-duce the total uncertainties in the determination of Absl.

The source of the asymmetry a has its nominal ori-gin in the semileptonic charge asymmetry of neutral Bmesons, defined in Eq. (5). However, various detectorand material-related processes also contribute to n±. Weclassify all muons into two categories according to theirorigin. The first category, “short”, denoted in the follow-ing as “S”, includes muons from weak decays of b andc quarks and τ leptons, and from electromagnetic de-cays of the short-lived mesons (φ, ω, η, ρ0). The muonsin the second, “long”, category denoted as “L”, comefrom decays of charged kaons and pions and from otherprocesses: charged kaons, pions, and protons not fullyabsorbed by the calorimeter and reaching the muon de-tectors (“punch-through”), and false matches of centraltracks produced by kaons, pions or protons to a tracksegment reconstructed in the muon detector. Thus, theL sample contains only the contribution from long-livedparticles. The total number of muons in the inclusivemuon sample is

n = n+ + n− = nS + nL, (7)

where nS is the number of S muons, and nL is the numberof L muons.

The initial number of observed µ+ (upper signs) or µ−

(lower signs) is

n± ∝ fS(1± aS)(1± δ) + fK(1± aK)

+fπ(1± aπ) + fp(1± ap). (8)

In this expression, the quantity δ is the charge asymme-try related to muon detection and identification, fK isthe fraction of muons from charged kaon decay, punch-through, or false association with a kaon track, and aKis their charge asymmetry. This asymmetry is measureddirectly in data as described in Sec. XI, and therefore,by definition, includes the contribution from δ. The

analogous quantities fπ and fp represent the fractionof muons from charged pion decay, punch-through orfalse muon association with a pion track, and protonpunch-through or false muon association with a protontrack, respectively, while aπ and ap represent the cor-responding charge asymmetries. The fraction fp alsoincludes a contribution from the association of falselyidentified tracks with muons. The quantity fbkg ≡nL/(nS+nL) = fK+fπ+fp is the L background fraction,fS ≡ nS/(nS +nL) = 1−fbkg is the fraction of S muons,and aS is related to the semileptonic charge asymmetryAbsl, as discussed in Sec. XIII. The charge asymmetry acan be expressed in terms of these quantities as

a = fS(aS + δ) + fKaK + fπaπ + fpap, (9)

where, because of the small values of δ and aS , only termsthat depend linearly on the asymmetries are considered.

The most important background term is fKaK , whichmeasures the contribution from kaon decay and punch-through. The asymmetry aK reflects the fact that the in-elastic interaction length of the K+ meson is greater thanthat of the K− meson [2]. This difference arises from ad-ditional hyperon production channels in K−-nucleon re-actions, which are absent for their K+-nucleon analogs.Since the interaction probability of K+ mesons is smaller,they travel further than K− in the detector material,and have a greater chance of decaying to muons, and alarger probability to punch-through the absorber mate-rial thereby mimicking a muon signal. As a result, theasymmetry aK is positive. Since all other asymmetriesare at least a factor of ten smaller than aK , neglecting thequadratic terms in Eq. (9) produces an impact of < 1%on the final result.

In analogy with Eq. (7), the number of like-signdimuon events can be written as

N = N++ +N−− = NSS +NSL +NLL, (10)

where NSS (NLL) is the number of like-sign dimuonevents with two S (L) muons, and, similarly, NSL is thenumber of events with one S and one L muon. A par-ticle producing an L muon can be a kaon, pion or pro-ton, and, correspondingly, we define the numbers Nx

SLwith x = K,π and p. In a similar way, we define Nxy

LLwith x, y = K,π, p. The corresponding fractions, de-fined per like-sign dimuon event, are F xSL ≡ Nx

SL/Nand F xyLL ≡ Nxy

LL/N . We also define FSS ≡ NSS/N ,FSL ≡ NSL/N , and FLL ≡ NLL/N .

The number of observed like-sign dimuon events µ+µ+

(upper signs) or µ−µ− (lower signs) is

N±± ∝ FSS(1±AS)(1±∆)2

+∑

x=K,π,p

F xSL(1±Ax)(1± aS)(1±∆)

+∑

x,y=K,π,

∑

p; y≥xF xyLL(1±Ax)(1±Ay). (11)

The charge asymmetry of NSS events contains the con-tribution from the expected asymmetry AS that we want

6

to measure, and the charge asymmetry ∆ related to thedetection and identification of muons. The asymmetry ofthe NSL events contains the contribution of backgroundasymmetries Ax (x = K,π, p) for one muon, and theasymmetry (1 ± aS)(1 ± ∆) for the other muon. Theasymmetry of NLL events contains the contribution frombackground asymmetries Ax for both muons. By defini-tion, the detection asymmetry ∆ is included in the valuesof AK , Aπ, and Ap.

Keeping only the terms linear in asymmetries, the un-corrected dimuon charge asymmetry defined in Eq. (1)can be expressed as

A ≡ N++ −N−−N++ +N−−

= FSSAS + FSLaS

+(2− Fbkg)∆ + FKAK + FπAπ + FpAp, (12)

where FK = FKSL + FKπLL + FKpLL + 2FKKLL is the totalnumber of muons from charged kaon decay or punch-through per like-sign dimuon event, and the quantitiesFπ and Fp are defined similarly for charged pions andprotons. The background fraction Fbkg is

Fbkg ≡ FK + Fπ + Fp = FSL + 2FLL. (13)

From Eqs. (10) and (13), it follows that

FSS + Fbkg − FLL = 1. (14)

As in Eq. (9), the largest background contribution inEq. (12) is from the term FKAK , and all other terms arefound to be at least a factor of ten smaller. The esti-mated contribution from the neglected quadratic termsin Eq. (12) is ≈ 2× 10−5, which corresponds to ≈ 4% ofthe statistical uncertainty on A.

In the following sections, we determine from data allthe parameters in Eqs. (9) and (12) used to relate themeasured uncorrected asymmetries a and A to the asym-metries aS and AS . The detection charge asymmetry ∆can differ from δ due to differences in the muon trans-verse momentum pT and pseudorapidity η [16] distribu-tions of the like-sign dimuon and inclusive muon datasamples. For the same reason, we expect the fractions fxin Eq. (9) and Fx in Eq. (12) for x = K,π and p to differ.On physics grounds we expect the asymmetries ax andAx to be identical for any particle of given pT and η.

All measurements are performed as a function of themuon pT measured in the central tracker. The rangeof pT values between 1.5 and 25 GeV is divided into fivebins, as shown in Table I. The term fKaK is obtained bythe weighted average of the measured values of f iKa

iK , i =

0, 1, 2, 3, 4, with weights given by the fraction of muonsin a given pT interval, f iµ, in the inclusive muon sample:

fKaK =

4∑

i=0

f iµfiKa

iK . (15)

TABLE I: Fractions of muon candidates in the inclusive muon(f iµ) and in the like-sign dimuon (F iµ, with two entries perevent) samples.

Bin Muon pT range (GeV) f iµ F iµ0 1.5 − 2.5 0.0055 0.04421 2.5 − 4.2 0.1636 0.27342 4.2 − 7.0 0.6587 0.50173 7.0 − 10.0 0.1175 0.12384 10.0 − 25.0 0.0547 0.0569

Similarly, the term FKAK is computed as

FKAK =

4∑

i=0

F iµFiKa

iK , (16)

where F iµ is the fraction of muons in a given pT interval inthe like-sign dimuon sample. Since the kaon asymmetryis determined by the properties of the particle and notthose of the event, we use the same asymmetry aiK for agiven pT interval in both the inclusive muon and the like-sign dimuon sample. We verify in Sec. XV that the finalresult does not depend significantly on muon η, nor uponkinematic properties of events, luminosity or the mass ofthe µµ system. The definition of the muon pT intervalsand the values of f iµ and F iµ are given in Table I. Thesame procedure is applied to all other terms in Eqs. (9)and (12), e.g.,

(2− Fbkg)∆ =

4∑

i=0

F iµ(2− F ibkg)δi. (17)

As in the case of aS , the source of the asymmetry AS isthe charge asymmetry in semileptonic B-meson decays.Thus, two independent measurements of Absl can be per-formed using the inclusive muon and like-sign dimuondata samples. The asymmetry aS is dominated by detec-tor effects, mostly due to the asymmetry arising from thedifferent interaction lengths of charged kaons. However,AS is far more sensitive to the asymmetry Absl becauseof the definition of A in Eq. (1), which has the num-ber of like-sign dimuon events, rather than all dimuonevents in the denominator. Although a weighted averageof these Absl measurements can be made, we take advan-tage of correlations among backgrounds and asymmetriesto further improve the precision of Absl through a linearcombination of A and a. In this combination, which isdiscussed in Sec. XIV, the detector effects and relatedsystematic uncertainties cancel to a large degree, result-ing in an improved measurement of Absl.

III. DETECTOR AND DATA SELECTION

The D0 detector is described in Refs. [12–14]. It con-sists of a magnetic central-tracking system that comprisesa silicon microstrip tracker (SMT) and a central fiber

7

tracker (CFT), both located within a 1.9 T supercon-ducting solenoidal magnet [13]. The SMT has ≈ 800,000individual strips, with a typical pitch of 50−80 µm, and adesign optimized for tracking and vertexing for |η| < 2.5.The system has a six-barrel longitudinal structure, eachwith a set of four layers arranged axially around the beampipe, and interspersed with 16 radial disks. In the springof 2006, a “Layer 0” barrel detector with 12288 addi-tional strips was installed [14], and two radial disks wereremoved. The sensors of Layer 0 are located at a ra-dius of 17 mm from the colliding beams. The CFT haseight thin coaxial barrels, each supporting two doubletsof overlapping scintillating fibers of 0.835 mm diameter,one doublet parallel to the collision axis, and the otheralternating by ±3◦ relative to the axis. Light signals aretransferred via clear fibers to visual light photon counters(VLPCs) that have ≈ 80% quantum efficiency.

The muon system [12] is located beyond the liquidArgon-Uranium calorimeters that surround the centraltracking system, and consists of a layer A of tracking de-tectors and scintillation trigger counters before 1.8 T irontoroids, followed by two similar layers B and C after thetoroids. Tracking for |η| < 1 relies on 10-cm wide drifttubes, while 1-cm minidrift tubes are used for 1 < |η| < 2.

The trigger and data acquisition systems are designedto handle the high instantaneous luminosities. Based oninformation from tracking, calorimetry, and muon sys-tems, the output of the first level of the trigger is used tolimit the rate for accepted events to < 2 kHz. At the nexttrigger stage, with more refined information, the rate isreduced further to < 1 kHz. These first two levels of trig-gering rely mainly on hardware and firmware. The thirdand final level of the trigger, with access to full eventinformation, uses software algorithms and a computingfarm, and reduces the output rate to < 200 Hz, which iswritten to tape.

The single muon and dimuon triggers used in this anal-ysis are based on the information provided by the muondetectors, combined with the tracks reconstructed by thetracking system. The single muon triggers with the low-est pT threshold are prescaled at high instantaneous lu-minosity, have a higher average pT threshold than thedimuon triggers and cover a smaller range of pseudora-pidity than the dimuon triggers.

In this analysis we select events with one or two muons.We therefore first apply track selections, and then requireeither one or two muons.

Track selection: we select tracks with pT in the range1.5 < pT < 25 GeV and |η| < 2.2. The upper limit on thetransverse momentum is applied to suppress the contri-bution of muons from W and Z boson decays. To ensurethat the muon candidate can pass through the detector,including all three layers of the muon system, we requireeither pT > 4.2 GeV or a longitudinal momentum compo-nent |pz| > 6.4 GeV. The selected tracks have to satisfythe following quality requirements: at least 2 axial and 1stereo hits in the SMT, and at least 3 axial and 3 stereohits in the CFT. The primary interaction vertex closest

to this track must contain at least five charged particles.This vertex is determined for each event using all re-constructed tracks. The average position of the collisionpoint in the plane transverse to the beam is measured foreach run and is used as a constraint. The precision of theprimary vertex reconstruction for each event is on aver-age ≈ 20 µm in the transverse plane and ≈ 40 µm alongthe beam direction. The transverse impact parameter ofthe selected track relative to the closest primary vertexmust be < 0.3 cm, with the longitudinal distance fromthe point of closest approach to this vertex < 0.5 cm.

Single muon selection: the selected track must have amatching track segment reconstructed in the muon sys-tem, with at least two hits in the layer A chambers, atleast two hits in the layer B or C chambers, and at leastone scintillator hit associated with the track. The χ2 forthe difference between the track parameters measured inthe central tracker and in the muon system must be lessthan 40 (with 5 d.o.f.); the measured time in at least oneof the scintillators associated with the muon candidatemust be within 5 ns of the expected time. The muonis assigned the charge of the track reconstructed in thecentral tracker. For muon pT < 25 GeV, the fractionof muons with mismeasured charge and their contribu-tion to the asymmetries are found to be negligible. Thescintillator timing and the track impact parameter re-quirements reduce the background from cosmic rays andfrom beam halo to a negligible level.

Dimuon selection: The two highest transverse momen-tum muons in the event must pass all the selections de-scribed above, and be associated to the same interactionvertex, applying the same requirements on the transverseimpact parameter and on the distance of closest approachto the primary vertex along the beam axis used in the sin-gle muon selection. To remove events in which the twomuons originate from the decay of the same b hadron,we require that the invariant mass of the two muons be> 2.8 GeV.

These requirements define the reference selections,which are changed while performing consistency checksof the analysis. Unless stated otherwise all figures, tablesand results in this article refer to these reference selec-tions.

This analysis uses two data samples. The inclusivemuon sample contains all events with at least one muoncandidate passing the muon selection and at least onesingle muon trigger. If an event contains more than onemuon, each muon is included in the inclusive muon sam-ple. Such events constitute about 0.5% of the total in-clusive muon sample. The like-sign dimuon sample con-tains all events with at least two muon candidates ofthe same charge that pass the reference dimuon selectionand at least one dimuon trigger. If more than two muonspass the single muon selection, the two muons with thehighest pT are selected for inclusion in the dimuon sam-ple. Such events comprise ≈ 0.7% of the total like-signdimuon sample.

The polarities of the toroidal and solenoidal magnetic

8

TABLE II: Weights assigned to the events with differentsolenoid and toroid polarities in the inclusive muon and like-sign dimuon samples.

Solenoid Toroid Weight Weightpolarity polarity inclusive muon like-sign dimuon−1 −1 0.895 0.879−1 +1 1.000 1.000+1 −1 0.954 0.961+1 +1 0.939 0.955

0

0.2

0.4

0.6

0.8

0 5 10 15 20 25pT(µ) [GeV]

1/N

dN

/dp T

[GeV

-1]

DØ, 6.1 fb-1

- dimuon sample- inclusive muon sample

FIG. 1: The normalized muon pT distribution. The pointscorrespond to the like-sign dimuon sample and the histogramcorrespond to the inclusive muon sample. The distribution forthe like-sign dimuon sample contains two entries per event.

fields are reversed on average every two weeks so that thefour solenoid-toroid polarity combinations are exposed toapproximately the same integrated luminosity. This al-lows for a cancellation of first order effects related withthe instrumental asymmetry [15]. To ensure such can-cellation, the events are weighted according to the in-tegrated luminosity for each dataset corresponding to adifferent configuration of the magnets’ polarities. Theseweights are given in Table II.

The normalized pT distributions of muons in the se-lected data samples are shown in Fig. 1. Differencesin these distributions are caused by the trigger require-ments.

IV. MONTE CARLO SIMULATION

Since almost all quantities are extracted from data,the MC simulations are used in only a limited way. Thesimulations of QCD processes used in this analysis are:

• Inclusive pp collisions containing a minimum trans-verse energy Emin

T > 10 or 20 GeV at the generatorlevel.

• Inclusive pp → bbX and pp → ccX final statescontaining a muon, with an additional requirement

that the b or c quark has transverse momentumpT > 3 GeV, and that the produced muon has pT >1.5 GeV and |η| < 2.1.

The samples with different EminT are used to study the

impact of the kinematics of generated events on the pa-rameters extracted from the simulation.

In all cases we use the pythia v6.409 [17] event gen-erator, interfaced to the evtgen decay package [18] andthe CTEQ6L1 [19] parton distribution functions. Thegenerated events are propagated through the D0 detec-tor using a geant [20] based program with full detectorsimulation. The response in the detector is digitized, andthe effects of multiple interactions at high luminosity aremodeled by overlaying hits from randomly triggered ppcollisions on the digitized hits from MC. The completeevents are reconstructed with the same program as usedfor data, and, finally, analyzed using the same selectioncriteria described above for data.

V. MEASUREMENT OF fK , FK

A kaon, pion, or proton can be misidentified as amuon and thus contribute to the inclusive muon and thelike-sign dimuon samples. This can happen because ofpion and kaon decays in flight, punch-through, or muonmisidentification. We do not distinguish these individ-ual processes, but rather measure the total fraction ofsuch particles using data. In the following, the notationK → µ stands for the phrase “kaon misidentified as amuon,” and the notations π → µ and p → µ havecorresponding meanings for pions and protons. In thisSection we discuss the measurement of fK and FK . Themeasurement of the corresponding factors for pions andprotons and of the asymmetries are discussed in the fol-lowing Sections.

The fraction fK in the inclusive muon sample is mea-sured using K∗0 → K+π− decays [11] with K → µ. Thefraction fK∗0 of these decays is related to the fraction fKby

fK∗0 = ε0fKR(K∗0), (18)

where R(K∗0) is the fraction of all kaons that result fromK∗0 → K+π− decays, and ε0 is the efficiency to recon-struct the pion from the K∗0 → K+π− decay, providedthat the K → µ track is reconstructed.

We also select KS mesons and reconstruct K∗+ →KSπ

+ decays. The number of these decays is

N(K∗+ → KSπ+) = εcN(KS)R(K∗+), (19)

where R(K∗+) is the fraction of KS that result fromK∗+ → KSπ

+ decays, and εc is the efficiency to recon-struct the additional pion in the K∗+ → KSπ

+ decay,provided that the KS meson is reconstructed. We useisospin invariance to set

R(K∗0) = R(K∗+). (20)

9

This relation is also confirmed by data as discussed inSec. VIII. We apply the same kinematic selection cri-teria to the charged kaon and KS candidates, and useexactly the same criteria to select an additional pion andreconstruct the K∗0 → K+π− and K∗+ → KSπ

+ de-cays. Therefore we set

ε0 = εc. (21)

This relation is confirmed by simulation. We assign a sys-tematic uncertainty related to this relation, as discussedin Sec. VIII. From Eqs. (18)–(21), we obtain

fK =N(KS)

N(K∗+ → KSπ+)fK∗0 . (22)

We use a similar relation to obtain the quantity FK ofK → µ tracks in the like-sign dimuon sample:

FK =N(KS)

N(K∗+ → KSπ+)FK∗0 , (23)

where FK∗0 is the fraction of K∗0 → K+π− decays withK → µ in the like-sign dimuon sample. The numbersN(KS) and N(K∗+ → KSπ

+) are obtained from theinclusive muon sample.

Since the kaon track parameters must be known toreconstruct the K∗0 meson, these measurements of fKand FK require the kaons to decay after being recon-structed in the central tracking system. A small num-ber of kaon decays occur close to the interaction point,so that the muon track is reconstructed by the tracker.These muons are counted in the inclusive muon and thelike-sign dimuon samples, but do not contribute to themeasurement of the K → µ fraction, because their pa-rameters differ significantly from the parameters of theoriginal kaon, and they do not produce a narrow K∗0 me-son peak. The fractions FK and fK measured in exclu-sive decays are therefore divided by a factor C that cor-responds to the fraction of correctly reconstructed kaonsamong all K → µ tracks. This factor is calculated fromsimulation as

C = 0.938± 0.006. (24)

Since the mean decay length of kaons in the laboratoryframe is much longer than the size of the D0 detector,the value of C is determined mainly by the detector ge-ometry, and its value is similar for both K → µ andπ → µ tracks. Therefore, we use the same coefficient Cfor the computation of the fraction of π → µ described inSec. VII. The difference in this coefficient for kaon andpion tracks observed in simulation is taken as the un-certainty on its value. The uncertainties from the eventgeneration and reconstruction produce a smaller impacton this coefficient.

Details of KS → π+π−, K∗0 → K+π−, and K∗+ →KSπ

+ selections and the fitting procedure to measurethe number of these decays are given in Appendix B. Allquantities in Eqs. (22) and (23) are obtained as a function

TABLE III: Fractions fK and FK for different muon pT bins.The correspondence between the bin number and the pT rangeis given in Table I. The last line shows the weighted averageof these quantities obtained with weights given by the fractionof muons in a given pT interval f iµ (F iµ) in the inclusive muon(dimuon) sample. Only the statistical uncertainties are given.

Bin fK × 102 FK × 102

0 14.45 ± 1.02 18.13 ± 4.621 14.14 ± 0.26 14.00 ± 1.142 15.78 ± 0.20 16.14 ± 0.773 15.63 ± 0.35 11.97 ± 1.604 15.26 ± 0.56 21.47 ± 2.31

All 15.46 ± 0.14 15.38 ± 0.57

0

0.1

0.2

0.3

5 10 15 20 25pT(K) [GeV]

f K

(a) DØ, 6.1 fb-1

0

0.1

0.2

0.3

5 10 15 20 25pT(K) [GeV]

FK

DØ, 6.1 fb-1(b)

FIG. 2: The fraction of K → µ tracks in the inclusive muonsample (a) and the like-sign dimuon sample (b), both as afunction of the pT of the kaon.

of the measured transverse momentum of the kaon. Themeasured number of K∗0 → K+π− decays with K → µin a given pT range is normalized by the total number ofmuons in that interval. The fraction FK∗0 includes a mul-tiplicative factor of two, because there are two muons ina like-sign dimuon event, and by definition it is normal-ized to the number of like-sign dimuon events. Figure 2and Table III give the resulting fractions fK and FK fordifferent pT bins. Only statistical uncertainties are given;systematic uncertainties are discussed in Sec. VIII.

10

VI. MEASUREMENT OF P (π → µ)/P (K → µ)AND P (p→ µ)/P (K → µ)

The probability P (K → µ) for a kaon to be misiden-tified as a muon is measured using φ → K+K− decays.Similarly, we use KS → π+π− and Λ→ pπ− decays [11]to measure the probabilities P (π → µ) and P (p → µ),respectively. In all cases we measure the number Nµof decays in which the candidate particle satisfies themuon selection criteria defined in Sec. III, and the num-ber of decays Ntr in which the tested particle satisfies thetrack selection criteria. When both kaons (pions) fromφ→ K+K− (KS → π+π−) satisfy the selection criteria,they contribute twice. The details of the event selectionsand of the fitting procedure used to extract the numberof φ, KS , and Λ decays are given in Appendix B. The ra-tio of Nµ(φ) to Ntr(φ) defines P (K → µ)ε(µ), where ε(µ)is the efficiency of muon identification. In the same way,the ratio of Nµ(KS) to Ntr(KS) yields P (π → µ)ε(µ),and the ratio of Nµ(Λ) to Ntr(Λ) gives the quantityP (p → µ)ε(µ). The ratios P (π → µ)/P (K → µ) andP (p→ µ)/P (K → µ) are obtained from

P (π → µ)

P (K → µ)=

Nµ(KS)/Ntr(KS)

Nµ(φ)/Ntr(φ),

P (p→ µ)

P (K → µ)=

Nµ(Λ)/Ntr(Λ)

Nµ(φ)/Ntr(φ). (25)

Since the initial selection for this measurement requiresat least one identified muon, we determine all these quan-tities in the sub-sample of single muon triggers that con-tain at least one muon not associated with the K → µ,π → µ , or p→ µ transitions.

We measure all these parameters as a function of theoriginal particle’s transverse momentum. Figures 3 and 4show the ratio P (π → µ)/P (K → µ) and P (p →µ)/P (K → µ) respectively, with the mean values av-eraged over pT determined to be

P (π → µ)/P (K → µ) = 0.540± 0.029, (26)

P (p→ µ)/P (K → µ) = 0.076± 0.021. (27)

The dominant uncertainty in Eqs. (26) and (27) stemsfrom the limited statistics of data, and the contribu-tion of all other uncertainties is much smaller. Theprobability of a pion to be misidentified as a muonis much larger than that of proton because the dom-inant contribution to this probability comes from theπ− → µ−ν decay. The measured ratios (26) and (27)agree well with the results obtained from MC, where weobtain P (π → µ)/P (K → µ)(MC) = 0.530 ± 0.011 andP (p→ µ)/P (K → µ)(MC) = 0.050± 0.003.

0

0.5

1

1.5

2

5 10 15 20 25pT [GeV]

P(π

→µ)

/P(K

→µ) DØ, 6.1 fb-1

FIG. 3: The ratio P (π → µ)/P (K → µ) as a function of thehadron transverse momentum. The horizontal dashed lineshows the mean value of this ratio.

0

0.2

0.4

0.6

0.8

1

5 10 15 20 25pT [GeV]

P(p

→µ)

/P(K

→µ) DØ, 6.1 fb-1

FIG. 4: The ratio P (p → µ)/P (K → µ) as a function of theparticle transverse momentum. The horizontal dashed lineshows the mean value of this ratio.

VII. MEASUREMENT OF fπ, fp, Fπ, Fp

The fraction fπ of π → µ tracks in the inclusive muonsample can be expressed as

fπ = fKP (π → µ)

P (K → µ)

nπnK

, (28)

where the measurement of the fraction fK is described inSec. V, that of the ratio P (π → µ)/P (K → µ) in Sec. VI,and the quantities nπ and nK are the mean multiplicitiesof pions and kaons in pp interactions. In a similar way,the fraction fp of p→ µ tracks is determined from

fp = fKP (p→ µ)

P (K → µ)

np + nf

nK, (29)

where np is the average number of protons produced inpp interactions. We include in the fraction fp the contri-bution from the number nf of false tracks, reconstructed

11

10-2

10-1

1

5 10 15 20 25pT [GeV]

Rat

io o

f m

ulti

plic

itie

s

- nπ / nK- np / nK- nf / nK

DØ MC

FIG. 5: The ratio of multiplicities nπ/nK , np/nK and nf/nKas a function of the transverse momentum obtained frompythia.

TABLE IV: Fractions fπ, fp, Fπ, and Fp for different pT bins.The correspondence between the bin number and the momen-tum range is given in Table I. The last line shows the weightedaverages obtained with weights given by the fraction of muonsin a given pT interval f iµ in the inclusive muon sample. Onlythe statistical uncertainties are given.

Bin fπ × 102 fp × 102 Fπ × 102 Fp × 102

0–1 35.6 ± 4.9 0.6 ± 0.4 32.2 ± 5.1 0.5 ± 0.42 24.3 ± 1.6 0.7 ± 0.2 22.4 ± 1.8 0.7 ± 0.2

3–4 21.7 ± 3.4 0.7 ± 0.7 19.0 ± 3.4 0.6 ± 0.6All 25.8 ± 1.4 0.7 ± 0.2 24.9 ± 1.5 0.6 ± 0.2

from random combinations of hits. The impact of falsetracks on the final result is found to be small and is takeninto account in the systematic uncertainty.

The values of nK , nπ, np, and nf are taken from thepythia simulation of inclusive hadronic interactions. Wecount the number of particles satisfying the track selec-tion criteria in the simulated interactions, and obtain thedependence of the ratios nπ/nK , np/nK and nf/nK onthe particle pT shown in Fig. 5.

Both fπ and fp are measured as a function of the par-ticle pT . However, they are poorly defined in the firstand last bins due to low statistics. Therefore, we com-bine these quantities for bins 0 and 1 and for bins 3 and4.

Figure 6 and Table IV provide the measured fractionsfπ and fp for different pT bins. Only statistical uncer-tainties are given. The systematic uncertainties relatedto these quantities are discussed in Sec. VIII.

The fractions Fπ and Fp in the like-sign dimuon sampleare determined in a similar way:

Fπ = FKP (π → µ)

P (K → µ)

NπNK

,

Fp = FKP (p→ µ)

P (K → µ)

Np +Nf

NK, (30)

0

0.2

0.4

5 10 15 20 25pT [GeV]

f π

(a)DØ, 6.1 fb-1

0

0.005

0.01

0.015

0.02

5 10 15 20 25pT [GeV]

f p

(b)DØ, 6.1 fb-1

FIG. 6: The fraction of (a) π → µ tracks and (b) p →µ tracks in the inclusive muon sample as a function of thetrack transverse momentum. The horizontal dashed linesshow the mean values of these fractions.

where the quantities NK , Nπ, Np, and Nf representthe average numbers of kaons, pions, protons and falsetracks for events with two identified muons with the samecharge. The simulation shows that the ratio Nπ/NK canbe approximated as

NπNK

= (0.90± 0.05)nπnK

. (31)

The main uncertainty in this value is due to the simula-tion of pion and kaon multiplicities in pp interactions andis discussed in Sec. VIII. The ratio Np/NK is also consis-tent with the factor given in Eq. 31. The value of Nπ/NKis smaller than that of nπ/nK because the main contribu-tion in the sample with one identified muon comes fromsemileptonic decays of b and c quarks, which usually alsocontain at least one kaon. Since the number of simulatedevents with one identified muon is small, we obtain theratios Nπ/NK and (Np + Nf)/NK using the approxima-tion of Eq. (31), i.e., multiplying the quantities nπ/nKand (np+nf)/nK by the factor 0.90±0.05. Figure 7 andTable IV give the fractions Fπ and Fp for different pTbins. Only the statistical uncertainties of the simulationare given. The systematic uncertainties related to thesequantities are discussed in Sec. VIII. As in the case offπ and fp, the mean value of these quantities are used inbins 0 and 1 and for bins 3 and 4.

12

0

0.2

0.4

5 10 15 20 25pT [GeV]

Fπ

(a)DØ, 6.1 fb-1

0

0.005

0.01

0.015

0.02

5 10 15 20 25pT [GeV]

Fp

(b)DØ, 6.1 fb-1

FIG. 7: The fraction of (a) π → µ tracks and (b) p →µ tracks in the like-sign dimuon sample as a function ofthe track transverse momentum. The horizontal dashed linesshow the mean values of these fractions.

VIII. SYSTEMATIC UNCERTAINTIES OFBACKGROUND FRACTIONS

We use Eqs. (20) and (21) to derive the fractions fKand FK , and verify the validity of Eq. (21) in simulation,and find that

(εc/ε0)MC = 0.986± 0.029, (32)

where the uncertainty reflects only the statistics of theMonte Carlo. The ratio R(K∗+)/R(K∗0) measured insimulation is

R(K∗+)/R(K∗0) = 0.959± 0.035. (33)

The validity of Eq. (20) in simulation relies mainly on theassumptions used in the fragmentation and hadronizationprocesses in the event generator. To confirm the valid-ity of Eq. (20), we use the existing experimental data onK+, KS , K∗0, and K∗+ multiplicities in jets, which wereobtained at e+e− colliders at different center-of-mass en-ergies [2]. From these data we obtain:

R(K∗+)/R(K∗0) = 1.039± 0.075. (34)

The simulation and data are consistent, and we assign arelative uncertainty of 7.5% to both fK and FK from theassumption of Eq. (20). We also assign an uncertainty of4% due to the fitting procedure used to extract the num-bers ofK∗+ andK∗0 events. This uncertainty is obtained

by varying the background parametrization and the fit-ting range. Since the same background model is used toobtain the number of K∗0 events, both in the inclusivemuon and the like-sign dimuon samples, this uncertaintyis taken to be the same for fK and FK . Adding all con-tributions in quadrature, and including the uncertaintyin Eq. (24), we find a relative systematic uncertainty of9.0% in fK and FK , with a 100% correlation between thetwo.

We assign an additional uncertainty of 2.0% on FKdue to the description of the background in the inclu-sive muon and like-sign dimuon events. This uncertaintyis estimated by varying the background parametrizationand range used for fitting, and by comparing with theresults of the alternative fitting method presented in Ap-pendix E.

We use the ratio N(KS)/N(K∗+ → KSπ+) to measure

both fK and FK , which is equivalent to the statementthat the ratios FK∗0/FK and fK∗0/fK are identical, i.e.,that the fraction of kaons originating from K∗0 is thesame in the inclusive muon and in the like-sign dimuonsamples. This is validated in simulation with an uncer-tainty of 3% due to the statistics of the simulation, whichwe assign as an additional systematic uncertainty to thefraction FK .

The uncertainty on the background fractions fπ, Fπ,fp, and Fp have an additional contribution from the ra-tios of multiplicities nπ/nK and np/nK extracted fromthe simulation. To test the validity of the simulation, wemeasure the multiplicity of kaons in the inclusive muonsample. We select events with one reconstructed muonand at least one additional charged particle that satisfiesthe track selection criteria. We determine the fractionof kaons among these tracks using the same method asin Sec. V, i.e., we find the fraction of tracks from theK∗0 → K+π− decay and convert this into the fraction ofkaons. We compare the kaon multiplicity in data usingthis method with that measured in the simulation, andwe find that they agree within 10%. Since part of thisdifference can be attributed to the uncertainties from theassumptions of Eqs. (20) and (21), and part is due to thefitting procedure described above, we find that the un-certainty of the kaon multiplicity in the simulation doesnot exceed 4%, and we assign this uncertainty to bothquantities nπ/nK and np/nK . We also assign this 4%uncertainty to the Eq. (31) used to derive the values ofNπ/NK and Np/NK .

Any falsely reconstructed track identified as a muon istreated in the analysis in the same way as a proton. Wecheck the impact of this approach by completely remov-ing the contribution of false tracks, or by increasing theircontribution by a factor of ten, and the final value of Abslchanges by less than 0.00016. We include this differenceas the systematic uncertainty on the contribution fromfalse tracks.

13

TABLE V: Fractions fS , fK , fπ, and fp+ff , measured in dataand in simulation (MC). Only the statistical uncertainties onthese measurements are shown.

fS × 102 fK × 102 fπ × 102 (fp + ff)× 102

Data 58.1 ± 1.4 15.5 ± 0.2 25.9 ± 1.4 0.7 ± 0.2MC 59.0 ± 0.3 14.5 ± 0.2 25.7 ± 0.3 0.8 ± 0.1

IX. MEASUREMENT OF fS, FSS

We use the measurements of the fractions of back-ground muons in the “long” category, obtained in theprevious sections to evaluate the fraction of muons inthe “short” category. In the inclusive muon sample thefraction fS is determined as

fS = 1− fK − fπ − fp. (35)

We check through simulation that the contribution fromall other sources to the inclusive muon sample, such asKL → πµν decays or the semileptonic decays of hyper-ons, is negligible. The muons from τ → µνµντ are in-cluded by definition in the fS . The fraction fS is mea-sured separately in each muon pT bin and then a weightedaverage is calculated with weights given by the fractionof muons in a given pT interval f iµ in the inclusive muonsamples. From data, we obtain

fS = 0.581± 0.014 (stat)± 0.039 (syst), (36)

where the systematic uncertainty comes from the uncer-tainty on the background fractions described in Sec. VIII.

To check the procedure for determining the back-ground fractions, the composition of the inclusive muonsample in data is compared to that from simulation in Ta-ble V, where only statistical uncertainties for both dataand simulation are shown. The agreement between dataand simulation is very good, and the remaining differ-ences are within the assigned systematic uncertainties.Although the values given in Table V for data and forsimulation are not independent, some, such as fK andP (π → µ)/P (K → µ) used to derive fπ, are measureddirectly in data. As a consequence, this result can beused as an additional confirmation of the validity of ourmethod.

The background fractions FK , Fπ, and Fp are obtainedfrom the same weighted average used for Eq. (36) of thequantities measured in each pT interval i, starting fromthe values given in Secs. V and VII (F iµ is used as weight

instead of f iµ). Using Eq. (13), we obtain

Fbkg = 0.409± 0.019 (stat)± 0.040 (syst). (37)

To evaluate the fraction FSS in the like-sign dimuonsample, we take into account that, in some events, bothmuons belong to the L category. The fraction of theseevents in all events with at least one L muon is measured

in simulation and found to be

FLLFSL + FLL

= 0.220± 0.012. (38)

The uncertainty in Eq. (38) includes the 4% systematicuncertainty related to the multiplicity of different parti-cles in the simulation, as discussed in Sec. VIII. UsingEqs. (13), (37), and (38), we obtain

FLL = 0.074± 0.003 (stat)± 0.008 (syst), (39)

and, finally, from Eqs. (14), (37), and (39) we obtain

FSS = 0.665± 0.016 (stat)± 0.033 (syst). (40)

X. MEASUREMENT OF δ

Table III of Ref. [15] gives a complete list of the contri-butions to the dimuon charge asymmetry that are causedby detector effects. The largest of these effects is ≈ 3%.The reversal of magnet polarities is a characteristic of theD0 experiment that allows the cancellation at first orderof these detector effects, reducing any charge asymmetryintroduced by the track reconstruction considerably [15].

Higher-order effects result in a small residual recon-struction asymmetry at the 10−3 level. This asymmetryis measured using J/ψ → µ+µ− decays. We select eventsthat pass at least one dimuon trigger and have at leastone identified muon and one additional particle of op-posite charge that satisfies the track selection criteria ofSec. III. We verify in Appendices C and D that the trackreconstruction and trigger selection do not introduce anadditional charge asymmetry. The residual asymmetryis measured as a function of the muon transverse mo-mentum. The probability to identify a muon with chargeQ = ±1 and pT corresponding to bin i is denoted byPi(1 + Qδi), where Pi is the mean probability for pos-itive and negative muons, and δi is the muon detectionasymmetry we want to measure. The probability of iden-tifying the second muon with pT in bin j, provided thatthe first muon has pT in bin i, is denoted by P ij (1+Qδj).

The number of events Nij with a positive muon in bini and negative muon in bin j is

Nij = NPi(1 + δi)Pij (1− δj), (41)

where N is the total number of selected J/ψ → µ+µ−

decays. The number of events with only one selectedmuon of charge Q is

NiQ = NPi(1 +Qδi)

1−

4∑

j=0

P ij (1−Qδj)

, (42)

where the sum extends over the five transverse momen-tum intervals.

The probabilities Pi and P ij are not independent. FromEq. (41), we have the following normalization condition

PiPij = PjP

ji . (43)

14

In addition, since the total probability to identify themuon is Ptot =

∑4i=0 Pi, we get the following normaliza-

tion condition

(Ptot)2 =

4∑

i,j=0

PiPij . (44)

Experimentally we measure the quantitiesNii, Σij , ∆ij

(i < j), Σi, and ∆i, which can be expressed as

Nii = NPiPii , (45)

Σij ≡ Nij +Nji = 2NPiPij ,

∆ij ≡ Nij −Nji = 2NPiPij (δi − δj),

Σi ≡ Ni+ +Ni− = 2NPi(1− P isum),

∆i ≡ Ni+ −Ni− = 2NPi(1− P isum)(δi + δisum),

where P isum =∑4j=0 P

ij and δisum = (

∑4j=0 P

ij δj)/(1 −

P isum).Since the number of measured quantities is greater

than the number of unknowns, Pi, Pij , and δi can be

obtained from Eqs. (43–45) by minimizing the χ2 of thedifference between the observed and expected quantities.The quantities Nii, Σij , ∆ij (i < j), Σi, and ∆i areobtained from fits to the J/ψ mass peak in the dimuoninvariant mass distribution M(µ+µ−) in each of the fivepT bins. The J/ψ signal is described by the sum of twoGaussians. An additional Gaussian is included to takeinto account the contribution from the ψ′. The back-ground is parametrized by a third degree polynomial.The mean position and R.M.S. of all Gaussian functionsin the fit of ∆ij and ∆i are fixed to the values obtained inthe fit of the corresponding quantities Σij and Σi. Exam-ples of the fits are shown in Figs. 8 and 9. The values ofδi obtained as a function of the muon pT are given in Ta-ble VI and are shown in Fig. 10. The correlations betweenvalues of δi in different bins are given in Table VII. Theweighted average for the residual muon asymmetry in theinclusive muon and the like-sign dimuon samples, calcu-lated using weights given by the fraction of muons in agiven pT interval f iµ (F iµ) in the inclusive muon (dimuon)sample, are given respectively by

δ =∑4i=0 f

iµδi = −0.00076± 0.00028, (46)

∆ =∑4i=0 F

iµδi = −0.00068± 0.00023, (47)

where only the statistical uncertainties are given. Thecorrelations among different δi are taken into account.These small values of the residual muon reconstructionasymmetry are a direct consequence of the regular rever-sal of the magnets polarities in the D0 experiment.

XI. MEASUREMENT OF aK , aπ, ap

The largest detector-related charge asymmetry is pro-duced by K → µ tracks. It is caused, as discussed in

0

20000

40000

60000

80000

2 2.5 3 3.5 4M(µ+µ-) [GeV]

Ent

ries

/50

MeV (a)DØ, 6.1 fb-1

χ2/dof = 29/27

-500

0

500

2 2.5 3 3.5 4M(µ+µ-) [GeV]

Ent

ries

/50

MeV (b)DØ, 6.1 fb-1

χ2/dof = 38/37

FIG. 8: The µ+µ− invariant mass distributions used to obtain(a) Σ23 = N23 + N32 and (b) ∆23 = N23 − N32. The solidline presents the result of the fit; the dashed line shows thenon-resonant background contribution.

0

500

1000

1500

2000

x 10 2

2 2.5 3 3.5 4M(µ+µ-) [GeV]

Ent

ries

/50

MeV (a)DØ, 6.1 fb-1

χ2/dof = 62/29

-1000

0

1000

2 2.5 3 3.5 4M(µ+µ-) [GeV]

Ent

ries

/50

MeV (b)DØ, 6.1 fb-1

χ2/dof = 51/36

FIG. 9: The µ+µ− invariant mass distributions used to obtain(a) Σ2 = N2+ + N2− and (b) ∆2 = N2+ − N2−. The solidline presents the result of the fit; the dashed line shows thenon-resonant background contribution.

15

TABLE VI: Muon reconstruction asymmetry δi for differentmuon pT bins. The correspondence between the bin numberand the pT range is given in Table I. Only the statisticaluncertainties are given.

Bin δi0 −0.00203 ± 0.001941 −0.00045 ± 0.000592 −0.00130 ± 0.000483 +0.00075 ± 0.001254 +0.00162 ± 0.00230

TABLE VII: Correlation coefficients among values of δi indifferent bins. The correspondence between the bin numberand the pT range is given in Table I.

Bin 0 1 2 3 40 +1.000 −0.189 −0.155 +0.024 −0.0511 −0.189 +1.000 −0.449 −0.117 −0.0592 −0.155 −0.449 +1.000 −0.242 −0.1243 +0.024 −0.117 −0.242 +1.000 −0.0064 −0.051 −0.059 −0.124 −0.006 +1.000

Sec. II, by the difference between the K−N and K+N in-teraction cross sections [2], resulting in a positive chargeasymmetry of muons coming from kaon decay or punch-through.

The asymmetry aK of K → µ tracks is measureddirectly in data using K∗0 → K+π− and φ → K+K−

decays. In both cases we select candidates with K →µ tracks, in the entire inclusive muon sample. We calcu-late separate mass distributions for positive and negativeK → µ tracks, and fit the sum and the difference of thesedistributions to extract the quantity ∆K , correspondingto the difference in the number of K∗0 or φ meson de-cays with positive and negative K → µ tracks, and thequantity ΣK , corresponding to their sum. The selectionof events and the fitting procedure used to extract the

-0.004

-0.002

0

0.002

0.004

5 10 15 20 25pT(µ) [GeV]

asym

met

ry δ

DØ, 6.1 fb-1

FIG. 10: Muon reconstruction asymmetry as a function of themuon pT .

number of signal decays are described in Appendix B.The asymmetry aK is measured as:

aK = C∆K/ΣK , (48)

where the coefficient C is the fraction of correctly recon-structed kaons among all K → µ tracks as in Eq. (24).In this measurement of aK , we require that the kaondecays after having been reconstructed in the trackingsystem, since its track parameters must be measured inorder to reconstruct the K∗0 or φ meson. However, theK → µ tracks in the inclusive sample also include kaonsdecaying before being reconstructed in the tracker. Sincethe kaon asymmetry is caused by the interactions of kaonswith the material of the detector, and the amount of ma-terial near the interaction point is negligible, the kaonsdecaying before being reconstructed by the tracker donot produce any significant asymmetry. They contributeonly in the denominator of Eq. (48). The factor C takesinto account the contribution of these tracks. Its numeri-cal value is given in Eq. (24). It should be noted that thisfactor cancels in the products fKaK , etc., since both fKand aK are measured using the correctly reconstructedK → µ tracks.

Figure 11(a) shows the value of aK(K∗0) measuredin K∗0 → K+π− decay as a function of the pT of theK → µ track. The asymmetry in φ → K+K− decaysameasK has to be corrected for the charge asymmetry of

the second kaon track atrackK :

aK(φ) = ameasK − atrack

K . (49)

The kaon track reconstruction asymmetry atrackK is dis-

cussed and measured as a function of kaon momentumin [22] using the decay D∗+ → D0π+ with D0 →K−µ+ν, and is taken from that article. It is convolutedwith the pT distribution of the second kaon for each binof the K → µ pT . Figure 11(b) shows the resulting asym-metry aK(φ).

The two measurements of aK are consistent. Theχ2/d.o.f. for their difference is 5.40/5. Therefore they canbe combined and the resulting asymmetry aK is shownin Fig. 12 and in Table VIII. Due to the requirement ofpT > 4.2 GeV or |pz| > 6.3 GeV, the first two bins inFig. 12 correspond to muons that traverse the forwardtoroids of the D0 detector. These muons have a largermomentum and a longer path length before the calorime-ter than central muons. As a result, aK drops at low pT .

The asymmetry aπ of π → µ tracks and the asymme-try ap of p→ µ tracks are expected to be much smaller.We measure these asymmetries using KS → π+π− andΛ → pπ− decays, respectively. The details of the KS

and Λ selections are given in Appendix B. The tech-nique used to measure the asymmetry is the same as inaK measurement. The same factor C is used to measurethe asymmetry aπ from Ks → π+π− decays. The un-certainty in C takes into account its difference for kaon

16

TABLE VIII: Asymmetries aK , aπ, and ap for different pTbins. The correspondence between the bin number and pTrange is given in Table I. The last line shows the mean asym-metries averaged over the inclusive muon sample. Only thestatistical uncertainties are given.

Bin aK aπ ap0 +0.0526 ± 0.0242

+0.0027± 0.0021 −0.104± 0.0761 +0.0424 ± 0.00272 +0.0564 ± 0.0013 +0.0013± 0.0012 +0.028± 0.0353 +0.0620 ± 0.0032

+0.0164± 0.0044 +0.077± 0.0554 +0.0620 ± 0.0048

All +0.0551 ± 0.0011 +0.0025± 0.0010 +0.023± 0.028

0

0.02

0.04

0.06

0.08

0.1

5 10 15 20 25pT(K) [GeV]

a K(K

*0)

(a)DØ, 6.1 fb-1

0

0.02

0.04

0.06

0.08

0.1

5 10 15 20 25pT(K) [GeV]

a K(φ

)

(b)DØ, 6.1 fb-1

FIG. 11: The asymmetry aK measured with (a) K∗0 →K+π− and (b) φ → K+K− decays as a function of theK → µ pT .

0

0.02

0.04

0.06

0.08

5 10 15 20 25pT(K) [GeV]

a K c

ombi

ned

DØ, 6.1 fb-1

FIG. 12: The combined asymmetry aK as a function of pT .

0

0.01

0.02

0.03

5 10 15 20 25pT(π) [GeV]

a π

(a)DØ, 6.1 fb-1

-0.1

0

0.1

5 10 15 20 25pT(p) [GeV]

a p

(b)DØ, 6.1 fb-1

FIG. 13: The asymmetry (a) aπ and (b) ap as a function ofthe pT of the pion and proton, respectively.

and pion tracks. Since the proton is stable, this fac-tor is not used in the computation of the asymmetry ofp→ µ tracks.

The asymmetries aπ and ap are shown in Fig. 13 asa function of the pT of the π → µ and p → µ tracks,respectively. The values of these asymmetries and theiraverages are listed in Table VIII for different pT bins.We use the mean value of these quantities in bins 0 and1 and in bins 3 and 4 since the statistics available in thefirst and last bin are not sufficient to perform separatemeasurements.

The asymmetries AK , Aπ and Ap are obtained fromaK , aπ and ap using Eq. 16 (and analogous relations forpions and protons).

XII. CORRECTIONS DUE TO BACKGROUNDASYMMETRIES

The corrections for the asymmetries of the background,obtained from Tables I, III, IV and VIII, are summarizedin Tables IX and X. The values fKaK , FKAK , etc.,are computed by averaging the corresponding quantitieswith weights given by the fraction of muons in a given pTinterval f iµ (F iµ) in the inclusive muon (dimuon) sample,see Eqs. (15) and (16). We use the mean value of fπ, Fπ,fp, Fp, aπ, and ap in bins 0 and 1 and in bins 3 and 4as the statistics available in the first and last bin are notsufficient to perform separate measurements.

17

TABLE IX: Corrections due to background asymmetriesfKaK , fπaπ, and fpap for different pT bins. The last lineshows the weighted averages obtained using weights given bythe fraction of muons in a given pT interval f iµ in the inclusivemuon sample. Only the statistical uncertainties are given.

Bin fKaK × 102 fπaπ × 102 fpap × 102

0 +0.760 ± 0.353+0.095± 0.076 −0.061± 0.060

1 +0.600 ± 0.0402 +0.889 ± 0.023 +0.033± 0.030 +0.020± 0.0263 +0.968 ± 0.054

+0.337± 0.109 +0.053± 0.0674 +0.946 ± 0.081

All +0.854 ± 0.018 +0.095± 0.027 +0.012± 0.022

TABLE X: Corrections due to background asymmetriesFKAK , FπAπ and FpAp for different pT bins. The last lineshows the weighted averages obtained using weights given bythe fraction of muons in a given pT interval F iµ in the dimuonsample. Only the statistical uncertainties are given.

Bin FKAK × 102 FπAπ × 102 FpAp × 102

0 +0.953 ± 0.501+0.086± 0.069 −0.056± 0.054

1 +0.594 ± 0.0612 +0.910 ± 0.048 +0.030± 0.027 +0.019± 0.0243 +0.741 ± 0.106

+0.294± 0.098 +0.046± 0.0584 +1.332 ± 0.176

All +0.828 ± 0.035 +0.095± 0.025 +0.000± 0.021

XIII. ASYMMETRIES aS AND AS

In the absence of new particles or interactions, the onlynon-instrumental source of the asymmetries aS and AS isthe semileptonic charge asymmetry Absl given by Eq. (5).Both aS and AS are proportional to Absl, through thecoefficients

cb ≡ aS/Absl, (50)

Cb ≡ AS/Absl, (51)

which are determined from simulation.The decays producing an S muon in the inclusive muon

sample, and their weights relative to the semileptonicdecay b → µX [11], are listed in Table XI. All weightsare computed using simulated events. The main process,denoted as T1, is the direct semileptonic decay of a bquark. It includes the decays b → µX and b → τX,with τ → µX. The weights w1a and w1b for semileptonicdecays of B mesons with and without oscillations arecomputed using the mean mixing probability

χ0 = f ′dχd0 + f ′sχs0, (52)

where f ′d and f ′s are the fractions of B0d and B0

s mesonsin a sample of semileptonic B-meson decays, and χd0 andχs0 are the B0

d and B0s mixing probabilities integrated

over time. We use the value χ0 = 0.147±0.011 measuredat the Tevatron and given in [2, 23]. The second processT2 concerns the sequential decay b → c → µX. For

TABLE XI: Heavy quark decays contributing to the inclu-sive muon and like-sign dimuon samples. Abbreviation “nos”stands for “non-oscillating,” and “osc” for “oscillating.” Allweights are computed using the MC simulation.

Process WeightT1 b→ µ−X w1 ≡ 1.T1a b→ µ−X (nos) w1a = (1− χ0)w1

T1b b→ b→ µ−X (osc) w1b = χ0w1

T2 b→ c→ µ+X w2 = 0.113± 0.010T2a b→ c→ µ+X (nos) w2a = (1− χ0)w2

T2b b→ b→ c→ µ+X (osc) w2b = χ0w2

T3 b→ ccq with c→ µ+X or c→ µ−X w3 = 0.062± 0.006T4 η, ω, ρ0, φ(1020), J/ψ, ψ′ → µ+µ− w4 = 0.021± 0.001T5 bbcc with c→ µ+X or c→ µ−X w5 = 0.013± 0.002T6 cc with c→ µ+X or c→ µ−X w6 = 0.660± 0.077

simplicity we use the same value of χ0 to compute theweights w2a and w2b of non-oscillating and oscillatingsequential decays b → c → µX. The process T3 is thedecay of a b hadron to a cc pair, with either the c or cquark producing a muon, while T4 includes the decays ofshort-lived mesons η, ω, ρ0, φ(1020), J/ψ, and ψ′ to aµ+µ− pair. We take into account both the decays of bhadrons to these particles and their prompt production.The process T5 represents four-quark production of bbccwith either the c or c quark decaying to a muon. Thedecays of b or b quark to a muon in this process andthe four-quark production of bbbb are taken into accountthrough processes T1, T2, and T3. Finally, the processT6 involves cc production followed by c → µX decay.We separate the processes T5 and T6 because only T5

contributes to the like-sign dimuon sample, while bothT5 and T6 contribute to the inclusive muon sample.

The uncertainty in the weights of different processescontains contributions from the uncertainty in the mo-mentum of the generated b hadrons and from the un-certainties of branching fractions for b-hadron decays.We reweight the simulated b-hadron momentum to getagreement of the of muon momentum spectrum in dataand in MC, and the difference in weights is assigned asthe systematic uncertainty on the momentum distribu-tion. The uncertainties in the inclusive branching frac-tions B → µX, B → cX and B → cX taken from [2] arepropagated into the uncertainties on the correspondingweights. We assign an additional uncertainty of 10% tothe weights w5 and w6 due to the uncertainties on theproduction cross sections of cc and bbcc processes.

Among all processes listed in Table XI, the process T1b

is directly related to the semileptonic charge asymmetryAbsl(see Appendix A for details). The process T2b pro-duces the flavor-specific charge asymmetry Afs. We setAfs = −Absl, where the negative sign appears because thecharge of the muon in the process T2b is opposite to thecharge of the muon in the process T1b. No other processcontributes to the charge asymmetry and therefore theyjust dilute the value of Absl. The coefficient cb is found

18

from:

cb =w1b − w2b

w1 + w2 + w3 + w4 + w5 + w6= 0.070± 0.006.

(53)

The computation of the coefficient Cb is more compli-cated. One of the selections for the like-sign dimuon sam-ple requires that the invariant mass of the two muons begreater than 2.8 GeV. This requirement suppresses thecontribution from processes in which both muons arisefrom the decay of the same quark. The probability thatthe initial b quark produces a µ− is

Pb ∝ w1a + w2b + 0.5(w3 + w4 + w5), (54)

where we apply the coefficient 0.5 because processes T3,T4, and T5 produce an equal number of positive and neg-ative muons. The probability that the accompanying bquark also produces a µ− is

Pb ∝ w1b + w2a + 0.5(w3 + w4 + w5). (55)

The total probability of observing like-sign dimuon eventsfrom decays of heavy quarks is

Ptot ∝ PbPb. (56)

The probability of processes contributing to the chargeasymmetry of dimuon events is

Pas ∝ w1b[w1a + 0.5(w3 + w4 + w5)]−w2b[w2a + 0.5(w3 + w4 + w5)]. (57)

The coefficient Cb is obtained from the ratio

Cb = Pas/Ptot = 0.486± 0.032. (58)

This relation assumes that the processes producing thetwo muons are independent and is verified by calculatingthe coefficient Cb in simulated like-sign dimuon events.We exclude the process T6 with cc pair production, sincethe mixing probability of D0 meson is small and theseevents do not contribute significantly to the like-signdimuon sample. We count the number of direct-directb-quark decays, Ndd, of direct-sequential decays, Nds,of sequential-sequential decays, Nss, of direct-randomevents, Ndr (“random” includes processes T3, T4, andT5), of sequential-random decays, Nsr, to obtain

Cb =Ndd −Nss + χ0(Ndr −Nsr)

Nls= 0.448± 0.071,

(59)

where Nls is the total number of like-sign dimuon events.This result agrees well with the value in Eq. (58). Theuncertainty of this method is larger because of the smallstatistics of simulated like-sign dimuon events.

TABLE XII: Sources of uncertainty on Absl in Eqs. (62), (63),and (65). The first eight rows contain statistical uncertainties,the next three rows contain systematic uncertainties.

Source δσ(Absl)(62) δσ(Absl)(63) δσ(Absl)(65)A or a (stat) 0.00066 0.00159 0.00179

fK or FK (stat) 0.00222 0.00123 0.00140P (π → µ)/P (K → µ) 0.00234 0.00038 0.00010P (p→ µ)/P (K → µ) 0.00301 0.00044 0.00011

AK 0.00410 0.00076 0.00061Aπ 0.00699 0.00086 0.00035Ap 0.00478 0.00054 0.00001

δ or ∆ 0.00405 0.00105 0.00077fK or FK (syst) 0.02137 0.00300 0.00128

π, K, p multiplicity 0.00098 0.00025 0.00018cb or Cb 0.00080 0.00046 0.00068

Total statistical 0.01118 0.00266 0.00251Total systematic 0.02140 0.00305 0.00146

Total 0.02415 0.00405 0.00290

XIV. ASYMMETRY Absl

The uncorrected asymmetries a and A are obtained bycounting the number of events of each charge in the inclu-sive muon and the like-sign dimuon samples, respectively.In total, there are 1.495×109 muons in the inclusive muonsample, and 3.731 × 106 events in the like-sign dimuonsample. We obtain

a = +0.00955± 0.00003, (60)

A = +0.00564± 0.00053. (61)

The results obtained in Secs. V–XIII are used to cal-culate the asymmetries aS and AS from these values,which are then used to evaluate the charge asymmetryfor semileptonic B meson decays.

The asymmetry Absl, extracted from the asymmetry aof the inclusive muon sample using Eqs. (9) and (50), is

Absl = +0.0094± 0.0112 (stat)± 0.0214 (syst). (62)

The contributions to the uncertainty on this value aregiven in Table XII. Figure 14(a) shows a compari-son of the asymmetry a and the background asymmetryabkg = fSδ + fKaK + fπaπ + fpap, as a function of themuon pT . There is excellent agreement between these twoquantities, with the χ2/d.o.f. for their difference being2.4/5. Figure 14(b) shows the value of fSaS = a− abkg,which is consistent with zero. The values a and abkg aregiven in Table XIII. This result agrees with expectations,since the value of the asymmetry a should be determinedmainly by the background, and the contribution fromAbsl should be strongly suppressed by the small factor ofcb = 0.070± 0.006.

The consistency of Absl with zero in Eq. (62) and thegood description of the charge asymmetry a for differentvalues of the muon pT shown in Fig. 14 constitute animportant tests of the validity of the background modeland of the analysis method discussed in this article.

19

0

0.005

0.01

0.015

0.02

5 10 15 20 25pT(µ) [GeV]

Asy

mm

etry (a) DØ, 6.1 fb-1- Asymmetry bkga

- Asymmetry a

-0.01

-0.005

0

0.005

0.01

5 10 15 20 25

a -

a bkg

pT(µ) [GeV]

(b) DØ, 6.1 fb-1

FIG. 14: (a) The asymmetry abkg (points with error bars) asexpected from our measurements of the fractions and asym-metries of the background processes is compared to the mea-sured asymmetry a of the inclusive muon sample (shown ashistogram, since the statistical uncertainties are negligible).The asymmetry from CP violation is negligible compared tothe background in the inclusive muon sample; (b) the differ-ence a − abkg. The horizontal dashed line shows the meanvalue of this difference.

TABLE XIII: The measured asymmetry a and the expectedbackground asymmetry abkg in the inclusive muon sample fordifferent pT bins. For the background asymmetry, the firstuncertainty is statistical, the second is systematic.

bin a× 102 abkg × 102

0 0.324 ± 0.036 0.693 ± 0.379± 0.6321 0.582 ± 0.007 0.611 ± 0.109± 0.0722 0.978 ± 0.003 0.865 ± 0.054± 0.0883 1.193 ± 0.008 1.405 ± 0.159± 0.1684 1.339 ± 0.011 1.438 ± 0.206± 0.408

The second measurement of the asymmetry Absl, ob-tained from the uncorrected asymmetry A of the like-signdimuon sample using Eqs. (12) and (51), is

Absl = −0.00736± 0.00266 (stat)± 0.00305 (syst). (63)

The contributions to the uncertainty on Absl for this mea-surement are also listed in Table XII.

The results (62) and (63) represent two different mea-surements of Absl. The uncertainties in Eq. (62) are muchlarger because the asymmetry as is divided by the smallcoefficient cb. Since the same background processes con-tribute to the uncorrected asymmetries a and A, their

0

0.002

0.004

0.006

0 0.5 1 1.5α

Ab sl u

ncer

tain

ty Total uncertaintyStatistical uncertaintySystematic uncertainty

DØ, 6.1 fb-1

FIG. 15: Statistical (dashed line), systematic (doted line),and total (full line) uncertainties on Absl as a function of theparameter α of Eq. (64).

uncertainties in Eqs. (62) and (63) are strongly corre-lated. We take advantage of this correlation to obtain asingle optimized value of Absl, with higher precision, usinga linear combination of the uncorrected asymmetries

A′ ≡ A− αa, (64)

and choosing the coefficient α in order to minimize thetotal uncertainty on the value of Absl.

It is shown in Secs. V–XII that the contributions frombackground sources in Eqs. (9) and (12) are of the sameorder of magnitude. On the other hand, the dependenceof A and a on the asymmetry Absl, according to Eqs. (53)and (58), is significantly different, with Cb À cb. As aresult, we can expect a reduction of background uncer-tainties in (64) for α ≈ 1 with a limited reduction of thestatistical sensitivity on Absl. Figure 15 shows the sta-tistical, systematic, and total uncertainties on Absl as afunction of the parameter α. The total uncertainty onAbsl has a minimum for α = 0.959, and the correspondingvalue of the asymmetry Absl is

Absl = −0.00957± 0.00251 (stat)± 0.00146 (syst). (65)

This value is our final result for Absl. It differs by 3.2standard deviations from the standard model predictionof Absl given in Eq. (4). The different contributions to thetotal uncertainty of Absl in Eq. (65) are listed in Table XII.

XV. CONSISTENCY CHECKS

To check the stability of the result, we repeat this mea-surement with modified selections, or with subsets of theavailable data sample. Changes are implemented in avariety of tests:

• Test A: Using only the part of the data sample cor-responding to the first 2.8 fb−1.

20

• Test B: In addition to the reference selections, re-quiring at least three hits in muon wire chamberlayers B or C, and the χ2 for a fit to a track seg-ment reconstructed in the muon detector to be lessthan 8.

• Test C: Since the background muons are producedby decays of kaons and pions, their track param-eters measured by the central tracker and by themuon system are different. Therefore, the fractionof background strongly depends on the χ2 of thedifference between these two measurements. Therequirement on this χ2 is changed from 40 to 4 inthis study.

• Test D: The maximum value of the transverse im-pact parameter is changed from 0.3 to 0.05 cm, andthe requirement on the longitudinal distance be-tween the point of closest approach to the beamand the associated interaction vertex is changedfrom 0.5 to 0.05 cm. This test serves also asa cross-check against the possible contaminationfrom muons from cosmic rays in the selected sam-ple.

• Test E: Using only low-luminosity events with fewerthan three interaction vertices.

• Test F: Using only events corresponding to two ofthe four possible configurations of the magnets, forwhich the solenoid and toroid polarities are identi-cal.

• Test G: Changing the requirement on the invariantmass of the two muons from 2.8 GeV to 12 GeV.

• Test H: Using the same muon pT requirement, pT >4.2 GeV, over the full detector acceptance.

• Test I: Requiring the muon pT to be < 7.0 GeV.

• Test J: Requiring the azimuthal angle φ of the muontrack to be in the range 0 < φ < 4 or 5.7 < φ <2π. This selection excludes muons directed to theregion of poor muon identification efficiency in thesupport structure of the detector.

• Test K: Requiring the muon η to be in the range|η| < 1.6 (this test serves also as a cross-checkagainst the possible contamination from muons as-sociated with the beam halo).

• Test L: Requiring the muon η to be in the range|η| < 1.2 or 1.6 < |η| < 2.2.

• Test M: Requiring the muon η to be in the range|η| < 0.7 or 1.2 < |η| < 2.2.

• Test N: Requiring the muon η to be in the range0.7 < |η| < 2.2.

• Test O: Using like-sign dimuon events passing atleast one single muon trigger, while ignoring therequirement of a dimuon trigger for these events.

• Test P: Using like-sign dimuon events passing bothsingle muon and dimuon triggers.

A summary of the results from these studies is pre-sented in Tables XIV and XV. The last line, denoted as“significance”, gives the difference between the referenceresult (column Ref) and each modification, divided by itsuncertainty, and taking into account the overlap betweenthe samples. The statistical uncertainties are used in thecalculation of the significance of the difference betweentwo results. These tests demonstrate an impressive sta-bility of the Absl result, and provide a strong confirmationof the validity of the method. As a result of the variationsof the selection criteria, all input quantities are changedover a wide range, while the asymmetry Absl remains wellwithin the assigned uncertainties. For example, the un-corrected asymmetry A changes by a factor ≈ 1.5 in testC, while the asymmetry Absl changes by less than 7%. Itshould also be noted that reducing the kaon backgroundin test C yields a negative asymmetry A.

Figure 16 shows the observed and expected uncor-rected like-sign dimuon charge asymmetry as a functionof the dimuon invariant mass. The expected asymme-try is computed using Eq. (12) and all the measure-ments of the sample composition and of the asymme-tries. We compare the expected uncorrected asymmetryusing two different assumptions for Absl. In Fig. 16(a)the observed asymmetry is compared to the expectationfor Absl = 0, while Fig. 16(b) shows the expected asym-metry for Absl = −0.00957. A possible systematic dis-crepancy between the observed and expected asymme-tries can be observed for Absl = 0, while it essentiallydisappears for the measured Absl value corresponding toEq. (65). It can also be seen that the observed asymme-try changes as a function of the dimuon invariant mass,and that the expected asymmetry reproduces this effectwhen Absl = −0.00957. This dependence of the asymme-try on the invariant mass of the muon pair is a complexfunction of the production mechanism, of the mass ofthe particles being produced and of their decays. Theagreement between the observed and expected asymme-tries indicates that the physics leading to the observedasymmetry is well described by the contributions fromthe backgrounds and from decaying b hadrons.

We conclude that our method of analysis provides aconsistent description of the dimuon charge asymmetryfor a wide range of input parameters, even for signifi-cantly modified selection criteria.

In addition to the described consistency checks, we per-form other studies to verify the validity of the analysismethod. These tests are described in Appendices C, D,and E. We determine the asymmetry of track recon-struction and the asymmetry of trigger selection. Wealso measure the ratio FK/fK using an alternative fit-ting procedure. These studies do not show any bias in

21

TABLE XIV: Measured asymmetry Absl with reference selections (column Ref) and variations A – H.

Ref A B C D E F G HN(µµ)× 10−6 3.731 1.809 2.733 1.809 1.785 2.121 1.932 1.736 1.783a× 102 +0.955 +0.988 +0.791 +0.336 +1.057 +0.950 +1.029 +0.955 +1.032A× 102 +0.564 +0.531 +0.276 -0.229 +0.845 +0.543 +0.581 +0.821 +0.632α 0.959 0.901 0.942 1.089 1.083 0.902 0.915 1.029 0.877[(2− Fbkg)∆− αfSδ]× 102 −0.065 −0.072 −0.143 −0.200 −0.074 −0.075 −0.069 −0.023 −0.061Fbkg 0.409 0.372 0.401 0.303 0.384 0.385 0.426 0.449 0.343

Absl × 102 −0.957 −0.976 −1.084 −0.892 −1.107 −0.888 −1.096 −0.873 −0.769σ(Absl)× 102 (stat) 0.251 0.330 0.293 0.315 0.402 0.328 0.375 0.388 0.336Significance 0.090 0.846 0.324 0.478 0.326 0.498 0.281 0.779

TABLE XV: Measured asymmetry Absl with reference selections (column Ref) and variations I – P.

Ref I J K L M N O PN(µµ)× 10−6 3.731 2.569 2.208 1.884 1.909 2.534 2.122 2.002 1.772a× 102 +0.955 +0.896 +1.002 +0.984 +1.098 +0.679 +1.097 +0.968 +0.968A× 102 +0.564 +0.407 +0.648 +0.576 +0.630 +0.353 +0.748 +0.722 +0.692α 0.959 0.975 0.913 0.895 0.877 0.940 0.949 0.983 0.934[(2− Fbkg)∆− αfSδ]× 102 −0.065 −0.101 −0.079 −0.125 −0.142 −0.081 −0.019 −0.046 −0.044Fbkg 0.409 0.439 0.412 0.363 0.365 0.412 0.452 0.419 0.398

Absl × 102 −0.957 −1.295 −0.710 −0.851 −0.801 −0.759 −1.102 −0.897 −0.833σ(Absl)× 102 (stat) 0.251 0.314 0.320 0.320 0.383 0.275 0.344 0.346 0.349Significance 1.798 1.241 0.482 0.539 1.317 0.622 0.240 0.485

the extracted value of Absl.

XVI. COMPARISON WITH EXISTINGMEASUREMENTS

The measured value of Absl places a constraint on thecharge asymmetries of semileptonic decays of B0

d and B0s

mesons, and the CP -violating phases of the B0d and B0

s

mass mixing matrices. Calculating the coefficients inEq. (A9) assuming the current PDG values [2] for allparameters (details are given in Appendix A), we obtain

Absl = (0.506± 0.043)adsl + (0.494± 0.043)assl. (66)

Figure 17 presents this measurement in the adsl–assl plane,

together with the existing direct measurements of adslfrom the B-Factories [23] and of our independent mea-surement of assl in B0

s → DsµX decays [24]. UsingEqs. (65) and (66) and the current experimental valueof adsl = −0.0047± 0.0046 [23], we obtain

assl = −0.0146± 0.0075. (67)

This agrees with our direct measurement of assl =−0.0017± 0.0091 [24].

An independent method for measuring φs is throughB0s → J/ψφ decays. Such measurements have been per-

formed by the D0 [25] and CDF [26] Collaborations. Allmeasurements are consistent and the combined value ofφs differs from the standard model prediction by abouttwo standard deviations [27].

Taking into account the experimental constraints onadsl [23], Fig. 18 shows the 68% and 95% C.L. regionsof ∆Γs and φs obtained from our measurement. The68% and 95% C.L. regions from the D0 measurementusing the B0

s → J/ψφ decay [25] are also included in thisfigure. Since the sign of ∆Γs is not known, there is alsoa mirror solution with φs → −π − φs, corresponding tothe change ∆Γs → −∆Γs. It can be seen that the D0results are consistent. Figure 19 shows the probabilitycontours in the (φs,∆Γs) plane for the combination ofour measurement with the result of Ref. [25].

XVII. CONCLUSIONS

We have measured the like-sign dimuon charge asym-metry Absl of semileptonic b-hadron decays:

Absl = −0.00957± 0.00251 (stat)± 0.00146 (syst). (68)

This measurement is obtained from a data set corre-sponding to 6.1 fb−1 of integrated luminosity collectedwith the D0 detector at Fermilab Tevatron collider. It isconsistent with our previous measurement [15] obtainedwith 1 fb−1 and supersedes it. This asymmetry is indisagreement with the prediction of the standard modelby 3.2 standard deviations. This is the first evidencefor anomalous CP-violation in the mixing of neutral B-mesons.

22

0

0.005

0.01

0.015

10 20 30 40 50M(µµ) [GeV]

Asy

mm

etry (a)DØ, 6.1 fb-1

- Observed asymmetry- Expected asymmetry for Ab

sl = 0

0

0.005

0.01

0.015

10 20 30 40 50M(µµ) [GeV]

Asy

mm

etry (b)DØ, 6.1 fb-1

- Observed asymmetry- Expected asymmetry for Ab

sl = -0.00957

FIG. 16: The observed and expected like-sign dimuon chargeasymmetries in bins of dimuon invariant mass. The expectedasymmetry is shown for (a) Absl = 0.0 and (b) Absl = −0.00957.

dsla

s sla -1DØ, 6.1 fb

b slDØ A

Standard ModelB Factory W.A.

Xµ sD→ sDØ B

-0.04-0.03-0.02-0.01 0 0.01

-0.03

-0.02

-0.01

0

0.01

FIG. 17: (Color online) Comparison of Absl in data with thestandard model prediction for adsl and assl. Also shown arethe existing measurements of adsl [23] and assl [24]. The errorbands represent the ±1 standard deviation uncertainties oneach individual measurement.

FIG. 18: (Color online) The 68% and 95% C.L. regions ofprobability for ∆Γs and φs values obtained from this mea-surement, considering the experimental constraints on adsl [23].The solid and dashed curves show respectively the 68% and95% C.L. contours from the B0

s → J/ψφ measurement [25].Also shown is the standard model (SM) prediction for φs and∆Γs.

-3 -2 -1

SM

0 1

0.4

0.2

0.0

-0.2

-0.4

68% CL95% CL99% CL

D , 2.8 - 6.1 fb-1

FIG. 19: (Color online) Probability contours in the (φs,∆Γs)plane for the combination of this measurement with the resultof Ref. [25], using the experimental constraints on adsl [23].

Acknowledgments

We thank the staffs at Fermilab and collaboratinginstitutions, and acknowledge support from the DOEand NSF (USA); CEA and CNRS/IN2P3 (France);FASI, Rosatom and RFBR (Russia); CNPq, FAPERJ,FAPESP and FUNDUNESP (Brazil); DAE and DST (In-dia); Colciencias (Colombia); CONACyT (Mexico); KRFand KOSEF (Korea); CONICET and UBACyT (Ar-gentina); FOM (The Netherlands); STFC and the RoyalSociety (United Kingdom); MSMT and GACR (CzechRepublic); CRC Program and NSERC (Canada); BMBF

23

and DFG (Germany); SFI (Ireland); The Swedish Re-search Council (Sweden); and CAS and CNSF (China).

APPENDIX A: THEORY

This Appendix is included for completeness and to de-fine the notations. Assuming CPT symmetry, the mixingand decay of the B0

q , B0q pair (q = s, d) is described [28]

by

id

dt

(B0q (t)

B0q (t)

)=

([Mq M12

q

(M12q )∗ Mq

]− i

2

[Γq Γ12

q

(Γ12q )∗ Γq

])

·(B0q (t)

B0q (t)

), (A1)

where Mq, M12q , Γq, and Γ12

q are the elements of the

mass matrix of the B0q B

0q system. The matrix element

M12q is due to box diagrams [2]. New particles foreseen in

extensions of the standard model can contribute to thesebox diagrams, and physics beyond the standard modelcan therefore modify the phase and amplitude of M 12

q .The eigenvalues of the mass matrix in Eq. (A1) are

Mq +1

2∆Mq −

i

2(Γq −

1

2∆Γq), (A2)

Mq −1

2∆Mq −

i

2(Γq +

1

2∆Γq), (A3)

where, by definition, ∆Mq > 0. Notice the sign conven-tions for ∆Mq and ∆Γq. With this convention, ∆Γq ispositive in the standard model. A violation of the CPsymmetry is caused by a non-zero value of the phase

φq ≡ arg

(−M

12q

Γ12q

). (A4)

The observable quantities are Mq, Γq, ∆Mq, ∆Γq andφq, with

∆Mq = 2∣∣M12

q

∣∣ , ∆Γq = 2∣∣Γ12q

∣∣ cosφq. (A5)

The charge asymmetry aqsl for “wrong-charge”semileptonic B0

q -meson decay induced by oscillations isdefined as

aqsl =Γ(B0

q (t)→ µ+X)− Γ(B0q (t)→ µ−X)

Γ(B0q (t)→ µ+X) + Γ(B0

q (t)→ µ−X). (A6)

This quantity is independent of the lifetime t, and canbe expressed as

aqsl =

∣∣Γ12q

∣∣∣∣M12

q

∣∣ sinφq =∆Γq∆Mq

tanφq. (A7)

The like-sign dimuon charge asymmetry Absl forsemileptonic decays of b hadrons produced in proton-antiproton (pp) collisions is defined as

Absl ≡N++b −N−−b

N++b +N−−b

, (A8)

where N++b and N−−b are the numbers of events contain-

ing two b hadrons that decay semileptonically, producingtwo positive or two negative muons, respectively, withonly the direct semileptonic decays b → µX consideredin the definition of N++

b and N−−b . The asymmetry Abslcan be expressed [10] as

Absl =fdZda

dsl + fsZsa

ssl

fdZd + fsZs, (A9)

where

Zq ≡1

1− y2q

− 1

1 + x2q

, (A10)

yq ≡∆Γq2Γq

, (A11)

xq ≡∆Mq

Γq. (A12)

with q = d, s. The quantities fd and fs are the pro-duction fractions for b → B0

d and b → B0s respectively.

These fractions have been measured for pp collisions atthe Tevatron [2]:

fd = 0.323± 0.037,

fs = 0.118± 0.015. (A13)

All other parameters in (A9) are also taken from Ref. [2]:

xd = 0.774± 0.008,

yd = 0,

xs = 26.2± 0.5,

ys = 0.046± 0.027. (A14)

Substituting these values in Eq. (A9), we obtain

Absl = (0.506± 0.043)adsl + (0.494± 0.043)assl. (A15)

Using the values of adsl, assl from Ref. [1],

adsl(SM) = (−4.8+1.0−1.2)× 10−4

assl(SM) = (2.1± 0.6)× 10−5, (A16)

the predicted value of Absl in the standard model is

Absl(SM) = (−2.3+0.5−0.6)× 10−4. (A17)

The current experimental values of the two semileptonicasymmetries are adsl = −0.0047 ± 0.0046 [23] and assl =−0.0017± 0.0091 [24].

It can be concluded from Eq. (A17) that the standardmodel predicts a small negative value of Absl with rathersmall uncertainty. Any significant deviation of Absl fromthe SM prediction on a scale larger than that of the un-certainty on Absl , would be an unambiguous signal of newphysics.

The asymmetry Absl is also equivalent to the chargeasymmetry of semileptonic decays of b hadrons to “wrongcharge” muons that are induced by oscillations [10], i.e.,

absl ≡Γ(B → µ+X)− Γ(B → µ−X)

Γ(B → µ+X) + Γ(B → µ−X)= Absl. (A18)

24

Without initial flavor tagging it is impossible to correctlyselect the decays producing a muon of “wrong charge”from a sample of semileptonic decays of b quarks. Thecharge asymmetry of semileptonic b hadron decays, con-trary to the charge asymmetry of like-sign dimuons, istherefore reduced by the contribution of decays produc-ing a muon with “correct” charge, and is consequentlyless sensitive to the asymmetry Absl.

New physical phenomena can change the phase andmagnitude of the standard model M 12,SM

s to

M12s ≡M12,SM

s ·∆s = M12,SMs · |∆s| eiφ

∆s , (A19)

where

φs = φSMs + φ∆s ,

φSMs = 0.0042± 0.0014. (A20)

Other changes expected as a result of new sources of CPviolation [1] are

∆Ms = ∆MSMs · |∆s| = (19.30± 6.74) ps−1 · |∆s| ,

(A21)

∆Γs = 2∣∣Γ12s

∣∣ cosφs = (0.096± 0.039) ps−1 · cosφs,

(A22)

∆Γs∆Ms

=

∣∣Γ12s

∣∣∣∣∣M12,SM

s

∣∣∣· cosφs|∆s|

= (4.97± 0.94) · 10−3 · cosφs|∆s|

,

(A23)

assl =

∣∣Γ12s

∣∣∣∣∣M12,SM

s

∣∣∣· sinφs|∆s|

= (4.97± 0.94) · 10−3 · sinφs|∆s|

.

(A24)

The B0s → J/ψφ decay can also be used to investigate

CP violation. In that case, the CP -violating phase ob-tained from fits to the B0

s → J/ψφ angular distributionsis modified as follows [1]:

φJ/ψφs = −2βSMs + φ∆s , (A25)

where

βSMs = arg[−VtsV ∗tb/(VcsV ∗cb)] = 0.019± 0.001 (A26)

and the quantities Vts, Vtb, Vcs, and Vcb are the parame-ters of the CKM matrix. The contribution of new physics

to φs and φJ/ψφs are identical.

APPENDIX B: RECONSTRUCTION OFEXCLUSIVE DECAYS

1. Reconstruction of KS mesons

The KS meson is used to reconstruct the K∗+ me-son [11] and to measure the fraction and asymmetry of

π → µ tracks. The KS → π+π− decay is reconstructedby requiring two tracks with opposite charge. Each trackmust have an impact parameter significance with respectto the interaction vertex > 3, where the significance is de-fined as

√[εT /σ(εT )]2 + [εL/σ(εL)]2, and εT (εL) is the

projection of the track impact parameter on the planetransverse to the beam direction (along the beam di-rection), and σ(εT )[σ(εL)] is its uncertainty. At leastone of the tracks must have an impact parameter signif-icance > 4, and at least one of the particles must havepT > 1.5 GeV. The two tracks must share a common ver-tex that is separated from the primary interaction pointby more than 4 mm in the transverse plane. The signifi-cance of the reconstructed impact parameter for the KS

must be < 4. All KS candidates satisfying these selec-tion criteria are used to reconstruct the K∗+ → KSπ

+

decay. In addition, for the measurement of the fractionand asymmetry of π → µ tracks, we require that one ofthe pions from KS decay pass the muon selection givenin Sec. III.

Figure 20 displays the π+π− invariant mass distribu-tion of KS → π+π− candidates in the inclusive muonsample for all π → µ with 7.0 < pT < 10.0 GeV.We show separately the sum and the difference of thedistributions for the samples with positive and negativeπ → µ tracks, which are used to measure the asymmetryof π → µ tracks. The KS signal is fitted with a dou-ble Gaussian, and the background is parameterized bya third degree polynomial for the sum of the two distri-butions and a straight line for their difference. Whilefitting the difference of the distributions all the param-eters describing the KS signal, except its normalization,are fixed to the values obtained from the fit to the sumof the distributions.

2. Reconstruction of K∗+ mesons

The K∗+ [11] signal is obtained by combining the re-constructed KS meson with an additional track whichis assigned the mass of the charged pion. The KS can-didate must satisfy the track selection criteria given inSec. III, except for the requirements on the number ofhits in the tracking detectors and the χ2 of the trackfit. The invariant mass of the π+π− system must be480 < M(π+π−) < 515 MeV. The additional track musthave at least 2 axial and 1 stereo hits in the silicon mi-crostrip detector, at least 3 axial and 3 stereo hits in thefiber tracker, and a track impact parameter significance< 3 relative to the interaction vertex. The cosine of theangle between the direction of the KS meson and theadditional track must be greater than 0.3. The KS andthe additional track must be consistent with sharing thesame interaction vertex.

Figure 21 shows the KSπ+ invariant mass distribution.

The K∗+ signal is fitted with a relativistic Breit-Wignerfunction convoluted with a Gaussian resolution, and the

25

0

5000

10000

15000

0.4 0.45 0.5 0.55 0.6M(π+π-) [GeV]

Ent

ries

/5 M

eV (a)DØ, 6.1 fb-1

χ2/dof = 60/40

0

100

200

300

400

0.4 0.45 0.5 0.55 0.6M(π+π-) [GeV]

Ent

ries

/5 M

eV (b)DØ, 6.1 fb-1

χ2/dof = 39/48

FIG. 20: The π+π− invariant mass distribution of KS can-didates in the inclusive muon sample for π → µ with7.0 < pT < 10.0 GeV. (a) The sum of the distributions forpositive and negative π → µ tracks and (b) their difference.The solid lines present the result of the fit; the dashed linesshow the background contribution.

background is parameterized by the function

fbck(M) = (M −MK −Mπ)p0

× exp(p1M + p2M2 + p3M

3), (B1)

which includes a threshold factor. Here M is the KSπ+

invariant mass, and p0, p1, p2 and p3 are free parameters.Figure 21(b), which shows the difference between datapoints and the result of the fit, demonstrates the goodquality of the fit with χ2/d.o.f. = 54/49. The measuredwidth of the K∗+ meson is Γ(K∗+) = 47.9 ± 1.4(stat)MeV, which is consistent with the current PDG value [2].

3. Reconstruction of K∗0 mesons

TheK∗0 meson is reconstructed by selecting two tracksof opposite charge and assigning one of them the mass ofthe charged kaon. This particle is required to be iden-tified as a muon and to pass the muon selection criteriagiven in Sec. III. The second track is assigned the massof a pion and required to satisfy the criteria used to selectthe pion in the K∗± reconstruction.

Figure 22 shows the K+π− [11] invariant mass distri-bution of the K∗0 candidates with K → µ in the inclu-sive muon sample, while Fig. 23 shows the correspondingmass distribution in the like-sign dimuon sample.

0

1000

2000

3000

x 10 2

0.8 0.9 1 1.1 1.2 1.3M(KSπ+) [GeV]

Ent

ries

/10

MeV (a) DØ, 6.1 fb-1

χ2/dof = 54/49

-1000

0

1000

0.8 0.9 1 1.1 1.2 1.3M(KSπ+) [GeV]

(dat

a-fi

t)/1

0 M

eV (b) DØ, 6.1 fb-1

FIG. 21: (a) The KSπ+ invariant mass distribution of K∗+

candidates in the inclusive muon sample. The solid linepresents the result of the fit; the dashed line shows the back-ground contribution. (b) The difference between data and thefit result.

The measurement of the number of K∗0 → K+π− de-cays with K → µ is complicated because of the largecombinatorial background under the K∗0 signal, and be-cause of the contribution of light meson resonances de-caying to π+π−. The most important contribution comesfrom the ρ0 → π+π− decay with π → µ. It produces apeak in the mass region close to the K∗0 mass. Figure 24shows the mass distribution of simulated ρ0 → π+π− de-cays with one pion assigned the kaon mass. This pion isalso required to satisfy the track selections.

To overcome these misidentification difficulties, the fitto the K+π− mass distribution is performed in severalsteps, assuming for the width of the K∗0 meson the valueobtained in the previous section for theK∗+ meson. Con-trary to the K+π− system, the decays of light resonancesdo not contribute into the KSπ

+ mass distribution be-cause the KS meson is identified unambiguously, and theK∗+ signal is clean and unbiased.

The K∗0 mass and detector resolution for K∗0 →K+π− with K → µ are obtained from a fit to the differ-ence of the K+π− and K−π+ mass distributions. Thereconstruction efficiency of K → µ tracks demonstratesa charge asymmetry ≈6%, (see Sec. XI). Such an asym-metry is significantly smaller for π → µ tracks, and thecontribution of ρ → π+π− and other light resonances istherefore suppressed in the difference of the K+π− andK−π+ mass distributions. In addition, the contributionof the combinatorial background is significantly reduced,

26

0

500

1000

1500

x 10 4

0.8 0.9 1 1.1 1.2 1.3M(K+π-) [GeV]

Ent

ries

/10

MeV (a) DØ, 6.1 fb-1

χ2/dof = 81/45

0

10000

x 10

0.8 0.9 1 1.1 1.2 1.3M(K+π-) [GeV]

(dat

a-fi

t)/1

0 M

eV (b) DØ, 6.1 fb-1

FIG. 22: (a) The K+π− invariant mass distribution of K∗0

candidates in the inclusive muon sample. The solid line cor-responds to the result of the fit and the dashed line shows thecontribution from the combinatorial background. The shadedhistogram is the contribution of ρ0 → π+π− events. (b) Thedifference between data and the result of the fit.

as can be seen in Fig. 25(a). The K∗0 signal is fittedwith a relativistic Breit-Wigner function convoluted witha Gaussian resolution, and the background is parameter-ized by the function (B1). Figure 25(b), which shows thedifference between data and the result of the fit, indicatesa moderate quality for the fit, with χ2/d.o.f. = 71/52.The fit gives σ(M) = 12.2 ± 1.5(stat) MeV for the K∗0

mass resolution of the detector. The mass difference be-tween K∗0 and K∗+ is

M(K∗0)−M(K∗+) = 3.50± 0.66(stat) MeV, (B2)

which is consistent with the PDG value of 4.34 ± 0.36MeV [2].

The number of K∗0 events in the inclusive muon andin the like-sign dimuon samples is determined from thefit of the mass distributions shown in Figs. 22 and 23.The signal is parameterized with the convolution of arelativistic Breit-Wigner function and a Gaussian resolu-tion. The K∗0 mass and width and the detector resolu-tion are fixed in the fit to the values obtained from thefit to the distribution in Fig. 25a. The mass distributionof the ρ0 → π+π− background is taken from the MCsimulation. To improve the quality of the fit, the param-eterization of the background is modified by adding two

0

20000

40000

60000

80000

0.8 0.9 1 1.1 1.2 1.3M(K+π-) [GeV]

Ent

ries

/10

MeV (a) DØ, 6.1 fb-1

χ2/dof = 48/52

0

500

1000

0.8 0.9 1 1.1 1.2 1.3M(K+π-) [GeV]

(dat

a-fi

t)/1

0 M

eV (b) DØ, 6.1 fb-1

FIG. 23: (a) The K+π− invariant mass distribution of K∗0

candidates in the like-sign dimuon sample. The solid linecorresponds to the result of the fit and the dashed line showsthe contribution from the combinatorial background. Theshaded histogram is the contribution of ρ0 → π+π− events.(b) The difference between data and the result of the fit.

0

500

1000

1500

0.8 0.9 1 1.1 1.2 1.3M(K+π-) [GeV]

Ent

ries

/10

MeV DØ MC

FIG. 24: The “K+π−” invariant mass distribution of simu-lated ρ0 → π+π− decays, where the mass of the charged kaonis assigned to one of the two reconstructed tracks.

additional Gaussian terms:

f ′bck(M) = fbck(M)

+ p4 exp(− (M −M1)2

2σ21

)

+ p5 exp(− (M −M2)2

2σ22

). (B3)

27

0

1000

2000

3000

x 10 2

0.8 0.9 1 1.1 1.2 1.3M(K+π-) [GeV]

Ent

ries

/10

MeV (a) DØ, 6.1 fb-1

χ2/dof = 71/52

-10000

0

10000

0.8 0.9 1 1.1 1.2 1.3M(K+π-) [GeV]

(dat

a-fi

t)/1

0 M

eV (b) DØ, 6.1 fb-1

FIG. 25: (a) The difference of the K+π− and K−π+ massdistributions of K∗0 candidates in the inclusive muon sample.The solid line represents the result of the fit, while the dashedline shows the background contribution. (b) The differencebetween data and the result of the fit.

Here fbck(M) is given in (B1). The additional terms areneeded to describe the distortion of the smooth behav-ior of the combinatorial background at large masses ofM ≈ 1.15 GeV, due to the contributions of other lightresonances, and should be considered as a parameteriza-tion of the observed mass distribution rather than thecontribution from specific sources. These terms are sig-nificant only because of the large statistics of the inclu-sive muon sample, which contains about 107 entries perbin in Fig. 22. The fit of the K∗0 signal in the like-signdimuon sample is of the same quality without these ad-ditional terms. The results do not change significantlyif these terms are omitted. The impact of these termson the final measurement is included in the systematicuncertainties of the fractions fK and FK discussed inSec. VIII.

In the fit to the inclusive muon distribution, the pa-rameters M1, M2, σ1, and σ2 and the contribution ofρ0 → π+π−, are allowed to vary. The ratio of the frac-tions of ρ0 and K∗0 mesons is constrained within 10%of the value obtained in the simulation. The fit yieldsM1 = 1.095 ± 0.005 GeV and M2 = 1.170 ± 0.007 GeV,which is far from the region of theK∗0 mass, and does notinfluence the fitted number of K∗0 mesons. The χ2/d.o.f.of the fit is 81/45. The results of the fit and correspond-ing residuals are shown in Fig. 22.

In the fit to the like-sign dimuon distribution the pa-rameters M1, M2, σ1, and σ2 are fixed to the values

obtained in the fit of the inclusive muon sample. Theχ2/d.o.f. of the fit is 48/52. The results of the fit andcorresponding residuals are shown in Fig. 23.

4. Reconstruction of φ(1020) mesons

The φ(1020) meson is reconstructed by selecting twotracks with opposite charge, and assigning both of themthe mass of the charged kaon. One track is required topass the track selections of Sec. III. The second one sat-isfies the same selection criteria as the pion in the K∗±

and K∗0 reconstructions.

Figure 26 shows the K+K− invariant mass distribu-tion of the φ(1020) → K+K− candidates in the inclu-sive muon sample, with an additional requirement onthe transverse momentum of the kaon misidentified asa muon, 4.2 < pT < 7.0 GeV. We display separatelythe sum and the difference of the distributions for theK → µ tracks with positive and negative charges, asdone in the case of KS candidates, and use these distri-butions to measure the asymmetry for K → µ tracks.The φ(1020) signal is fitted with a double Gaussian andthe background is parameterized by the threshold func-tion

fbck(M) = (M − 2MK)p0

× exp(p1M + p2M2 + p3M

3). (B4)

All the parameters describing the signal, except its nor-malization, are fixed in the fit of the difference of theinvariant mass distributions to the values obtained fromthe fit to the sum of the distributions.

5. Reconstruction of Λ baryons

The selection of Λ → pπ− decays [11] follows that ofKS → π+π−, except that one of the tracks is assignedthe mass of the proton. Figure 27 shows the pπ− in-variant mass distribution of Λ → pπ− candidates in theinclusive muon sample, with an additional requirementon the transverse momentum of the proton misidentifiedas a muon, for 4.2 < pT < 7.0 GeV. Also in this case wedisplay separately the distributions for the sum and thedifference of the distributions for Λ and Λ decays, anduse them to determine the asymmetry for p→ µ tracks.The Λ baryon signal is fitted with a Gaussian, while thebackground is parameterized by a fourth (second) degreepolynomial for the sum (difference) of the invariant massdistributions. All parameters describing the signal, ex-cept its normalization, are fixed in the fit of the differenceof the invariant mass distributions to the values obtainedfrom the fit to the sum of the distributions.

28

0

2000

4000

6000

x 10 2

0.98 1 1.02 1.04 1.06M(K+K-) [GeV]

Ent

ries

/2 M

eV (a)DØ, 6.1 fb-1

χ2/dof = 64/27

0

5000

10000

15000

0.98 1 1.02 1.04 1.06M(K+K-) [GeV]

Ent

ries

/2 M

eV (b)DØ, 6.1 fb-1

χ2/dof = 22/35

FIG. 26: The K+K− invariant mass distribution of φ(1020)candidates in the inclusive muon sample for K → µ with4.2 < pT < 7.0 GeV. (a) The sum of distributions of positiveand negative K → µ tracks and (b) their difference. Thesolid lines present the result of the fit and the dashed linesshow the background contribution.

APPENDIX C: TRACK RECONSTRUCTIONASYMMETRY

In this measurement of Absl, we assume that the chargeasymmetry of track reconstruction cancels as a result ofthe regular reversal of the magnets polarity. The methoddeveloped in Secs. V and XI provides a way of evaluatingthis assumption in data by comparing the track chargeasymmetry atrack with that expected from already anal-ysed sources. We select events with one reconstructedmuon and at least one additional track satisfying the se-lection criteria of Sec. III. The muon is not used in thisstudy, but is required since the events are collected withsingle muon triggers. Nevertheless, the charges of themuon and the additional track can be correlated, andthe asymmetry of the inclusive muon events can bias theobserved track asymmetry. To eliminate this bias, weconsider separately events in which the muon and thetrack have equal and opposite charges. The asymmetriesin these samples can be expressed as

aopp = atrack − a,aequal = atrack + a. (C1)

0

10000

20000

1.08 1.1 1.12 1.14 1.16 1.18M(p+π-) [GeV]

Ent

ries

/2 M

eV (a) DØ, 6.1 fb-1

χ2/dof = 33/19

-200

0

200

400

600

1.08 1.1 1.12 1.14 1.16 1.18M(p+π-) [GeV]

Ent

ries

/2 M

eV (b) DØ, 6.1 fb-1

χ2/dof = 53/44

FIG. 27: The pπ− invariant mass distribution of Λ candidatesin the inclusive muon sample for p→ µ with 4.2 < pT < 7.0GeV. (a) The sum of distributions of positive and negativep→ µ tracks and (b) their difference. The solid lines presentthe result of the fit and the dashed lines show the backgroundcontribution.

The asymmetry a is defined in Eq. (6), and the asymme-tries aopp and aequal are computed as

aopp =n+− − n−+

n+− + n−+,

aequal =n++ − n−−n++ + n−−

, (C2)

where nij is the number of events containing a track withcharge i and a muon with charge j. The track asymmetryatrack is computed as

atrack =1

2(aopp + aequal). (C3)

As discussed in Sec. XI, we expect the value of atrack

to contain a contribution from the asymmetry of kaon re-construction, even after averaging over the different mag-net polarities. The expected value of atrack is thereforegiven by:

atrack = atrackK f track

K , (C4)

where f trackK is the fraction of reconstructed tracks that

are kaons, and atrackK is the charge asymmetry of kaon

reconstruction.The fraction f track

K is measured using K∗0 → K+π−

decays [11]. The selected charged particle is assigned the

29

kaon mass and combined with an additional track to pro-duce the K∗0 candidate. The K∗0 selection and fittingprocedure is described in Appendix B. The measurednumber of K∗0 mesons is converted into the number ofkaons using a method similar to that presented in Sec. V.The measured f track

K fraction is assigned a systematic un-certainty as in Sec. VIII.

The same K∗0 → K+π− decay is used to measure thekaon reconstruction asymmetry. This measurement canbe biased by the asymmetry of the muon, because thecharge of the kaon and the muon can be correlated. Thekaon asymmetry is therefore measured separately in thesamples in which the muon and the kaon have equal oropposite charges. The asymmetry atrack

K is computed ina way similar to Eq. (C3):

atrackK =

1

2(aoppK + aequal

K ). (C5)

The K∗0 mass distribution is plotted separately for posi-tive and negative kaons in each sample, and the sum andthe difference of these distributions is fitted to extractthe quantity ∆, corresponding to the difference in thenumber of K∗0 decays with positive and negative kaons,and the quantity Σ, corresponding to their sum. Theasymmetry aopp

K is measured as aoppK = ∆opp/Σopp, and

a similar relation is used to obtain the asymmetry aequalK .

The expected and observed track reconstruction asym-metry, i.e., the right and left side of Eq. (C4), are com-pared in Fig. 28 as a function of track pT . There isexcellent agreement between these two quantities. Theχ2/d.o.f. for their difference is 5.4/5. The fit of δtrack =atrack − atrack

K f trackK to a constant yields the following es-

timate for a residual track asymmetry of

δtrack = +0.00011± 0.00035. (C6)

We conclude that the residual track asymmetry is consis-tent with zero as expected. The uncertainty on this valueis about a factor of 16 times smaller than the observedcharge asymmetry in the like-sign dimuon events. Thisstudy provides an additional confirmation of the validityof the method used in this analysis.

APPENDIX D: TRIGGER ASYMMETRY

We determine the kaon, pion and proton charge asym-metries using events passing at least one single muontrigger, and we apply the same asymmetries to the like-sign dimuon events collected with dimuon triggers. Sim-ilarly, we measure the muon reconstruction asymmetryusing events passing the dimuon triggers, and we use thesame quantity for events collected with the single muontriggers. If the trigger selection is charge asymmetric,and this asymmetry is different for single muon and fordimuon triggers, the obtained value of Absl can be biased.Since we extract the asymmetry Absl from the differenceA−αa, and because the value of α is very close to unity,

0

0.002

0.004

0.006

5 10 15 20 25pT(track) [GeV]

Asy

mm

etry (a) DØ, 6.1 fb-1

-0.002

0

0.002

5 10 15 20 25pT(track) [GeV]

δ trac

k

(b) DØ, 6.1 fb-1

FIG. 28: (a) The expected (points with errors) and measured(histogram with negligible uncertainties) track reconstructionasymmetry. (b) The quantity δtrack = atrack − atrack

K f trackK .

our measurement is especially sensitive to a difference be-tween the charge asymmetry of dimuon and single muontriggers.

To examine the impact of this difference on our re-sult, we repeat the measurement of Absl using dimuonevents passing any single muon trigger without requiringdimuon triggers. The result of this test, given in columnO of Table XV, does not indicate a bias from the trig-ger selection. In addition, we measure Absl using dimuonevents passing both single muon and dimuon triggers.The result of this test is given in column P of Table XV.These two tests provide a residual difference δT betweenthe asymmetry of dimuon triggers and single muon trig-gers of

δT = +0.00010± 0.00029. (D1)

From this result, we conclude that the trigger selectionsdo not produce any significant bias to the value of Absl.

APPENDIX E: ALTERNATIVE MEASUREMENTOF FK/fK

We consider two methods to obtain the parametersαi ≡ F iK/f iK in the pT interval i from

αi = 2Ni(K

∗0 → K → µ)

Ni

nini(K∗0 → K → µ)

, (E1)

30

TABLE XVI: Values of αi ≡ F iK/fiK obtained through two

methods, with their statistical uncertainties.

Bin αi from Table III αi from null fit0 1.309 ± 0.340 0.954 ± 0.2171 0.987 ± 0.082 0.942 ± 0.0692 1.022 ± 0.050 1.031 ± 0.0273 0.758 ± 0.101 0.806 ± 0.0554 1.406 ± 0.159 1.292 ± 0.079

All 0.998 ± 0.038 0.990 ± 0.022

where Ni refers to the like-sign dimuon sample and nirefers to the inclusive muon sample. Ni(K

∗0 → K →µ) and ni(K

∗0 → K → µ) are obtained by fitting theinvariant mass histograms of K∗0 → πK → µ in the like-sign dimuon and inclusive muon samples, respectively.These fits require precise modeling of the ρ0 resonanceand of other backgrounds. In the first method we usethe results listed in Table III and obtain the values of αilisted in Table XVI.

A second set of values for the αi parameters can beobtained by finding a scale factor which minimizes the

differences between invariant mass distributions for theK∗0 candidates in the inclusive muon and dimuon sam-ples (null fit method). Invariant mass distributions forK∗0 candidates analogous to the ones shown in Fig. 22and 23 are built for each bin ofK → µ transverse momen-tum. We scale the invariant mass distribution in the in-clusive muon sample by a factor αiNi/(2ni) and subtractit from the invariant mass distribution obtained from thedimuon sample. The contributions from the ρ resonanceand from other backgrounds cancel to first order in thedifference of the two invariant mass distributions, sim-plifying the convergence of mass fits. We then vary thefactor αi and find the value that yields a null normal-ization factor for the residual K∗0 signal. The statisticaluncertainty on αi is obtained by choosing the value ofthe scale factor which yields a positive (negative) valueof this normalization factor which is equal to its uncer-tainty. The values of αi obtained with this method arealso listed in Table XVI, with their statistical uncertain-ties. There is remarkable agreement between the valuesof αi obtained using the two methods.

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