Measurement of the ratio of branching fractions <em>B(B^± -&gt; J/ψπ^±)/B(B^± -&gt; J/ψK^±)</em>

Article

Reference

Measurement of the ratio of branching fractions B(B

-> J/ψπ

)/B(B

-> J/ψK

)

CDF Collaboration

CAMPANELLI, Mario (Collab.), et al .

Abstract

We report a measurement of the ratio of branching fractions of the decays B±→J/ψπ± and B±→J/ψK± using the CDF II detector at the Fermilab Tevatron Collider. The signal from the Cabbibo-suppressed B±→J/ψπ± decay is separated from B±→J/ψK± using the B±→J/ψK±

invariant mass distribution and the kinematical differences of the hadron track in the two decay modes. From a sample of 220  pb−1 of pp collisions at s√=1.96  TeV, we observe 91±15 B±→J/ψπ± events together with 1883±34 B±→J/ψK± events. The ratio of branching fractions is found to be B(B±→J/ψπ±)/B(B±→J/ψK±)=(4.86±0.82(stat)±0.15(syst))%.

CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the ratio of branching fractions B(B

-> J/ψπ

)/B(B

-> J/ψK

) . Physical Review. D , 2009, vol. 79, no. 11, p.

112003

DOI : 10.1103/PhysRevD.79.112003

Available at:

http://archive-ouverte.unige.ch/unige:38607

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

1 / 1

Measurement of the ratio of branching fractions BðB

! J= c

Þ=BðB

! J= c K

Þ

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

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

4Baylor University, Waco, Texas 76798, USA

5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy

6Brandeis University, Waltham, Massachusetts 02254, USA

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

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

9University of California, San Diego, La Jolla, California 92093, USA

10University of California, Santa Barbara, Santa Barbara, California 93106, USA

11Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

12Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

14Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

15Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

16Duke University, Durham, North Carolina 27708, USA

17Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

18University of Florida, Gainesville, Florida 32611, USA

19Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

20University of Geneva, CH-1211 Geneva 4, Switzerland

21Glasgow University, Glasgow G12 8QQ, United Kingdom

22Harvard University, Cambridge, Massachusetts 02138, USA

23Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

24University of Illinois, Urbana, Illinois 61801, USA

A. ABULENCIAet al. PHYSICAL REVIEW D79,112003 (2009)

112003-2

25The Johns Hopkins University, Baltimore, Maryland 21218, USA

26Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

27High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan

28Center for High Energy Physics: Kyungpook National University, Taegu 702-701, Korea;

Seoul National University, Seoul 151-742, Korea; and SungKyunKwan University, Suwon 440-746, 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, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7

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

44University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

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

46University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

47Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena, and Scuola 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

52Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza’’, I-00185 Roma, Italy

53Rutgers University, Piscataway, New Jersey 08855, USA

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

55Istituto Nazionale di Fisica Nucleare, University of Trieste/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 25 January 2007; revised manuscript received 19 February 2009; published 10 June 2009) We report a measurement of the ratio of branching fractions of the decaysB!J=c andB! J=cK using the CDF II detector at the Fermilab Tevatron Collider. The signal from the Cabbibo- suppressed B!J=c decay is separated from B!J=cK using the B!J=cK invariant mass distribution and the kinematical differences of the hadron track in the two decay modes. From a sample of 220 pb¹ of pp collisions at ffiffiffi

ps¼1:96 TeV, we observe 9115 B!J=c events together with188334B!J=cKevents. The ratio of branching fractions is found to beBðB! J=cÞ=BðB!J=cKÞ ¼ ð4:860:82ðstatÞ 0:15ðsystÞÞ%.

DOI:10.1103/PhysRevD.79.112003 PACS numbers: 13.25.Hw, 14.40.Nd

kVisiting from Nagasaki Institute of Applied Science.

gVisiting from University of Edinburgh.

mVisiting from University of London, Queen Mary, and Westfield College.

oVisiting from IFIC (CSIC-Universitat de Valencia).

fVisiting from University of Dublin.

eVisiting from University of Cyprus.

dVisiting from Cornell University.

bVisiting from University of Bristol.

hVisiting from University of Heidelberg.

cVisiting from University Libre de Bruxelles.

aVisiting from University of Athens.

nVisiting from Texas Tech University.

jVisiting from University of Manchester.

iVisiting from Universidad Iberoamericana.

lVisiting from University de Oviedo.

MEASUREMENT OF THE RATIO OF BRANCHING. . . PHYSICAL REVIEW D 112003 (2009)

The B!J=c decay is a Cabibbo-suppressed mode proceeding via a b!ccd transition. If the leading-order tree diagram is the dominant contribution, its branching fraction is expected to be5%of that of the Cabibbo-favored mode B !J=c^K. Detailed predic- tions of the ratio are obtained using the hypothesis of factorization of the hadronic matrix elements [1,2], a theo- retical approach widely used in the treatment of nonlep- tonic decays ofBmesons. However, the absence of strong theoretical arguments supporting factorization and the use of phenomenological models, which are a source of theo- retical uncertainties, weaken the reliability of those pre- dictions, which need to be accurately tested on data. Until now, the measurements on theB !J=c ^{decay were} performed by many experiments. The BABAR collabora- tion reported BðB!J=cÞ=BðB!J=c^KÞ ¼ ð5:370:45Þ% with24420B!J=c events [3].

The Belle collaboration reported BðB !J=cÞ ¼ ð3:80:6Þ 10⁵ [4]. A previous study of the B ! J=c decay was also performed by the CLEO collabo- ration [5]. The result of this analysis supersedes the pre- vious CDF result [6].

This paper presents a measurement of the ratio of branching fractions BðB!J=cÞ=BðB ! J=c^KÞ. We use a sample of fully reconstructed B ! J=c^K decays, where J=c !^þ, corresponding to an integrated luminosity offfiffiffi 220 pb¹ of pp collisions at ps

¼1:96 TeV collected by the CDF II detector at Fermilab between February 2002 and August 2003.

The CDF II detector is a multipurpose detector [7] with a central geometry and has a tracking system surrounded by calorimeters and muon detectors. The components of the detector most relevant to this analysis are described briefly here. Charged particle trajectories are reconstructed in the pseudorapidity range jj<1:0, where ¼ lnðtan₂Þ, and is the polar angle measured from the beam line [8]. Trajectories are reconstructed from hits in the silicon microstrip detector [9] and the central outer tracker (COT) [10] which are immersed in a 1.4 T solenoidal magnetic field. The silicon microstrip detector consists of five con- centric layers made of double-sided silicon detectors with radii between 2.5 and 10.6 cm, each providing a position measurement with 15m resolution in ther plane.

The COT is an open-cell drift chamber with 96 measure- ment layers, between 40 and 137 cm in radius, organized into eight alternating axial and2stereo superlayers. The transverse momentum (p_T) resolution is _pT=p_T ’ 0:15%p_TðGeV=cÞ¹. Muon detectors consisting of multi- layer drift chambers are located radially around the outside of the calorimeter [11]. The central muon detector (CMU) covers a range in the pseudorapidity of jj<0:6. The central muon extension (CMX) extends the pseudorapidity coverage to0:6<jj<1:0.

The data sample used in this analysis required a dimuon trigger sensitive to J=c !^þ. The CDF II detector

employs a three-level trigger system to select events of interest efficiently. At the first trigger level, muon candi- dates are identified by matching track segments in the CMU and CMX to coarsely reconstructed COT tracks obtained with the extremely fast tracker [12]. Dimuon triggers use combinations of CMU-CMU and CMU- CMX muons with p_T>1:5ð2:0Þ GeV=c for CMU (CMX) muons. For the data presented here, no additional requirements are made at the second level. At the third trigger level, a detailed reconstruction is performed, and oppositely charged dimuon events with an invariant mass in the range of2:7–4:0 GeV=c² are selected.

In this analysis, we reconstructB!J=c^Kdecays.B meson decay modes involving the well-known J=c ! ^þ decay have been extensively used in other mea- surements at CDF, and their selection criteria are well established. We follow the selection requirements devel- oped in the bhadron mass measurement [13] and apply them to theBdecay mode of interest. To ensure the best momentum scale calibration, the data sample used for this analysis is also kept the same as that for the mass measurement.

The B!J=c^K reconstruction begins by selecting J=c !^þ candidates with pairs of oppositely charged tracks which satisfy the requirements of the di- muon triggers. J=c candidates are further selected by requiring their invariant mass to be within80 MeV=c² of the world averageJ=c mass [14]. After aJ=c candidate is identified, any other charged track is assumed to be a kaon and is combined with the J=c candidate to make a B candidate. The tracks of the kaon and two muons are then fitted to a common three dimensional vertex (3D) while constraining the invariant mass of two muons to the world averageJ=c mass [14]. To ensure good vertex resolution, each track must have hits in at least three silicon vertex detector layers in the r plane and the probability resulting from the 3D vertex fit is required to be greater than 1%.

A number of further requirements are made to improve the signal-to-background separation. Prompt background, with tracks coming directly from the primary vertex, can be reduced by exploiting variables sensitive to the long lifetime of the B meson. To reduce prompt background, the transverse decay length (L_xy) of theB is required to exceed200m, whereL_xy is defined as the vector from the primary vertex to theB decay vertex projected onto thep_T of theB candidate. To further reduce combinato- rial background, we require p_T >6:5 GeV=c for the B candidate andp_T>2:0 GeV=cfor the hadron from theB decay. The values used in the above selection criteria are determined by an iterative optimization procedure in which the significance S= ffiffiffiffiffiffiffiffiffiffiffiffiffi

SþB

p is maximized. The quantityS represents the number of accepted signal events, in this case taken from a Monte Carlo simulation sample, andBis the number of selected B candidates within the mass sidebands of the data.

A. ABULENCIAet al. PHYSICAL REVIEW D79,112003 (2009)

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We measure the following ratio:

BðB!J=cÞ

BðB!J=c^KÞ ¼N_J=c

N_J=cKJ=cK

_J=c ¼r_obs 1 _rel;

(1) wherer_obsðN_J=c=N_J=cKÞis the ratio of the yields of each decay mode, and_relð_J=c=_J=cKÞ is the rela- tive reconstruction efficiency. In this analysis, the quantity r_obsis extracted from an unbinned maximum likelihood fit using the differences between the two decay modes in the mass distribution and is corrected with_relobtained from Monte Carlo simulation.

To build the probability density function (PDF) used in the unbinned maximum likelihood fit, we choose the in- variant mass ofJ=c and a kaon (M_J=cK) as an observable.

There are three components in the distribution of the M_J=cK variable: the B !J=c^K signal, the B ! J=c signal, and the combinatorial background. As demonstrated in the high statistics Dand B mass recon- structions with similar decay topology, the invariant mass distribution of B !J=c^K decay at CDF is well de- scribed by a Gaussian function with a width determined by CDF’s tracking resolution [13,15,16]. Therefore, we model the B !J=c^K signal as a Gaussian centered at the mass ofB (M_B) with a width_K. If the pion mass were assigned to the hadron track originating from the B ! J=c decay, the resulting spectrum would also be a Gaussian centered at M_B. However, assigning the kaon mass to this track produces a spectrum partially overlap- ping theB!J=c^K and shifted in the positive direc- tion. The shifted invariant mass ofB!J=c ^{can be} calculated by an approximation, which has a good agree- ment with the exact value [17],

M⁰²BðÞ ’M²_Bþ ð1þÞðM²_KM²Þ; (2) whereM_KandMare, respectively, the kaon and the pion masses. The purely kinematic variableis defined as E_J=c=P_K, where E_J=c is the J=c ^{energy and P}K is the magnitude of the momentum of the hadron track. Using Eq. (2), theB !J=csignal is modeled as a Gaussian centered atM⁰BðÞwith a width. We find _Kand have almost the same value from the Monte Carlo simula- tion, so we constrain them to be the same value in the fit.

We assume the background mass distribution is a first order polynomial. In the likelihood, we also include the PDF functions of for B!J=c^{K andB}!J=c ^as the distributions for the two signals are found to be slightly different. We parametrize PDF distributions from the Monte Carlo simulation. We also parametrize thedistri- bution of the background, which is obtained from the mass sidebands of the data. These mass sidebands are chosen from 5:2< M_J=cK<5:24 and 5:4< M_J=cK<

5:6 GeV=c² to avoid signal contaminations and other backgrounds from partially reconstructed B mesons that

fall below5:2 GeV=c². The empirical functions used in the parametrizations are

h_J=cXð;f_i; _i; aÞ ¼X³

i¼1

f_iðaÞe ⁱ; (3)

h_bkgð;f_i; _i; aÞ ¼X³

i¼1

f_iðaÞ³e ⁱ; (4) where the symbolXdenotesKorin Eq. (3), andf₁,f₂, andf₃are to be the fractional contributions of each type of function when the functions are properly normalized to 1.

Because of the requirement on thep_T of the hadron track and also of the dimuon triggers, alldistributions show a cutoff around 0.5 in thevariable, and these cutoff values are parametrized byain Eqs. (3) and (4). These parameters of the functions describing thedistributions are fixed in the fit. The distributions of the signal and background, and the results of the parameters are shown in Fig.1. With models for each signal and background, and with the chosen observables, the PDF of theith event is written as p_i¼f_s

1

1þr_obsGðM_J=ⁱ _cKM_B; Þh_J=cKðⁱÞ þ r_obs

1þr_obsGðM_J=ⁱ _cKM⁰BðⁱÞ; Þh_J=cðⁱÞ þ ð1f_sÞBðMⁱ_J=cKÞh_bkgðⁱÞ; (5) wheref_sis the fraction of signal events in the data sample, andr_obsis the ratio between the yields of each signal. The functions,GðMⁱ_J=cKM_B;ÞandGðMⁱ_J=cKM⁰_BðⁱÞ;Þ,

/ PK ψ

EJ/

α

0 2 4 6 8 10 12 14

Entries / 0.1

0 10 20 30 40 50

10-3

×

K+

ψ

→ J/

B+

Background

FIG. 1. The distributions ofB!J=cK, which are ob- tained with Monte Carlo simulation and background obtained from the nonsignal data sample. The solid curves are the corre- sponding parametrization functions from Eqs. (3) and (4). The distributions of the two signals are very similar in shape due to the almost identical kinematics of the two decay modes. To avoid confusion from it, we plot the distribution ofB! J=cK only.

MEASUREMENT OF THE RATIO OF BRANCHING. . . PHYSICAL REVIEW D 112003 (2009)

are Gaussians with a width describing the mass distri- butions of B!J=c^{K and B}!J=c^{, respec-} tively, andBðM_J=ⁱ _cKÞis a first order polynomial function which describes the background mass distribution. The fitting range (5:2< M_J=cK<5:6 GeV=c²) is selected to avoid the backgrounds from partially reconstructedBme- sons, but to include enough of the background region to determine accurately the background shape.L¼Q_N

i¼1p_i is then maximized to obtain the best fit values forM_B,, f_s, and r_obs. The fitter is extensively tested with Monte Carlo samples.

The fit to 2683 candidates falling in the fitting range returns the signal fraction, f_s¼0:7360:012, and the ratio of the yields of each decay mode, r_obs¼ ð4:82 0:81Þ%. These values give188334signal events in the B!J=c^K decay mode and 9115 events in the B!J=c decay mode. The distributions in M_J=cK andfor the events in the data sample are shown in Figs.2 and3, along with the likelihood fit results.

Possible biases in the fitting procedure are investigated by performing the fit on Monte Carlo samples generated by the PDF in Eq. (5), with known composition and with the same size as the data sample. The difference of the ratio between the extracted and the input values is consistent with zero, and the width of the pull distributions is one.

In order to determine the ratio of branching fractions, the ratio of the yields of each decay mode must be corrected with the relative reconstruction efficiency. The relative reconstruction efficiency depends in turn on the different decay in flights and nuclear interaction probabilities of the kaon and pion from the two decay modes and on the slightly different track momentum spectra. The relative reconstruction efficiency for the two decay modes is_rel¼ 0:9910:005 which is derived from the Monte Carlo simulation.

In this analysis, we use a Monte Carlo simulation to parametrize the distributions of each signal and to de-

termine the relative reconstruction efficiency for the two decay modes. The Monte Carlo generation proceeds as follows. Transverse momentum and rapidity distributions of single bquarks are generated based on next-to-leading order perturbative QCD calculation [18]. B meson kine- matic distributions are obtained by simulating Peterson fragmentation [19] on quark-level distributions.

Additional fragmentation particles, correlated bbproduc- tion, and the underlying event structure are not generated.

TheBmeson spectrum used in the Monte Carlo simulation is from the inclusive B!J=c^X measurement [7]. The

CLEOMCprogram [20] is used to decayBmesons into the final states of interest. The simulation of the CDF II detector and trigger is based on aGEANT[21] description.

Since both decay modes of interest have almost identical decay topology and kinematics, most systematic uncertain- ties cancel in this ratio measurement, including uncertain- ties in total integrated luminosity and trigger and reconstruction efficiencies. Remaining systematic uncer- tainties come from the uncertainties in the shapes of the mass distribution, the parametrized PDFs in thevariable, and from the determination of the relative reconstruction efficiency. The largest systematic uncertainty originates from the unknown shape of the combinatorial background in the mass distribution. To estimate this effect, a second order polynomial function is considered as an alternative model for the shape of the background mass distribution.

The modeling of the width of the invariant mass distribu- tion is determined from momentum scale resolution studies [13]. An alternative model from a simple Gaussian is to include an additional Gaussian for potential different mo- mentum resolutions of tracks reconstructed in different detector geometry coverage. We replace a Gaussian with a double Gaussian for modeling each signal mass distribu- tion and fit again to evaluate the uncertainty coming from the non-Gaussian tails in the B !J=c^K mass distri-

/ PK ψ

EJ/

α

0 2 4 6 8 10 12 14

Entries / 0.15

0 20 40 60 80 100 120 140 160 180 200

FIG. 3. The distribution in the data sample (points) com- pared with the results of the likelihood fit; overall (solid line), B!J=cK (dotted line), B!J=c (dashed line), and background (dash-dotted line).

2] )[GeV/c K+

µ-

µ+

M(

5.2 5.25 5.3 5.35 5.4 5.45 5.5 5.55 5.6

2 Entries / 5 MeV/c

0 50 100 150 200 250 300

2] )[GeV/c K+ µ- µ+ M(

5.2 5.25 5.3 5.35 5.4 5.45 2Entries / 5 MeV/c

5 10 15 20 25 30 35 40 45 50

FIG. 2. The invariant mass distribution in the data sample (points) projected with the results of the likelihood fit; overall (solid line),B!J=cK(dotted line),B!J=c(dashed line), and background (dash-dotted line). The inset shows the magnified region of theB!J=c signal.

A. ABULENCIAet al. PHYSICAL REVIEW D79,112003 (2009)

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bution. The uncertainties in the function parameters de- scribing the PDFs, in Eqs. (3) and (4), generate an uncertainty for the ratio measurement. The contribution of this uncertainty is estimated by performing the fit by varying the parametrzation variables of the PDFs by the 1, obtained from Monte Carlo simulation. The uncer- tainty in_reloriginates from the uncertainties of the nuclear interaction and the material description in the detector simulation. TheGEANTsimulation calculates nuclear inter- action probabilities of4%for^þ, andK, and 3% for K^þ. We then assign a 25% uncertainty to the calculated nuclear interaction probabilities as the uncer- tainty of the detector material description in the detector simulation and take the resulting uncertainty in _rel as a systematic uncertainty. We determine the total systematic uncertainty of 3.0% on the measurement by adding the individual uncertainties in quadrature, and the contribu- tions from each source are summarized in TableI.

From Eq. (1), we derived the ratio of branching frac- tions,

BðB!J=cÞ

BðB!J=c^KÞ ¼ ð4:860:82ðstatÞ 0:15ðsystÞÞ%; where the first error is statistical, and the second is systematic.

In conclusion, we present the measurement of the ratio of branching fractions betweenB !J=c ^andB ! J=c^K. This result is consistent with theoretical expecta- tions and the previous measurements, and will improve the present world averageð5:30:4Þ%[14].

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 the 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 Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, UK; the Russian Foundation for Basic Research; the Comisio´n Interministerial de Ciencia y Tecnologı´a, Spain; in part by the European Community’s Human Potential Programme under Contract No. HPRN- CT-2002-00292; and the Academy of Finland.

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[17] M⁰²_BðÞ ¼ M_B² þ ðM²_K M²Þ þ2EJ=cð ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

M²_KþP²_K

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M²þP²_K

q Þ ’ M_B² þ ð1þÞðM²_K M²Þ, assuming p_KM_Kandp_KM. All momentums are calculated in Lab frame.

[18] P. Nason, S. Dawson, and R. K. Ellis, Nucl. Phys.B303, TABLE I. Summary of systematic uncertainties for the ratio of branching fractions,BðB!J=cÞ=BðB!J=cKÞ.

Source Uncertainty of the ratio (%)

Background shape 2.5

Non-Gaussian tail ofB!J=cK 1.2

PDFs parametrization 1.0

Relative reconstruction efficiency 0.5

Total uncertainty 3.0

MEASUREMENT OF THE RATIO OF BRANCHING. . . PHYSICAL REVIEW D 112003 (2009)

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