Measurements of branching fraction ratios and <em>CP</em> asymmetries in B^± -&gt; D_CPK^± decays in hadron collisions

Article

Reference

Measurements of branching fraction ratios and CP asymmetries in B

-> D

K

decays in hadron collisions

CDF Collaboration

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

Abstract

We reconstruct B±→DK± decays in a data sample collected by the CDF II detector at the Tevatron collider corresponding to 1  fb−1 of integrated luminosity. We select decay modes where the D meson decays to either K−π+ (flavor eigenstate) or K−K+, π−π+ (CP-even eigenstates), and measure the direct CP asymmetry ACP+=0.39±0.17(stat)±0.04(syst), and the double ratio of CP-even to flavor eigenstate branching fractions RCP+=1.30±0.24(stat)±0.12(syst). These measurements will improve the determination of the Cabibbo-Kobayashi-Maskawa angle γ. They are performed here for the first time using data from hadron collisions.

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

-> D

K

decays in hadron collisions. Physical Review. D , 2010, vol. 81, no. 03, p. 031105

DOI : 10.1103/PhysRevD.81.031105

Available at:

http://archive-ouverte.unige.ch/unige:38652

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

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Measurements of branching fraction ratios and CP asymmetries in B

! D

K

decays in hadron collisions

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(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, 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

7Brandeis University, Waltham, Massachusetts 02254, USA

8University of California, Davis, Davis, California 95616, USA

9University of California, Los Angeles, Los Angeles, California 90024, USA

10University of California, San Diego, La Jolla, California 92093, USA

11University of California, Santa Barbara, Santa Barbara, California 93106, USA

12Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

13Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

14Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

15Comenius University, 842 48 Bratislava, Slovakia;

Institute of Experimental Physics, 040 01 Kosice, Slovakia

16Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

17Duke University, Durham, North Carolina 27708, USA

18Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

19University of Florida, Gainesville, Florida 32611, USA

20Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

21University of Geneva, CH-1211 Geneva 4, Switzerland

22Glasgow University, Glasgow G12 8QQ, United Kingdom

23Harvard University, Cambridge, Massachusetts 02138, USA

24Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

T. AALTONENet al. PHYSICAL REVIEW D81,031105(R) (2010)

031105-2

25University of Illinois, Urbana, Illinois 61801, USA

26The Johns Hopkins University, Baltimore, Maryland 21218, USA

27Institut fu¨r Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany

28Center 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

29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

30University of Liverpool, Liverpool L69 7ZE, United Kingdom

31University College London, London WC1E 6BT, United Kingdom

32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

34Institute 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

35University of Michigan, Ann Arbor, Michigan 48109, USA

36Michigan State University, East Lansing, Michigan 48824, USA

37Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

38University of New Mexico, Albuquerque, New Mexico 87131, USA

39Northwestern University, Evanston, Illinois 60208, USA

40The Ohio State University, Columbus, Ohio 43210, USA

41Okayama University, Okayama 700-8530, Japan

42Osaka City University, Osaka 588, Japan

43University of Oxford, Oxford OX1 3RH, United Kingdom

44aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

44bUniversity of Padova, I-35131 Padova, Italy

45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

46University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

47aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy

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

nVisitor from Kinki University, Higashi-Osaka City, Japan 577-8502.

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47bUniversity of Pisa, I-56127 Pisa, Italy

47cUniversity of Siena, , I-56127 Pisa, Italy

47dScuola Normale Superiore, I-56127 Pisa, Italy

48University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

49Purdue University, West Lafayette, Indiana 47907, USA

50University of Rochester, Rochester, New York 14627, USA

51The Rockefeller University, New York, New York 10021, USA

52aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy

52bSapienza Universita` di Roma, I-00185 Roma, Italy

53Rutgers University, Piscataway, New Jersey 08855, USA

54Texas A&M University, College Station, Texas 77843, USA

55aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, I-33100 Udine, Italy

55bUniversity of Trieste/Udine, I-33100 Udine, Italy

56University of Tsukuba, Tsukuba, Ibaraki 305, Japan

57Tufts University, Medford, Massachusetts 02155, USA

58Waseda University, Tokyo 169, Japan

59Wayne State University, Detroit, Michigan 48201, USA

60University of Wisconsin, Madison, Wisconsin 53706, USA

61Yale University, New Haven, Connecticut 06520, USA (Received 2 November 2009; published 26 February 2010)

We reconstructB!DKdecays in a data sample collected by the CDF II detector at the Tevatron collider corresponding to1 fb¹ of integrated luminosity. We select decay modes where theDmeson decays to eitherK^þ(flavor eigenstate) orKK^þ,^þ(CP-even eigenstates), and measure the direct CP asymmetry ACPþ¼0:390:17ðstatÞ 0:04ðsystÞ, and the double ratio of CP-even to flavor eigenstate branching fractionsRCPþ¼1:300:24ðstatÞ 0:12ðsystÞ. These measurements will improve the determination of the Cabibbo-Kobayashi-Maskawa angle. They are performed here for the first time using data from hadron collisions.

DOI:10.1103/PhysRevD.81.031105 PACS numbers: 13.25.Hw, 11.30.Er, 14.40.Nd

The measurement of CP asymmetries and branching ratios ofB !DK [1] decay modes allows a theoreti- cally clean extraction of the Cabibbo-Kobayashi-Maskawa (CKM) angle ¼argðV_udV_ub =V_cdV_cb Þ, a fundamental parameter of the standard model [2]. In these decays the interference between the tree amplitudes of theb!cus andb!ucs processes leads to observables that depend on their relative weak phase (), their relative strong phase (_B), and the magnitude ratior_B¼ j^Aðb!uÞ_Aðb!cÞj. These quan- tities can all be extracted from data by combining several experimental observables. This can be achieved in several ways, from a variety ofDdecay channels [3–5].

An accurate knowledge of the value ofis instrumental in establishing the possible presence of additional non- standard modelCP-violating phases in higher-order dia- grams [6,7]. Its current determination is based on a combi- nation of several B!DK measurements performed in e^þe collisions at the ð4SÞ resonance [8–10] and its uncertainty is between 12 and 30 deg, depending on the method [11]. This uncertainty is almost completely deter- mined by the limited size of the data samples available, with theoretical uncertainties playing a negligible role (1%). The large production of B mesons available at hadron colliders could offer a unique opportunity to im- prove the current experimental determination of the angle . However, the feasibility of this kind of measurement in

the larger background conditions of hadronic collisions has never been demonstrated.

In this paper we describe the first measurement of the branching fraction ratios and CP asymmetries of B! DK modes performed in hadron collisions, based on an integrated luminosity of 1 fb¹ ofpp collisions at ffiffiffi

ps

¼ 1:96 TeV collected by the upgraded Collider Detector (CDF II) at the Fermilab Tevatron. We reconstruct events where the D meson decays to the flavor-specific mode K^þ (D⁰_f), or to one of theCP-even modesKK^þand ^þ [DCPþ ¼ ðD⁰þD⁰Þ= ffiffiffi

p2

]. From these modes, the following observables can be defined:

A_CPþ ¼BðB!DCPþKÞ BðB^þ!DCPþK^þÞ BðB!DCPþKÞ þBðB^þ!DCPþK^þÞ;

(1)

RCPþ ¼2BðB!DCPþKÞ þBðB^þ!DCPþK^þÞ BðB !D⁰_fKÞ þBðB^þ!D⁰_fK^þÞ :

(2) With the assumption of noCPviolation inD⁰ decays, and neglecting D⁰-D⁰ mixing [12], these quantities are related to the CKM angleby the equations [3]

RCPþ¼1þr²_Bþ2rcosBcos; (3)

T. AALTONENet al. PHYSICAL REVIEW D81,031105(R) (2010)

031105-4

ACPþ¼2rBsinBsin=RCPþ: (4) For our measurements we adopt the usual approxi- mation RCPþ^R_R^þ, which is valid up to a term r jV_usV_cd=V_udV_csj ’0:01[13], where

R¼BðB !D⁰_fKÞ þBðB^þ!D⁰_fK^þÞ

BðB!D⁰_fÞ þBðB^þ!D⁰_f^þÞ; (5)

Rþ ¼BðB !D_CPþKÞ þBðB^þ!D_CPþK^þÞ BðB!DCPþÞ þBðB^þ!DCPþ^þÞ: (6) The CDF II detector is a multipurpose magnetic spec- trometer surrounded by calorimeters and muon detectors.

The components relevant for this analysis are briefly de- scribed here. A more detailed description can be found elsewhere [14]. Silicon microstrip detectors (SVX II and ISL) [15] and a cylindrical drift chamber (COT) [16]

immersed in a 1.4 T solenoidal magnetic field allow re- construction of charged particles in the pseudorapidity range jj<1:0 [17]. The SVX II detector consists of microstrip sensors arranged in five concentric layers with radii between 2.5 and 10.6 cm, divided into three contig- uous sections along the beam directionz, for a total length of 90 cm. The two additional silicon layers of the ISL help to link tracks in the COT to hits in the SVX II. The COT has 96 measurement layers between 40 and 137 cm in radius, organized into alternating axial and 2 stereo superlayers, and provides a resolution on the trans- verse momentum of charged particles pT=pT ’ 0:15%pT=ðGeV=cÞ. The specific energy loss by ionization (dE=dx) of charged particles in the COT can be measured from the collected charge, which is encoded in the output pulse width of each sense wire.

Candidate events for this analysis are selected by a three-level trigger system. At level 1, charged particles are reconstructed in the COT axial superlayers by a hard- ware processor, the extremely fast tracker (XFT) [18]. Two oppositely charged particles are required, with transverse momenta p_T 2 GeV=c and scalar sum p_T1þp_T2 5:5 GeV=c. At level 2, the silicon vertex trigger (SVT) [19] associates SVX IIrposition measurements with XFT tracks. This provides a precise measurement of the track impact parameter,d0, which is defined as the distance of closest approach to the beam line. The resolution of the impact parameter measurement is50mfor particles with pT of about2 GeV=c, including a30mcontribution due to the transverse beam size, and improves for higher transverse momenta. We select B hadron candidates by requiring two SVT tracks with120 d0 1000m. To reduce background from light-quark jet pairs, the two trigger tracks are required to have an opening angle in the transverse plane 2 90, and to satisfy the requirement L_xy>200m, where L_xy is defined as the distance in the transverse plane from the beam line to the two-track vertex, projected onto the two-track momentum

vector. The level 1 and 2 trigger requirements are then confirmed at trigger level 3, where the event is fully reconstructed.

Reconstruction ofB hadrons begins by looking for a track pair that is compatible with aD⁰decay. The invariant mass (M_D) of the pair is required to be close to the nominal D⁰ mass (1:8< M_D<1:92 GeV=c²). This is checked separately for each of the four possible mass assignments to the two outgoing particles:K^þ,K^þ,K^þK, and ^þ. The D⁰ candidate is combined with a negative charged track in the event with pT >0:4 GeV to form B candidates. A kinematic fit of the decay is performed by constraining the two tracks forming theDcandidate to a common vertex and to the nominalD⁰ mass, theDcandi- date and the remaining track to a separate vertex, and the reconstructed momentum of the B candidate to point back to the luminous region in the transverse plane.

To complete the selection, further requirements are ap- plied on additional observables: the impact parameter (dB) of the reconstructedBcandidate relative to the beam line;

the isolation of the Bcandidate (IB) [20]; the goodness of fit of the decay vertex (²_B); the transverse distance of the D, both relative to the beam [LxyðDÞ] and to theBvertex [L_xyBðDÞ], and the significance of the B hadron decay length [LxyðBÞ=L_xyðBÞ]. We chose the requirement LxyBðDÞ>100m to reduce contamination from (non- resonant) three-body decays of the type B^þ!h^þhh^þ (from here on, we will usehto indicate eitherK or), in which all tracks come from a common decay vertex. In addition, we reject all candidates comprising a pair of tracks with an invariant mass compatible with a J=c ! ^þdecay within2. The threshold values for all other requirements, whose purpose is to reduce combinatorial background, were determined by an unbiased optimization procedure aimed at achieving the best resolution onA_CPþ. This resolution was parametrized as a function of the expected signal yield Sand background level B, by per- forming repeated fits on samples of simulated data ex- tracted from the same multidimensional distribution used as likelihood function in the fit [Eq. (7)]. For each choice of thresholds, the signal S was determined by rescaling the number of observedB!D⁰_f, and the background B was determined from the upper mass sidebands of each data sample (5:4< M_B<5:8 GeV=c²). Based on this optimization procedure, we adopted the following set of requirements: I_B>0:65, ²_B<13, d_B<70m, LxyðBÞ=_LxyðBÞ>12, andLxyðDÞ>400m.

For every B!Dh candidate, a nominal invariant mass is evaluated by assigning the charged pion mass to the particlehcoming from theBdecay. The distributions obtained for the three modes of interest (D!K,KK, or ) are reported in Fig.1. A clear B!D signal is seen in each. Events fromB!DKdecays are expected to form much smaller and wider peaks in these plots, located about 50 MeV=c² below the B !D peaks,

and as such cannot be resolved. The dominant residual backgrounds are random track combinations that meet the selection requirements (combinatorial background), misreconstructed physics background such as B ! D⁰ decay, and, in the D⁰ !KK final state, the non- resonantB!K^þKKdecay, as determined by a study performed on CDF simulation.

We used an unbinned likelihood fit, exploiting kinematic and particle identification information from the measure- ment of dE=dx in a similar way to [21], to separate statistically theB !DKcontributions from theB ! D signals and from the combinatorial background. To make best use of the available information, we fit the three modes simultaneously using a single likelihood function, to take advantage of the presence of parameters common to the three modes.

The likelihood function is L ¼Y

i

ð1bÞX

j

fjL^kin_j L^PID_j þbL^kinc L^PIDc ; (7)

where clabels combinatorial background quantities, bis the combinatorial background fraction, andL^kinandL^PID are defined below. The indexjruns over the modesB ! DK, B!D, nonresonant B!K^þKK and B!^þK, and B!D⁰ (where a soft or ⁰ from theD⁰is undetected) andfjare the fractions to be determined by the fit. The fraction of the physics background (B!D⁰) with respect to the signal is common to the three decays and the fraction of theB ! D_CPþis common to the twoD_CPmodes. As determined from simulation, these modes are the only significant con- tributions within the mass range5:17< M <5:60 GeV=c² chosen for our fit.

Kinematic information is given by three loosely corre- lated observables: (a) the massMD, calculated by assign- ing the pion mass to the track from the B decay; (b) the momentum imbalance , defined as

¼1ptr=pD>0 if ptr< pD;

¼ ð1pD=ptrÞ 0 if ptrpD;

whereptris the momentum of the track from theBcandi- date; and (c) the scalar sum of the Dmomentum and the momentum of the track from theBcandidate (ptot¼ptrþ pD). The above variables uniquely identify the invariant mass MDK evaluated with a kaon mass assignment to the track from theBdecay, through the (exact) relations [22]

M_DK² ¼M_D² þm²m²_K þ2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m²_Dþ p²tot

ð2 Þ²

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m²þ

ptotð1 Þ 2

₂ s

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m²_Kþ

ptotð1 Þ 2

₂

s

; if >0;

M²_DK ¼M²_Dþm²m²_K þ2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m²_Dþ

ptotð1þ Þ 2þ

₂

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

m²þ ptot

2þ ₂ s

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m²_Kþ

ptot

2þ ₂

s

;

if 0. Using these variables, we can write L^kin_j ¼PjðM_Dj ; ptotÞP_jð ; ptotÞ and L^PID_j ¼ PjðdE=dxj ; ptotÞ, where Pj is the probability density function for decay modej. Distributions of the kinematic variables for the signals are obtained from samples of events from the full CDF simulation, while for the combi- natorial background they are obtained from the mass side- bands of data. The shape of the mass distribution assigned to each signal process (B!D andB!DK de- cays) has been modeled in detail from a dedicated study including the effect of final state QED radiation [23]. The simulation results were tested on high-statistics data

2] mass [GeV/c π

π K

5.2 5.3 5.4 5.5

2Events per 5 MeV/c

0 100 200 300 400 500 600

700 B^±→ D_f⁰π±

π±

D0

±→ B

K±

D0

±→ B

π±

D*0

±→ B

combinatorial background

2] mass [GeV/c π

KK

5.2 5.3 5.4 5.5

2Events per 10 MeV/c

0 20 40 60 80 100 120 140 160 180

200 B^±→ D_CP+π^±→ [K^- K⁺]π± π±

DCP+

±→ B

K±

DCP+

±→ B

π±

D*0

±→ B

K±

K+

K-

±→ B

combinatorial background

2] mass [GeV/c π

π π

5.2 5.3 5.4 5.5

2Events per 20 MeV/c

0 20 40 60 80

100 B^±→ D_CP+π^±→ [π^-π⁺]π± π±

DCP+

→ B±

K±

DCP+

±→ B

π±

D*0

±→ B

combinatorial background

FIG. 1 (color online). Invariant mass distributions ofB!Dcandidates for each reconstructed decay mode. The pion mass is assigned to the charged track from theBcandidate decay vertex. The projections of the common likelihood fit (see text) are overlaid for each mode.

T. AALTONENet al. PHYSICAL REVIEW D81,031105(R) (2010)

031105-6

samples ofD⁰ decays, in order to ensure the reliability of the extraction of theDKcomponent in the vicinity of the larger D peak. Exponential functions were used to model the mass distribution of combinatorial background for each mode. The normalization and the slope of these functions are independently determined in the maximum likelihood fit. The particle identification (PID) model of the combinatorial background allows for pion and kaon com- ponents, which are free to vary in the fit.

A large sample ofD^þ!D⁰ð!K^þÞ^þdecays was used to calibrate the dE=dx response of the detector to kaons and pions, using the charge of the pion in theD^þ decay to determine the identity of theD⁰ decay products.

The calibration includes the dependence of the shape and the average of the response curve on particle momentum, and the shape of the distribution of common-mode fluctu- ations. The calibrateddE=dxinformation provides a1:5 separation power between pion and kaon particles ofpT >

2 GeV=c. Uncertainties on the calibration parameters are included in the final systematic uncertainty of ACPþ and RCPþ[22].

The B !DK and B !D signal event yields obtained from the fit to the data are reported in TableI. The fraction of the B!^þK was set by the fit to its lower bound at zero, compatible with the expectation of a negligible contribution, and will be ignored in the follow- ing. The uncorrected values of the double ratio of branch- ing fractions R_CPþ and of the CP asymmetry A_CPþ obtained from the fit areR_CPþ¼1:270:24andA_CPþ ¼ 0:390:17. In the fit,R_CPþandA_CPþare functions of the

fractions [f_jin Eq. (7)] and the total number of events in each subsample.

As a check of the goodness of the fit, and to visualize better the separation between signal and background, we plot distributions of the relative signal likelihoods:

RL¼ pdfðB!DKÞ

pdfðB!DKÞ þpdfðbackgroundÞ (8) where pdfðB!DKÞ is the probability density under the signal hypothesis, and pdf (background) is the probability density under the background hypothesis (including both physics and combinatorial backgrounds, with their mea- sured relative fractions). These distributions are compared to the prediction of our fit in Fig.2, showing a very good agreement. In addition, we plot projections of the fit on the invariant mass distributions, both for the entire sample (Fig. 1), and for a kaon-enriched subsample, where the interesting B!DK components have been enhanced with respect to theB!D by means of adE=dxcut (Fig. 3). All these projections show very good agreement between our fit and the data.

Some corrections are needed to convert our fit results into measurements of the parameters of interest. First, we correct for small biases in the fit procedure itself, as measured by repeated fits on simulated samples:

ðR_CPþÞ ¼ 0:0270:005 and ðA_CPþÞ ¼0:015 0:003. These biases are independent of the true values of A_CPþandR_CPþused in the simulated samples.R_CPþdoes not need any further corrections because detector effects TABLE I. B!DKandB!D event yields obtained from the fit to the data.

Dmode B^þ!D^þ B!D B^þ!DK^þ B!DK B^þ! ½hh^þK^þ B! ½hh^þK K^þ 376968 376368 25026 26627

K^þK 38125 39926 228 4911 31 31 ^þ 10113 11714 66 146

K± f

D0

±→ Relative Likelihood B

0 0.2 0.4 0.6 0.8 1

Frequency per 0.04 ²¹⁰ 103

104

K± f

D0

±→ B

Background

K±

DCP+

±→ Relative Likelihood B

0 0.2 0.4 0.6 0.8 1

Frequency per 0.04 ₁₀ 102

103

] K±

K-

[K+

±→

CP+K

→ D B±

Background

K±

DCP+

±→ Relative Likelihood B

0 0.2 0.4 0.6 0.8 1

Frequency per 0.04

1 10 102

] K±

π-

π+

→ [ K±

DCP

±→ B

Background

FIG. 2 (color online). Relative likelihood forB!DKcandidates for each reconstructed decay mode. The points with the error bars show the distribution obtained on the fitted data sample while the histograms show the distributions obtained by generating signal and background events directly from the total probability distribution function (pdf ) of the fit composition.

cancel in the double ratio of branching fractions. The direct CPasymmetryA_CPþneeds to be corrected for the different probability for K^þ and K mesons to interact with the tracker material. This effect is reproduced well by CDF II detector simulation (traced byGEANT [24]), which yields an estimate ^ðK_ðK^þÞÞ¼1:01780:0023ðstatÞ 0:0045ðsystÞ [25] which has been verified by measurements on data [26].

The corrected results are

R_CPþ¼1:300:24ðstatÞ; (9) ACPþ¼0:390:17ðstatÞ; (10) whereA_CPþwas corrected using the following equation:

A_CPþ¼NðB!D⁰_CPþKÞ^ðK_ðK^þÞÞNðB^þ!D⁰_CPþK^þÞ NðB!D⁰_CPþKÞ^ðK_ðK^þÞÞþNðB^þ!D⁰_CPþK^þÞ:

(11) Systematic uncertainties are listed in TableII. They were determined by generating simulated samples of pseudoex- periments with different underlying assumptions, and checking the effect of such changes on the results of our

measurement procedure. The dominant contributions are uncertainty on thedE=dxcalibration and parametrization, uncertainty on the kinematics of the combinatorial back- ground, and uncertainty on the physics background (B! D⁰) mass distribution. Variations in the model of the combinatorial background included different functional forms of the mass distribution, and alternative ð ; ptotÞ distributions, constrained by comparison with real data in the mass sidebands.

2] mass [GeV/c π

KK

5.2 5.3 5.4 5.5

2Events per 20 MeV/c

0 10 20 30 40 50

60 B^-→ D_CP+π^-→ [K^- K⁺]π-

Negative charge:

π-

DCP+

→ B-

K-

DCP+

→ B-

π-

D*0

→ B-

K-

K+

K-

→ B-

combinatorial background

2] mass [GeV/c π

KK

5.2 5.3 5.4 5.5

2Events per 20 MeV/c

0 10 20 30 40

50 B⁺→ D_CP+π⁺→ [K^- K⁺]π+

Positive charge:

π+

DCP+

→ B+

K+

DCP+

→ B+

π+

D*0

→ B+

K+

K+

K-

→ B+

combinatorial background

2] mass [GeV/c π

π π

5.2 5.3 5.4 5.5

2Events per 20 MeV/c

0 2 4 6 8 10 12 14

16 B^-→ D_CP+π^-→ [π^-π⁺]π-

Negative charge:

π-

DCP+

→ B-

K-

DCP+

→ B-

π-

D*0

→ B-

combinatorial background

2] mass [GeV/c π

π π

5.2 5.3 5.4 5.5

2Events per 20 MeV/c

0 2 4 6 8 10 12 14

16 B⁺→ D_CP+π⁺→ [π^-π⁺]π+

Positive charge:

π+

DCP+

→ B+

K+

DCP+

→ B+

π+

D*0

→ B+

combinatorial background

FIG. 3 (color online). Invariant mass distributions ofB!Dcandidates for each reconstructed decay mode. The pion mass is assigned to the prompt track from theBdecay. A requirement on the PID variable was applied to suppress theDcomponent and favor theDKcomponent. The projections of the likelihood fit for each mode are overlaid. Thepvalue for agreement of data with the fit is 0.95

TABLE II. Summary of systematic uncertainties.

Source R_CPþ A_CPþ

dE=dxmodel 0.056 0.030

D⁰mass model 0.025 0.006

InputB mass to the fit 0.004 0.002

Combinatorial background mass model 0.020 0.001 Combinatorial background kinematics 0.100 0.020

Dkinematics 0.002 0.001

DK kinematics 0.002 0.004

D⁰kinematics 0.004 0.002

Fit bias 0.005 0.003

Total (sum in quadrature) 0.12 0.04

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031105-8