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Measurements of Branching Fractions and Decay Amplitudes in B- Jpsi K^ decays

Measurements of Branching Fractions and Decay Amplitudes in B- Jpsi K^ decays
Measurements of Branching Fractions and Decay Amplitudes in B- Jpsi K^ decays

a r X i v :h e p -e x /0205021v 2 15 M a y 2002BELLE

KEK preprint 2002-17

Belle preprint 2002-11

Measurements of Branching Fractions and Decay Amplitudes in B →J/ψK ?decays K.Abe 9,K.Abe 43,T.Abe 44,I.Adachi 9,Byoung Sup Ahn 16,H.Aihara 45,M.Akatsu 23,Y.Asano 50,T.Aso 49,V.Aulchenko 2,T.Aushev 13,A.M.Bakich 40,Y.Ban 34,E.Banas 28,A.Bay 19,P.K.Behera 51,A.Bondar 2,A.Bozek 28,T.E.Browder 8,B.C.K.Casey 8,Y.Chao 27,B.G.Cheon 39,R.Chistov 13,S.-K.Choi 7,Y.Choi 39,M.Danilov 13,L.Y.Dong 11,S.Eidelman 2,V.Eiges 13,Y.Enari 23,F.Fang 8,C.Fukunaga 47,T.Gershon 9,K.Gotow 52,R.Guo 25,J.Haba 9,K.Hanagaki 35,T.Hara 32,H.Hayashii 24,M.Hazumi 9,E.M.Heenan 22,I.Higuchi 44,T.Higuchi 45,T.Hokuue 23,Y.Hoshi 43,S.R.Hou 27,W.-S.Hou 27,H.-C.Huang 27,T.Igaki 23,T.Iijima 23,K.Inami 23,A.Ishikawa 23,H.Ishino 46,R.Itoh 9,M.Iwamoto 3,H.Iwasaki 9,Y.Iwasaki 9,P.Jalocha 28,J.H.Kang 54,J.S.Kang 16,P.Kapusta 28,S.U.Kataoka 24,N.Katayama 9,H.Kawai 3,Y.Kawakami 23,N.Kawamura 1,T.Kawasaki 30,H.Kichimi 9,D.W.Kim 39,Heejong Kim 54,H.J.Kim 54,H.O.Kim 39,Hyunwoo Kim 16,K.Kinoshita 5,S.Korpar 21,14,P.Kriˇz an 20,14,P.Krokovny 2,R.Kulasiri 5,S.Kumar 33,Y.-J.Kwon 54,https://www.wendangku.net/doc/ea7399863.html,nge 6,36,G.Leder 12,S.H.Lee 38,D.Liventsev 13,J.MacNaughton 12,G.Majumder 41,T.Matsuishi 23,S.Matsumoto 4,T.Matsumoto 23,47,W.Mitaro?12,K.Miyabayashi 24,Y.Miyabayashi 23,H.Miyake 32,H.Miyata 30,

G.R.Moloney 22,S.Mori 50,T.Mori 4,T.Nagamine 44,Y.Nagasaka 10,

T.Nakadaira 45,E.Nakano 31,M.Nakao 9,J.W.Nam 39,Z.Natkaniec 28,

S.Nishida 17,O.Nitoh 48,T.Nozaki 9,S.Ogawa 42,F.Ohno 46,T.Ohshima 23,

T.Okabe 23,S.Okuno 15,S.L.Olsen 8,W.Ostrowicz 28,H.Ozaki 9,

P.Pakhlov 13,H.Palka 28,C.W.Park 16,H.Park 18,K.S.Park 39,

L.E.Piilonen 52,M.Rozanska 28,K.Rybicki 28,H.Sagawa 9,S.Saitoh 9,

Y.Sakai 9,M.Satapathy 51,A.Satpathy 9,5,O.Schneider 19,S.Schrenk 5,

S.Semenov 13,K.Senyo 23,R.Seuster 8,M.E.Sevior 22,H.Shibuya 42,

B.Shwartz 2,V.Sidorov 2,J.B.Singh 33,S.Staniˇc 50,?,A.Sugi 23,

A.Sugiyama 23,K.Sumisawa 9,T.Sumiyoshi 9,47,K.Suzuki 9,S.Suzuki 53,

S.Y.Suzuki 9,T.Takahashi 31,F.Takasaki 9,N.Tamura 30,M.Tanaka 9,

G.N.Taylor 22,Y.Teramoto 31,S.Tokuda 23,M.Tomoto 9,T.Tomura 45,

S.N.Tovey 22,K.Trabelsi 8,T.Tsuboyama 9,T.Tsukamoto 9,S.Uehara 9,

S.Uno9,S.E.Vahsen35,G.Varner8,K.E.Varvell40,C.H.Wang26, J.G.Wang52,M.-Z.Wang27,Y.Watanabe46,E.Won38,B.D.Yabsley52, Y.Yamada9,A.Yamaguchi44,Y.Yamashita29,M.Yamauchi9,

M.Yokoyama45,K.Yoshida23,Y.Yuan11,Y.Yusa44,J.Zhang50, Z.P.Zhang37,V.Zhilich2,Z.M.Zhu34,and D.ˇZontar50

(The Belle Collaboration)

1Aomori University,Aomori

2Budker Institute of Nuclear Physics,Novosibirsk

3Chiba University,Chiba

4Chuo University,Tokyo

5University of Cincinnati,Cincinnati OH

6University of Frankfurt,Frankfurt

7Gyeongsang National University,Chinju

8University of Hawaii,Honolulu HI

9High Energy Accelerator Research Organization(KEK),Tsukuba

10Hiroshima Institute of Technology,Hiroshima

11Institute of High Energy Physics,Chinese Academy of Sciences,Beijing

12Institute of High Energy Physics,Vienna

13Institute for Theoretical and Experimental Physics,Moscow

14J.Stefan Institute,Ljubljana

15Kanagawa University,Yokohama

16Korea University,Seoul

17Kyoto University,Kyoto

18Kyungpook National University,Taegu

19Institut de Physique des Hautes′Energies,Universit′e de Lausanne,Lausanne

20University of Ljubljana,Ljubljana

21University of Maribor,Maribor

22University of Melbourne,Victoria

23Nagoya University,Nagoya

24Nara Women’s University,Nara

25National Kaohsiung Normal University,Kaohsiung

26National Lien-Ho Institute of Technology,Miao Li

27National Taiwan University,Taipei

28H.Niewodniczanski Institute of Nuclear Physics,Krakow

29Nihon Dental College,Niigata

30Niigata University,Niigata

31Osaka City University,Osaka

32Osaka University,Osaka

33Panjab University,Chandigarh

34Peking University,Beijing

35Princeton University,Princeton NJ

36RIKEN BNL Research Center,Brookhaven NY

37University of Science and Technology of China,Hefei

38Seoul National University,Seoul

39Sungkyunkwan University,Suwon

40University of Sydney,Sydney NSW

41Tata Institute of Fundamental Research,Bombay

42Toho University,Funabashi

43Tohoku Gakuin University,Tagajo

44Tohoku University,Sendai

45University of Tokyo,Tokyo

46Tokyo Institute of Technology,Tokyo

47Tokyo Metropolitan University,Tokyo

48Tokyo University of Agriculture and Technology,Tokyo

49Toyama National College of Maritime Technology,Toyama

50University of Tsukuba,Tsukuba

51Utkal University,Bhubaneswer

52Virginia Polytechnic Institute and State University,Blacksburg VA

53Yokkaichi University,Yokkaichi

54Yonsei University,Seoul

?on leave from Nova Gorica Polytechnic,Slovenia

1Introduction

The decay B0→J/ψK?0(K?0→K Sπ0)has the same quark level diagram as B0→J/ψK S and may,therefore,be used for a determination of the CP vio-lation parameter sin2φ1.However,since the J/ψK?system has three possible helicity states with di?erent superpositions of CP eigenstates,the dilution of the CP asymmetry depends on the degree of polarization of the decay.The mix of CP even and odd states must be known before a measurement of sin2φ1 can be attempted.

The CP mix can be determined through a full angular analysis of the?nal state particles to obtain the decay amplitudes of the system in the transversity basis.Once the CP mix is measured,the CP eigenstates of the events may be projected out in a statistical way.The full angular analysis also serves as a test of the factorization hypothesis by measuring the imaginary part of the decay amplitudes.

In this paper,we report the measurements of branching fractions for B0→J/ψK?0and B+→J/ψK?+and the decay amplitudes of the system ob-tained by a full three-dimensional angular analysis.The determination of sin2φ1based on the reconstruction of these decays is described elsewhere[1].

2Data sample

The data sample used in this analysis corresponds to an integrated luminosity of29.4fb?1recorded with the Belle detector[2]at the KEKB electron-positron collider[3].Events are required to satisfy the hadronic event selection criteria[1] and have R2<0.5,where R2is the ratio of the second to zeroth Fox-Wolfram parameters[4].

The branching fractions and decay amplitudes are measured by reconstructing neutral and charged B mesons in B0→J/ψK?0and B+→J/ψK?+(inclusion of charge conjugate modes is implied throughout this paper).The reconstruc-tion of the J/ψis performed using the dilepton decays,J/ψ→e+e?and μ+μ?.For the e+e?mode,electrons and positrons are identi?ed by matching between the energy measured in the electromagnetic calorimeter(ECL)and the momentum measured in the central drift chamber(CDC),the shape of the cluster energy deposit in the ECL,the dE/dx measured in the CDC,and the light yield in the aerogelˇCerenkov counters(ACC).A likelihood is calcu-lated from these measurements and required to be consistent with the electron hypothesis.To correct for energy lost by?nal state radiation,the energy of any cluster in the ECL within0.05radians of the track momentum is added

to that of the track.The invariant mass of each pair of identi?ed electrons is calculated,and the pair is identi?ed as J/ψ→e+e?if the mass is in the range

2.95GeV/c2

3.15GeV/c2.Tracks are identi?ed as muons by means of a likelihood number based on(i)a comparison of the number of layers

with associated hits in the muon detector(KLM)with the number expected based on momentum and(ii)the energy of the associated hit in the ECL.An oppositely charged pair of identi?ed muons is identi?ed as J/ψ→μ+μ?if the

invariant mass is in the range3.05GeV/c2

pectations.The kaon likelihood is obtained by combining measurements of the time of?ight measured by the scintillation counters(TOF),dE/dx by the CDC and the hit information in the ACC.Tracks which are not identi-?ed as kaons and not used as leptons in the J/ψreconstruction are treated as charged pion candidates.K S candidates are reconstructed from pairs of oppositely charged tracks which satisfy three conditions:1)the distance of the closest approach of both tracks to the nominal interaction point is larger than0.03cm,2)the angle between the K S momentum vector and the vec-tor displacement of the K S vertex point from the J/ψvertex is less than 0.15radians,and3)the reconstructed decay vertex of the K S is at least0.1 cm away from the interaction point.Each pair with invariant mass satisfying 0.47GeV/c2

3Measurement of branching fractions

Candidate B0and B+mesons are reconstructed by selecting events with a J/ψand a K?and examining two quantities in the center-of-mass of theΥ(4S), the beam-constrained mass(M bc)and the energy di?erence between the B candidate and the beam energy(?E).The beam-constrained mass,which is the invariant mass of a reconstructed J/ψand K?calculated taking the energy to be the beam energy,is required to be in the range5.20?5.29GeV/c2.For

modes with charged tracks only,|?E|is required to be less than30MeV.For decay modes that include aπ0,?E is required to satisfy?50MeV

For each reconstructed mode,the distribution in M bc is binned and?tted to a parameterized function of the form

f i cf(M bc)+f nr(M bc)+f combi(M bc),(1)

N(M bc)=f sig(M bc)+

i

where f sig,f i cf,f nr,and f combi are the shapes for the signal,background from other B→J/ψK?modes(which we will refer to as cross-feed),background from non-resonant B→J/ψKπ,and combinatorial background,respectively.

f si

g is a Gaussian wit

h the peak position?xed at the B mass and a width that is determined from Monte Carlo.Only the amplitude is varied in?t-ting.f

i cf is described by a separate Gaussian for each of the three J/ψK?decay modes other than the signal mode.Monte Carlo simulations are used to determine the mean and width for each mode,as well as the e?ciency for it to pass the signal mode criteria.The amplitudes of f i cf are scaled such that the ratios of cross-feed to signal e?ciency are?xed assuming equal pro-duction rates and decay branching fractions for the neutral and charged B’s. The rate of cross-feed from B→J/ψK modes is also estimated using Monte Carlo and found to be negligible.The total amount of the cross-feed is esti-mated to be1.8–6.2%(depending on the mode)of the events in the signal region.The shape of f nr is also assumed to be a Gaussian.While the mean and width are expected to be similar to those of f sig,they are determined separately to allow for minor kinematic di?erences,using events in the K?mass sideband(1.1GeV/c2

account the contamination of the combinatorial background in the functions. The estimated contribution of the non-resonant decay in the signal region is 5.2%.f combi is the line shape for the combinatorial background and is modeled by the“ARGUS function”[6],where the parameters are free in the?t.Fig.2 shows the results of the?ts to four modes.The?ts indicate the contamination of the combinatorial background is less than1%in the signal region.

The branching fraction is calculated from the yield in the signal region ob-tained from the?tted f sig.The detection e?ciency for each mode is esti-mated by applying the selection criteria to Monte Carlo event samples.Events are generated unpolarized in the J/ψK?system using the QQ event gen-erator[7]and are passed through a detector simulation program based on GEANT3[8].The estimated e?ciencies are28.4%,20.7%,11.8%,and8.1%, for J/ψK?0(K+π?),J/ψK?+(K Sπ+),J/ψK?+(K+π0)and J/ψK?0(K Sπ0), respectively.The branching fractions of secondary decays are?xed to the PDG values[5]and the numbers of neutral and charged B

B events(1.0%),7)polarization(1.7%),and8)branch-ing fraction for secondary decays(1.7%).The estimate of the non-resonant B→J/ψKπbackground has a relatively large uncertainty because the?t to the Kπmass distribution is poor in the region of Kπmass from1.1GeV/c to1.3GeV/c,where some excess is observed.This excess has also been seen elsewhere[9,10],and there has been some speculation as to its origin[9].As its source is not established,we estimate the uncertainty in its contribution to the signal by including in the?t to the Kπmass distribution an additional term that is constrained to zero at the mass threshold and extends linearly to 1.35GeV/c2.The change to the signal yield due to this modi?cation is taken to be the uncertainty.

The resulting branching fractions are summarized in Table1with the esti-mated systematic errors.

4Measurement of decay amplitudes

The decay amplitudes of B→J/ψK?decays are measured in the transversity basis[11].The direction of motion of the J/ψin the rest frame of the B can-didate is de?ned to be the x-axis.The y-axis is de?ned to be in the direction of the projection of the K momentum into the plane perpendicular to the

x-axis in the B rest frame.The x-y plane contains the momenta of the J/ψ, the K,and theπ.The z-axis is de?ned to be perpendicular to the x-y plane according to the right-hand rule.The angle between the l+direction and the z-axis in the J/ψrest frame is de?ned asθtr.The angle between the x-axis and the projection of the l+momentum onto the x-y plane is de?ned asφtr in the same frame.The angleθK?is de?ned as described in the previous section. The distribution of these three angles for B→J/ψK?decays is described in terms of three amplitudes[12]:

1

d cosθtr d cosθK?dφtr =

9

B0and B?).

|A0|2denotes the longitudinal polarization of J/ψwhile|A⊥|2(|A |2)is the transverse polarization component along the z-axis(y-axis).Also,|A0|2+|A |2 is the amplitude corresponding to the CP-even state,while|A⊥|2is the CP-odd component in B0→J/ψK?0(K?0→K Sπ0).These amplitudes are normalized so that:

|A0|2+|A |2+|A⊥|2=1.(3)

The amplitudes are determined by?tting this function to the measured three-dimensional distribution inθtr,φtr andθK?,taking into account the detection e?ciency and background.The resolution of the angular measurements is estimated by Monte Carlo and found to be typically less than0.02radians. The value ofηis determined from the charge of pions or kaons used in the K?reconstruction.We do not include the B0→J/ψK?0(K Sπ0)mode in the?t since in this caseηis not well-de?ned.

The?t is performed using an unbinned maximum likelihood method.The probability density function(PDF)is de?ned using the theoretical distribution in(2)and can be expressed as

P DF(x,y,z,M bc)=N×[f sig(M bc)×?(x,y,z)×1

dxdydz

(x,y,z)

+

i

f i cf(M bc)×ADF cf(x,y,z)

+f nr(M bc)×ADF nr(x,y,z)

+f combi(M bc)×ADF combi(x,y,z)],(4)

where x=cosθtr,y=φtr,and z=cosθK?,N is the normalization factor of the PDF,?(x,y,z)is the detection e?ciency as a function of the three angles, and ADF cf,ADF nr,ADF combi are the angular shapes for the cross-feed,non-resonant and combinatorial backgrounds,respectively.

Here,f sig(M bc),f i cf(M bc),f nr(M bc),and f combi(M bc)are the fractions of signal events,cross-feed contamination,non-resonant contamination and combina-torial background as a function of beam constrained mass,respectively.These fractions are obtained from the measurements of the branching fractions de-scribed in the previous section.

The detection e?ciency function?(x,y,z)is obtained from a large Monte Carlo sample of1million events for each mode generated without any polarization of the B→J/ψK?system.Events are histogrammed in a20×20×20grid in a cosθtr?φtr?cosθK?cube.The distribution is?tted to a three-dimensional polynomial with correlations taken into account.The e?ciency is almost?at except in the region cosθK?~1,where the pion is slow so that the e?ciency is reduced.

The angular distribution function for the cross-feed background(ADF cf)is determined from the distribution in Monte Carlo events.The function for the non-resonant production(ADF nr)is determined from events in the sideband of the Kπmass distribution.The distribution for the combinatorial background (ADF combi)is obtained from events in the sideband of the beam-constrained mass.These distributions are parameterized as polynomials where the param-eters are determined from the?t.

In the?t to the angular distributions,the imaginary part of A0is de?ned to be zero relative to the imaginary parts of the other amplitudes since the over-all phase of the decay amplitudes is arbitrary.By applying the normalization condition(3),four parameters,|A0|2,|A⊥|2,arg(A )and arg(A⊥)are left be determined from the?t.The normalization of the PDF(N)is calculated by numerical integration over the three dimensional angular cube whenever pa-rameter values are changed.A likelihood is de?ned as the product of the PDF for all the events and the values of parameters are determined by maximizing the likelihood.We perform separate?ts to the three decay modes as well as a combined?t by de?ning a single likelihood.The parameter values determined from these?ts are summarized in Table2.The projected angular distributions

of the data for all K?modes combined are shown in Fig.3.The distributions

are corrected for the e?ects of detector acceptance and backgrounds. Systematics in the?t are studied for the following uncertainties:1)e?ciency

function(Monte Carlo statistics and e?ect of polarization),2)angular dis-tribution functions for backgrounds,3)background fractions,4)slow pion

e?ciency,and5)?t algorithm.These contributions to the systematic error

are summarized in Table3.The dominant contributions arise from the de-pendence of the e?ciency and background functions on the polarization,and

also the uncertainty in the detection e?ciency for slow pions.The?rst un-

certainty is estimated by comparing the functions obtained for Monte Carlo samples generated with and without the polarization in the J/ψK?system.

The second uncertainty dominates in the cosθK?distribution where cosθK?is close to1.The uncertainty is estimated by comparing with the results with a

cut at cosθK?<0.9for decay modes withπ±and with a cut at cosθK?<0.7 for the mode withπ0.The systematics in the?t algorithm are studied using toy Monte Carlo events.The di?erences between input decay amplitudes for

Monte Carlo and the values obtained by the?t are taken as the uncertainties. 5Conclusion

Branching fractions for B0→J/ψK?0and B+→J/ψK?+are measured via reconstruction of K?0→K+π?,K?0→K Sπ0,K?+→K+π0,and K?+→K Sπ+with leptonic decays of J/ψ.The resultant branching frac-tions are Br(B0→J/ψK?0)=(1.29±0.05±0.13)×10?3and Br(B+→J/ψK?+)=(1.28±0.07±0.14)×10?3.These values are consistent with the measurements by CLEO[10]and BaBar[13](Table4).

The decay amplitudes for B→J/ψK?are measured by?tting the angular distribution of?nal state particles in the transversity basis to a theoretical distribution with the e?ects of the detector acceptance and the background taken into account.In the?t,the sum of amplitudes is normalized to1(|A0|2+ |A |2+|A⊥|2=1)and arg(A0)is de?ned to be zero.The?t is performed using an unbinned maximum likelihood method.From the?t,the values obtained are|A0|2=0.618±0.020±0.027,|A⊥|2=0.191±0.023±0.026,arg(A )= 2.83±0.19±0.08,and arg(A⊥)=?0.09±0.13±0.06.The measured value of|A⊥|2shows that the CP even component dominates in the decay B0→J/ψK?0(K Sπ0).The value is used in the determination of sin2φ1as described in[1].Table5shows the comparison with other measurements.The parameter arg(A )is sensitive to?nal state interactions(FSI).A shift from0orπshows the existence of the FSI.The measured value is consistent with results from other experiments[9][14].However,the signi?cance of its deviation fromπis not su?cient to conclude the existence of FSI.

We wish to thank the KEKB accelerator group for the excellent operation of the KEKB accelerator.We acknowledge support from the Ministry of Ed-ucation,Culture,Sports,Science,and Technology of Japan and the Japan Society for the Promotion of Science;the Australian Research Council and the Australian Department of Industry,Science and Resources;the National Science Foundation of China under contract No.10175071;the Department of Science and Technology of India;the BK21program of the Ministry of Education of Korea and the CHEP SRC program of the Korea Science and Engineering Foundation;the Polish State Committee for Scienti?c Research under contract No.2P03B17017;the Ministry of Science and Technology of the Russian Federation;the Ministry of Education,Science and Sport of the Republic of Slovenia;the National Science Council and the Ministry of Education of Taiwan;and the U.S.Department of Energy.

References

[1]K.Abe et al.(Belle Collaboration),“Observation of Mixing-induced CP

Violation in the Neutral B Meson System”,hep-ex/0202027(2002),submitted to Phys.Rev.D;K.Abe et al.(Belle Collaboration),Phys.Rev.Lett.87,091802 (2001).

[2] A.Abashian et al.(Belle Collaboration),Nucl.Inst.and Meth.A479,117

(2002).

[3] E.Kikutani ed.,KEK Preprint2001-157(2001),to appear in Nucl.Inst.and

Meth.A.

[4]G.Fox and S.Wolfram,Phys.Rev.Lett41,1581(1978).

[5] D.E.Groom et al.(Particle Data Group),Eur.Phys.J.C15,1(2000).

[6]H.Albrecht et al.,Phys.Lett.B241,278(1990).

[7]See https://www.wendangku.net/doc/ea7399863.html,/public/CLEO/soft/QQ/.

[8]R.Brun et al.,GEANT3.21,CERN Report No.DD/EE/84-1(1987).

[9] B.Aubert et al.(BaBar Collaboration),Phys.Rev.Lett.87,241801(2001).

[10]C.S.Jessop et al.(CLEO Collaboration),Phys.Rev.Lett.79,4533(1997);

CLEO Collaboration,CLEO CONF96-24(1996).

[11]I.Dunietz,H.Quinn,A.Snyder,W.Toki and H.J.Lipkin,Phys.Rev.D43,2193

(1991).

[12]K.Abe,M.Satpathy and H.Yamamoto,“Time-dependent angular analysis of B

decays”,hep-ex/0103002(2001).

[13]B.Aubert et al.(BaBar Collaboration),Phys.Rev.D65,032001(2002).

[14]T.A?older et al.(CDF Collaboration),Phys.Rev.Lett.85,4668(2000).

Table1

Measured branching fractions for B0→J/ψK?0and B+→J/ψK?+.

Mode

B0→J/ψK?0(K+π?)

1.20±0.20±0.15

1.29±0.05±0.13

1.23±0.11±0.15

B+→J/ψK?+(K+π0)

B+→J/ψK?+

|A0|2arg(A )

B0→J/ψK?0(K+π?)0.195±0.0230.04±0.13 B+→J/ψK?+(K Sπ+)0.171±0.057?0.45±0.33 B+→J/ψK?+(K+π0)0.194±0.087?0.23±0.56

0.617±0.0202.83±0.19

|A0|2arg(A )

E?ciency0.0030.03

ADF for backgrounds0.0030.04

Background fractions0.0010.01

Slow pion e?ciency0.0260.02

Fit algorithm0.0010.01

0.0270.08

Br(B0→J/ψK?0)(×10?3)

CLEO[10]1.41±0.20±0.24

BaBar[13]1.37±0.09±0.11

1.29±0.05±0.13

Table5

Comparison with previous measurements of decay amplitudes in B→J/ψK?.The

?rst(second)quoted error is statistical(systematic).

Group|A⊥|2arg(A⊥)

0.52±0.07±0.043.00±0.37±0.04

0.59±0.06±0.012.2±0.5±0.1

0.60±0.03±0.022.50±0.20±0.08

This measurement0.19±0.02±0.03?0.09±0.13±0.06

M(K +π-

)0(GeV/c 2)

E n t r i e s Fig.1.The invariant Kπmass distribution for B 0→J/ψK ?0(K +π?)candidates.The solid line shows a ?t to two Breit-Wigner functions corresponding to K ?(892)

and K ?2

(1430)with a background function (dashed line).

(GeV/c 2)

M bc E n t r i e s Fig.2.The distributions of the beam-constrained mass for four reconstructed modes.The solid lines show the ?ts.

cos θ

tr φ

tr cos θK *00

N o r m a l i z e d Y i e l d s Fig.3.Projected distributions of cos θtr ,φtr and cos θK ?for the combined data.The distributions are background subtracted and acceptance corrected.The solid line shows the theoretical predictions with the obtained decay amplitudes.

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