Measurements of branching fraction ratios and <em>CP</em>-asymmetries in suppressed B⁻ -&gt; D(-&gt; K⁺π⁻)K⁻ and B⁻ -&gt; D(-&gt; K⁺π⁻)π⁻ decays

Article

Reference

Measurements of branching fraction ratios and CP -asymmetries in suppressed B

-> D(-> K

π

)K

and B

-> D(-> K

π

)π

decays

CDF Collaboration

CLARK, Allan Geoffrey (Collab.), et al.

Abstract

We report the first reconstruction in hadron collisions of the suppressed decays B−→D(→K+π−)K− and B−→D(→K+π−)π−, sensitive to the Cabibbo-Kobayashi-Maskawa phase γ, using data from 7  fb−1 of integrated luminosity collected by the CDF II detector at the Tevatron collider. We reconstruct a signal for the B−→D(→K+π−)K− suppressed mode with a significance of 3.2 standard deviations, and measure the ratios of the suppressed to favored

branching fractions R(K)=[22.0±8.6(stat)±2.6(syst)]×10−3,

R+(K)=[42.6±13.7(stat)±2.8(syst)]×10−3, R−(K)=[3.8±10.3(stat)±2.7(syst)]×10−3 as well as the direct CP-violating asymmetry A(K)=−0.82±0.44(stat)±0.09(syst) of this mode.

Corresponding quantities for B−→D(→K+π−)π− decay are also reported.

CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Measurements of branching fraction ratios and CP -asymmetries in suppressed B

-> D(-> K

π

)K

and B

-> D(-> K

π

)π

decays.

Physical Review. D , 2011, vol. 84, no. 09, p. 091504

DOI : 10.1103/PhysRevD.84.091504

Available at:

http://archive-ouverte.unige.ch/unige:38700

Disclaimer: layout of this document may differ from the published version.

1 / 1

Measurements of branching fraction ratios and CP -asymmetries in suppressed B

! Dð! K

ÞK

and B

! Dð! K

Þ

decays

T. Aaltonen,²¹B. A´ lvarez Gonza´lez,^9,xS. Amerio,^41aD. Amidei,³²A. Anastassov,³⁶A. Annovi,¹⁷J. Antos,¹² G. Apollinari,¹⁵J. A. Appel,¹⁵A. Apresyan,⁴⁶T. Arisawa,⁵⁶A. Artikov,¹³J. Asaadi,⁵¹W. Ashmanskas,¹⁵ B. Auerbach,⁵⁹A. Aurisano,⁵¹F. Azfar,⁴⁰W. Badgett,¹⁵A. Barbaro-Galtieri,²⁶V. E. Barnes,⁴⁶B. A. Barnett,²³ P. Barria,^44c,44aP. Bartos,¹²M. Bauce,^41b,41aG. Bauer,³⁰F. Bedeschi,^44aD. Beecher,²⁸S. Behari,²³G. Bellettini,^44b,44a J. Bellinger,⁵⁸D. Benjamin,¹⁴A. Beretvas,¹⁵A. Bhatti,⁴⁸M. Binkley,^15,aD. Bisello,^41b,41aI. Bizjak,^28,bbK. R. Bland,⁵ B. Blumenfeld,²³A. Bocci,¹⁴A. Bodek,⁴⁷D. Bortoletto,⁴⁶J. Boudreau,⁴⁵A. Boveia,¹¹L. Brigliadori,^6b,6aA. Brisuda,¹²

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A. Robson,¹⁹T. Rodrigo,⁹T. Rodriguez,⁴³E. Rogers,²²S. Rolli,^54,iR. Roser,¹⁵M. Rossi,^52aF. Rubbo,¹⁵ F. Ruffini,^44c,44aA. Ruiz,⁹J. Russ,¹⁰V. Rusu,¹⁵A. Safonov,⁵¹W. K. Sakumoto,⁴⁷Y. Sakurai,⁵⁶L. Santi,^52b,52aL. Sartori,^44a

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K. Yi,^15,nJ. Yoh,¹⁵K. Yorita,⁵⁶T. Yoshida,^39,kG. B. Yu,¹⁴I. Yu,²⁵S. S. Yu,¹⁵J. C. Yun,¹⁵A. Zanetti,^52a Y. Zeng,¹⁴and S. Zucchelli^6b,6a

(CDF Collaboration)

1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3University of Athens, 157 71 Athens, Greece

4Institut de Fisica d’Altes Energies, ICREA, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

5Baylor University, Waco, Texas 76798, USA

6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy

6bUniversity of Bologna, I-40127 Bologna, Italy

7University of California-Davis, Davis, California 95616, USA

8University of California-Los Angeles, Los Angeles, California 90024, USA

9Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

10Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

11Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

12Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

14Duke University, Durham, North Carolina 27708, USA

15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

16University of Florida, Gainesville, Florida 32611, USA

17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

18University of Geneva, CH-1211 Geneva 4, Switzerland

19Glasgow University, Glasgow G12 8QQ, United Kingdom

20Harvard University, Cambridge, Massachusetts 02138, USA

21Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

22University of Illinois, Urbana, Illinois 61801, USA

23The Johns Hopkins University, Baltimore, Maryland 21218, USA

24Institut fu¨r Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany

25Center for High Energy Physics: Kyungpook National University, Daegu 702-701, Korea;

Seoul National University, Seoul 151-742, Korea; Sungkyunkwan University, Suwon 440-746, Korea;

Korea Institute of Science and Technology Information, Daejeon 305-806, Korea;

Chonnam National University, Gwangju 500-757, Korea;

Chonbuk National University, Jeonju 561-756, Korea

26Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

27University of Liverpool, Liverpool L69 7ZE, United Kingdom

28University College London, London WC1E 6BT, United Kingdom

29Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

30Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

T. AALTONENet al. PHYSICAL REVIEW D84,091504(R) (2011)

091504-2

31Institute of Particle Physics: McGill University, Montre´al, Que´bec, Canada H3A 2T8; Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6; University of Toronto, Toronto, Ontario, Canada M5S 1A7;

and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3

32University of Michigan, Ann Arbor, Michigan 48109, USA

33Michigan State University, East Lansing, Michigan 48824, USA

34Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

35University of New Mexico, Albuquerque, New Mexico 87131, USA

36Northwestern University, Evanston, Illinois 60208, USA

37The Ohio State University, Columbus, Ohio 43210, USA

38Okayama University, Okayama 700-8530, Japan

39Osaka City University, Osaka 588, Japan

40University of Oxford, Oxford OX1 3RH, United Kingdom

41aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

41bUniversity of Padova, I-35131 Padova, Italy

42LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

44aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy

44bUniversity of Pisa, I-56127 Pisa, Italy

44cUniversity of Siena, I-53100 Siena, Italy

44dScuola Normale Superiore, I-56127 Pisa, Italy

45University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

46Purdue University, West Lafayette, Indiana 47907, USA

47University of Rochester, Rochester, New York 14627, USA

48The Rockefeller University, New York, New York 10065, USA

49aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy

49bSapienza Universita` di Roma, I-00185 Roma, Italy

50Rutgers University, Piscataway, New Jersey 08855, USA

51Texas A&M University, College Station, Texas 77843, USA

52aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, I-33100 Udine, Italy

52bUniversity of Udine, I-33100 Udine, Italy

53University of Tsukuba, Tsukuba, Ibaraki 305, Japan

54Tufts University, Medford, Massachusetts 02155, USA

55University of Virginia, Charlottesville, Virginia 22906, USA

aDeceased

bVisiting from Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy

cVisiting from University of California-Irvine, Irvine, CA 92697, USA

dVisiting from University of California-Santa Barbara, Santa Barbara, CA 93106, USA

eVisiting from University of California-Santa Cruz, Santa Cruz, CA 95064, USA

fVisiting from CERN, CH-1211 Geneva, Switzerland

gVisiting from Cornell University, Ithaca, NY 14853, USA

hVisiting from University of Cyprus, Nicosia CY-1678, Cyprus

iVisiting from Office of Science, U.S. Department of Energy, Washington, DC 20585, USA

jVisiting from University College Dublin, Dublin 4, Ireland

kVisiting from University of Fukui, Fukui City, Fukui Prefecture, Japan 910-0017

lVisiting from Universidad Iberoamericana, Mexico D.F., Mexico

mVisiting from Iowa State University, Ames, IA 50011, USA

nVisiting from University of Iowa, Iowa City, IA 52242, USA

oVisiting from Kinki University, Higashi-Osaka City, Japan 577-8502

pVisiting from Kansas State University, Manhattan, KS 66506, USA

qVisiting from University of Manchester, Manchester M13 9PL, United Kingdom

rVisiting from Queen Mary, University of London, London, E1 4NS, United Kingdom

sVisiting from University of Melbourne, Victoria 3010, Australia

tVisiting from Muons, Inc., Batavia, IL 60510, USA

uVisiting from Nagasaki Institute of Applied Science, Nagasaki, Japan

vVisiting from National Research Nuclear University, Moscow, Russia

wVisiting from University of Notre Dame, Notre Dame, IN 46556, USA

yVisiting from Texas Tech University, Lubbock, TX 79609, USA

zVisiting from Universidad Tecnica Federico Santa Maria, 110v Valparaiso, Chile

aaVisiting from Yarmouk University, Irbid 211-63, Jordan

xVisiting from Universidad de Oviedo, E-33007 Oviedo, Spain

bbOn leave from J. Stefan Institute, Ljubljana, Slovenia

56Waseda University, Tokyo 169, Japan

57Wayne State University, Detroit, Michigan 48201, USA

58University of Wisconsin, Madison, Wisconsin 53706, USA

59Yale University, New Haven, Connecticut 06520, USA (Received 1 September 2011; published 30 November 2011)

We report the first reconstruction in hadron collisions of the suppressed decaysB!Dð!K^þÞK and B!Dð!K^þÞ, sensitive to the Cabibbo-Kobayashi-Maskawa phase , using data from 7 fb¹ of integrated luminosity collected by the CDF II detector at the Tevatron collider.

We reconstruct a signal for the B!Dð!K^þÞK suppressed mode with a significance of 3.2 standard deviations, and measure the ratios of the suppressed to favored branching fractionsRðKÞ ¼

½22:08:6ðstatÞ 2:6ðsystÞ 10³,R^þðKÞ ¼ ½42:613:7ðstatÞ 2:8ðsystÞ 10³,RðKÞ ¼ ½3:8 10:3ðstatÞ 2:7ðsystÞ 10³ as well as the direct CP-violating asymmetry AðKÞ ¼ 0:82 0:44ðstatÞ 0:09ðsystÞ of this mode. Corresponding quantities for B!Dð!K^þÞ decay are also reported.

DOI:10.1103/PhysRevD.84.091504 PACS numbers: 13.25.Hw, 11.30.Er, 14.40.Nd

The measurement of CP-violating asymmetries and branching ratios of B !DK [1] decay modes allows a theoretically clean extraction of the phase ¼argðVudV_ub =VcdV_cb Þ of the Cabibbo-Kobayashi- Maskawa (CKM) quark-mixing matrixVCKM, a fundamen- tal parameter of the standard model [2]. In these decays the interference between the first-order tree amplitudes of the b!cus and b!ucs processes leads to observables that depend on their relative weak phase, their relative strong phaseB, and the magnitude of the amplitude ratio rB [3]. These quantities can all be extracted from data by combining several experimental observables. This can be achieved in several ways, using a variety of D decay channels [4–6]. An accurate knowledge of the value of is instrumental in establishing the possible presence of additional nonstandard modelCP-violating phases in pro- cesses where higher-order diagrams are involved [7,8]. Its current determination has a relative uncertainty, dominated by statistical uncertainties, between 15 and 20%, depend- ing on the method [9].

A promising class of processes consists of B meson decays that are a coherent superposition of the color favored B!D⁰K followed by the doubly Cabibbo suppressed decay D⁰ !K^þ, and of the color sup- pressed B!D⁰K followed by the Cabibbo favored decayD⁰!K^þ. The magnitude of the two amplitudes is comparable, allowing for large CP-violating asymme- tries sensitive to the phase. The following observables can be defined [5]:

RðKÞ¼BðB!½K^þDKÞþBðB^þ!½K^þDK^þÞ BðB!½K^þ_DKÞþBðB^þ!½K^þ_DK^þÞ; RðKÞ¼BðB!½K_DKÞ

BðB!½KDKÞ;

AðKÞ¼BðB!½K^þDKÞBðB^þ!½K^þDK^þÞ BðB!½K^þ_DKÞþBðB^þ!½K^þ_DK^þÞ; where B! ½K^þDK is the suppressed (sup) mode andB! ½K^þ_DK is the favored (fav) mode. In the

approximation of negligibleCPviolation inDdecays and negligibleD⁰-D⁰ mixing, whose effects were shown to be small in Ref. [10], these quantities are related to the CKM phaseby the equations [5]R¼r²_Dþr²_Bþ2rDrBcos cosðBþDÞ, R¼r²_Dþr²_Bþ2rDrBcosðBþDÞ, and A¼2rBrDsinsinðBþDÞ=R, where rD ¼ j^AðD_AðD^00!K_!K^þþÞÞjandD is the corresponding relative strong phase. The smallness of the product of branching fractions for these suppressed final states (Oð10⁷Þ) has been a strong limitation to their use in determinations.

Evidence for the suppressed B!DK channel has only recently been obtained by the Belle Collaboration [11]. The large production rate of B mesons available at hadron colliders offers a unique opportunity for improving the experimental determination of the angle . Measurements of branching fractions and CP-violating asymmetries ofB!DKmodes in less suppressed final states of theDmeson (CP-even modesKK^þand^þ) have already been performed in hadron collisions [12].

However, the small decay rates along with large potential backgrounds from misidentified favored decays, which only differ for the identity of the final particles, make the reconstruction of suppressed modes in hadron collisions significantly more challenging.

In this paper, we describe the first reconstruction of B!DsupK modes performed in hadron collisions, based on data from a total integrated luminosity of 7 fb¹ of pp collisions at ffiffiffi

ps

¼1:96 TeV, collected by the upgraded Collider Detector (CDF II) at the Fermilab Tevatron. We report measurements of RðKÞ, RðKÞ, and AðKÞ for those modes. We also report measurements re- lated to the correspondingDmodes, since measurable, albeit smaller, -dependent asymmetries may also be found in these modes [9]. The maximum possible value of the asymmetry is Amax¼2rBrD=ðr²_Bþr²_DÞ, where rB

can be rBðKÞ or rBðÞ. Taking into account the CKM structure of the contributing processes, we expect that rBðÞis suppressed by a factorjV_cdVus=VudVcsj tan²C

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with respect to r_BðKÞ, where _C is the Cabibbo angle, and we assume the same color suppression factor for both DK and D modes. Using rBðKÞ ¼0:103^þ0:015_0:024 [9], rBðÞ 0:005 [9], and r²_D ¼ ð3:800:18Þ 10³ [13], we expectAmaxðKÞ 0:90andAmaxðÞ 0:16.

CDF II is a multipurpose magnetic spectrometer sur- rounded by calorimeters and muon detectors, and is de- scribed in detail elsewhere [14–17]. The resolution on transverse momentum of charged particles is _pT=p_T ’ 0:07%pT=ðGeV=cÞ, corresponding to a typical mass reso- lution of18 MeV=c² for our signals. The specific ioniza- tion energy loss dE=dx of charged particles can be measured from the charge collected by a gaseous drift chamber, the central outer tracker (COT), and provides 1:5separation between pion and kaon particles forp >

2 GeV=c. Candidate events for this analysis are selected by a three-level online event-selection system (trigger). At level 1, charged particles are reconstructed in the COT by a hardware processor, the extremely fast tracker (XFT) [18]. Two oppositely charged particles are required, with transverse momentapT 2 GeV=cand scalar sum pT1þpT2 5:5 GeV=c. At level 2, another processor, a silicon vertex trigger (SVT) [19], associatesr- position measurements from an inner silicon detector with XFT tracks. This provides a precise measurement of the track impact parameter d0, the transverse distance of closest approach to the beam line. The resolution of the impact parameter measurement is50mfor particles withp_T of about2 GeV=c, including a30mcontribution due to the transverse beam size, and improves for higher trans- verse momenta.

We selectB hadron candidates by requiring two SVT tracks with120d01000m. To reduce background from light-quark jet pairs, the two trigger tracks are re- quired to have an opening angle in the transverse plane 290, and to satisfy the requirement Lxy>

200m, whereL_xyis defined as the distance in the trans- verse plane from the beam line to the reconstructed two-track vertex. The level 1 and 2 trigger requirements are then confirmed at trigger level 3, where the event is fully reconstructed in software.

The events collected by the trigger are further selected by searching for a pair of oppositely charged particles compatible with a two-bodyDdecay. The invariant mass MD of the pair is reconstructed for both pion and kaon assignments of particle identities. Events are accepted for the analysis only when one of the possible masses is compatible with the nominal D mass 1:8495M_D 1:8815 GeV=c², and the alternative combination, MSWðDÞ, is outside a veto region of1:8245MSWðDÞ 1:9045 GeV=c² around the nominalD mass. TheDcan- didate is then combined with a negatively charged particle in the event withp_T >0:4 GeV=cto form aBcandidate.

A three-dimensional kinematic fit of each decay candidate trajectory is performed by constraining the two tracks

forming the D candidate to a common vertex and to the nominalDmass; theDcandidate and the remaining track to a separate vertex; and the reconstructed momentum of theB candidate to point back to the primarypp interac- tion vertex determined from other tracks in the event.

The events are then divided into two nonoverlapping samples, nominally classified as favored or suppressed, according to the relative charge of the B candidate with the decay product of theDthat has been classified as the kaon. The veto requirements applied to theDmass recon- structed with the alternative particle assignment remove a large fraction of the background of favored decays from the sample classified as suppressed, and vice versa, ensuring no overlap between the samples and a complete symmetry of the selection, which is a crucial aspect of the analysis.

The small residual contamination of each sample from events with an incorrect identification ofDdecay products is accounted for as part of the inclusive backgroundB! Dð!XÞ, where X are modes other than K (see be- low). A further veto is applied to the invariant mass formed by the track from the B candidate and the oppositely charged track from theD candidate, again requiring it to be incompatible with the Dmeson mass, using the same range as the first veto. This requirement suppresses the contamination from tracks from real B decays that have been incorrectly labeled as Ddecay products, and is ap- plied symmetrically to both samples. A further suppression of this background is achieved by requiring that the trans- verse distance between B and D decay vertex is greater than 100m. This has the additional effect of reducing contamination from nonresonant three-body decays of the type B^þ!h^þhh^þ, in which all tracks come from a common decay vertex, and wherehindicates eitherKor. Additional requirements are applied to the following observables: the impact parameterd_Bof the reconstructed Bcandidate relative to the beam line; the isolation of theB candidate IB [20]; the goodness of fit of the decay vertex ²_B; the significance of the B hadron decay length LxyðBÞ=L_xyðBÞ; the angle between the three-dimensional momentum of theB candidate and the three-dimensional decay length;R¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

²þ²

p between the track from the B hadron and the D meson; the cosine of the angle between the Dand the flight direction of the B, in the B meson rest frame,cos_D; the difference of the kaon proba- bility [21] values of the tracks forming theDto discrimi- nate kaon-pion pairs from pion-pion and kaon-kaon pairs, . The threshold values for all these requirements, and for the allowed D mass window mentioned above, were determined by an unbiased optimization procedure, max- imizing the quantityNS=ð1:5þ ffiffiffiffiffiffiffi

NB

p Þ[22], with no use of simulated signal. The signalNS is defined as the expected rate of suppressedB!Dsup events. We take advan- tage of our large sample of favoredB!Dfavdecays, using it as a model for the kinematical and particle iden- tification properties of the suppressed decay by simply

considering the swap in sign. The resulting requirements are the following: LxyðBÞ=_LxyðBÞ>12, dB<50m, ²_B<13,IBðcone¼1Þ>0:4,IBðcone¼0:4Þ>0:7, <

0:15,R <1:5,jcos_Dj<0:6, >1. After applying all the above selection criteria, the invariant mass of each B!Dh candidate is evaluated using a nominal pion mass assignment to the particle h coming from the B decay. Figure1shows the distributions forBcandidates.

With the help of large simulated samples ofB mesons, we determine that the only modes contributing non- negligible backgrounds are B!Dð!XÞh, B! D⁰, with D⁰ !D⁰=⁰, nonresonant B ! K^þ, andB⁰ !D₀ l^þ_l. The large contribution of B!Dð!K^þKÞh reported in Refs. [11,23] is strongly suppressed by our selection, since we reconstruct theDmass in theKmass hypothesis.

We use an extended unbinned maximum likelihood fit, exploiting mass and particle identification (PID) informa- tion to statistically separate the B !DK and B ! Dsignals, the combinatorial background, and the phys- ics backgrounds. PID information on the track from theB decay is incorporated in the kaon probability observable [21]. The extended likelihood function is defined asL¼ Q

iPiLi, where i runs over the favored and suppressed modes, positive and negative charges. The Poisson distri- butionPiis equal to^N

tot i

N_i^tot!e, whereN_i^totis the number of events of each subsample and is the expected mean value. The individual likelihood components have the fol- lowing structure:Li¼QN_i^tot

r P

jfjPjðMr; rjrÞ, wheref

and PðM_r; _rj_rÞ are the fractions and the probability density functions of the signal and background modes, and r are other free parameters of the fit, a mass scale parameter with respect to the nominalBmass and a scale factor multiplying the width of the shapes of the B! Dð!K^þÞh signals. The fit is simultaneously per- formed on the favored and suppressed samples. Common parameters are the exponential function for the combina- torial background, whose normalization and slope are de- termined by the fit; the functional expression for signal and background modes; and the ratio between B!D⁰ andB!Dfractions. The numbers of events and the fractions of signal and background are determined by the fit and the observables are extracted from them. We tested on simulation that our fit does not exhibit any significant bias.

The shape of the mass distribution assigned to each signal and physics background has been modeled using simulated events including the effect of final state QED radiation and parametrized with different functions.

Systematic uncertainties are assessed by varying the values of those function parameters within their errors.

A large sample of D^þ!D⁰ð!K^þÞ^þ decays is used to calibrate the averagedE=dxresponse of the detec- tor to kaons and pions, using the charge of the pion in the D^þdecay to determine the identity of theDdecay prod- ucts. The shape of the distribution is calibrated within our own sample, by using kaons and pions from the decay of theDmeson in the favored sample. Uncertainties on the calibration parameters are included in the final systematic uncertainty of A, R, and R, taking into account the full correlation matrix of the parameters characterizing the shape of thedistribution [24].

TheB!DKandB !Devent yields obtained from the fit to the data are reported in TableI. Fit projec- tions on the invariant mass distributions are given in Fig.1.

They provide a consistent description of the observed distributions in the data. We find evidence for a signal in TABLE I. B!DKandB!Devent yields obtained

from the fit to the data. Only statistical uncertainties are quoted.

Dmode B^þ!D^þ B!D B^þ!DK^þ B!DK K^þ(favored) 9882103 9892103 69439 76741

K^þ(suppressed) 249 3110 299 38

2] mass [GeV/c π-

π-

K+

5.2 5.3 5.4 5.5 5.6

2Events per 14 MeV/c

0 10 20 30

40 _-

-) h

+π

→ K D (

-→

B

Data Total

π- -)

+π

→ K

→ D(

B-

) K-

π-

K+

→

→ D(

B-

Physics background Combinatorial background

2] mass [GeV/c π+

π+

K-

5.2 5.3 5.4 5.5 5.6

2Events per 14 MeV/c

0 10 20 30

40 ₊

+) h

-π

→ K D (

→ B+

Data Total

π+ +)

-π

→ K

→ D(

B+

) K+

π+

K-

→

→ D(

B+

Physics background Combinatorial background

FIG. 1 (color online). Invariant mass distributions ofB!Dhfor the suppressed mode (bottom meson on the left and antibottom on the right). The pion mass is assigned to the charged track from theB candidate decay vertex. The projections of the common likelihood fit (see text) are overlaid.

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the B!DK suppressed mode with a significance of 3:2. The significance is evaluated by comparing the likelihood-ratio observed in data with the distribution ex- pected in statistical trials. Several distributions are gener- ated corresponding to different choices of systematic parameters. The quoted significance corresponds to the distribution yielding the most conservativepvalue.

The raw fit results are then corrected for the reconstruc- tion efficiency, due to different probabilities ofK^þ,K, ^þ and to interact with the tracker material. We use previous measurements of^ðK_ðK^þÞÞ¼1:01780:0023ðstatÞ 0:0045ðsystÞ and ^ð_ð^þÞÞ¼0:9970:003ðstatÞ0:006ðsystÞ [25]. We extract ^ðK_ðKþ^þÞÞ¼0:9980:015ðstatÞ 0:016ðsystÞfrom our own sample of favored B!D decays.

Systematic uncertainties are determined by repeating the fit changing the mass and thedE=dxmodel (TableII). The dominant contribution is the uncertainty on the B ! Dð!XÞshape. This is the largest physics background, and it lies under the signal peak.

In summary, we find evidence for the B!Dð!

K^þÞK suppressed mode with a significance of 3.2 Gaussian standard deviations. We measure the ratios of the suppressed ð½K^þ_DK=Þ to favored ð½K^þDK=Þ branching fractions RðKÞ ¼ ½22:0 8:6ðstatÞ 2:6ðsystÞ 10³,R^þðKÞ¼½42:613:7ðstatÞ 2:8ðsystÞ10³, RðKÞ ¼ ½3:810:3ðstatÞ 2:7ðsystÞ 10³ and RðÞ ¼ ½2:80:7ðstatÞ 0:4ðsystÞ 10³, R^þðÞ ¼ ½2:41:0ðstatÞ0:4ðsystÞ 10³, RðÞ ¼ ½3:11:1ðstatÞ 0:4ðsystÞ 10³ as well as the directCP-violating asymmetries

AðKÞ ¼ 0:820:44ðstatÞ 0:09ðsystÞ;

AðÞ ¼0:130:25ðstatÞ 0:02ðsystÞ:

The observed asymmetryAðKÞ deviates from zero by 2.2 standard deviations.

These measurements, performed here for the first time in hadron collisions, are in agreement with previous measure- ments from BABAR [23] and Belle [11] with comparable uncertainties. These results can be combined with other B!DK measurements to improve the determination of the CKM angle.

We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions. This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada;

the National Science Council of the Republic of China;

the Swiss National Science Foundation; the A. P. Sloan Foundation; the Bundesministerium fu¨r Bildung und Forschung, Germany; the Korean World Class University Program, the National Research Foundation of Korea; the Science and Technology Facilities Council and the Royal Society, UK; the Institut National de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Ministerio de Ciencia e Innovacio´n, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; the Academy of Finland; and the Australian Research Council (ARC).

[1] DindicatesD⁰andD⁰, and the charge conjugate state is implied throughout the paper, except in formulas and sentences where both are mentioned explicitly.

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49, 652 (1973); N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963).

[3] rB is defined as the magnitude of the amplitude ratio of the suppressed processb!uover the favored process b!c,rB¼ j^Mðb!uÞ_Mðb!cÞj. Since the suppressed transition is

associated with the B!D⁰K decay and the favored transition with B!D⁰K, rB corresponds also to j^MðB_MðB^!!D^D00KK^ÞÞj. In the text we will distinguish between rB of the kaon, rBðKÞ, and of the pion, rBðÞ. The definitions for the pion are analogous to the definitions for the kaon.

[4] M. Gronau and D. Wyler, Phys. Lett. B 265, 172 (1991); M. Gronau and D. London, Phys. Lett. B 253, 483 (1991).

TABLE II. Summary of systematic uncertainties.

Source RðÞ R^þðÞ RðÞ RðKÞ R^þðKÞ RðKÞ AðÞ AðKÞ

dE=dxmodel <0:0001 <0:0001 <0:0001 0.0001 0.0003 0.0001 <0:01 <0:01 B!Dð!XÞ shape 0.0004 0.0004 0.0004 0.0025 0.0026 0.0026 0.01 0.09 Other backgrounds <0:0001 <0:0001 <0:0001 0.0006 0.0006 0.0005 <0:01 0.02 Efficiency <0:0001 <0:0001 <0:0001 0.0003 0.0009 0.0001 0.01 <0:01 Total 0.0004 0.0004 0.0004 0.0026 0.0028 0.0027 0.02 0.09

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[17] CDF II uses a cylindrical coordinate system in whichis the azimuthal angle,ris the radius from the nominal beam line, andzpoints in the proton-beam direction, with the

origin at the center of the detector. The transverse plane is the plane perpendicular to thezaxis.

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[20] Isolation is defined as IB¼pTðBÞ=ðp_TðBÞ þP

ipTiÞ, wherepTðBÞis the transverse momentum of theBcandi- date, and the sum runs over all other tracks within a cone in thespace around theBflight-direction. Its value is typically higher for bottom-flavored hadrons than for random track combinations.

[21] The kaon probability is defined as ¼

dE=dxmeasdE=dxexpðÞ

dE=dxexpðKÞdE=dxexpðÞ, where dE=dxmeas is the measured specific energy loss of the track and dE=dxexp is the expected energy loss; has an average value of 1 for kaons and 0 for pions.

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