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Search for B+ → J/ψη′K+ and B0 → J/ψη′K0 Decays S Q. L. Xie,10 K. Abe,8 I. Adachi,8 H. Aihara,46 D. Anipko,1 K. Arinstein,1 V. Aulchenko,1 T. Aushev,18,13 T. Aziz,42 S. Bahinipati,4 A. M. Bakich,41 V. Balagura,13 E. Barberio,21 M. Barbero,7 A. Bay,18 I. Bedny,1 K. Belous,12 U. Bitenc,14 I. Bizjak,14 S. Blyth,24 A. Bozek,27 M. Braˇcko,8,20,14 T. E. Browder,7 M.-C. Chang,5 Y. Chao,26 A. Chen,24 K.-F. Chen,26 W. T. Chen,24 B. G. Cheon,3 R. Chistov,13 Y. Choi,40 Y. K. Choi,40 S. Cole,41 J. Dalseno,21 M. Dash,50 A. Drutskoy,4 S. Eidelman,1 D. Epifanov,1 N. Gabyshev,1 T. Gershon,8 A. Go,24 G. Gokhroo,42 H. Ha,16 J. Haba,8 K. Hayasaka,22 H. Hayashii,23 M. Hazumi,8 D. Heffernan,32 T. Hokuue,22 Y. Hoshi,44 S. Hou,24 W.-S. Hou,26 T. Iijima,22 K. Ikado,22 A. Imoto,23 K. Inami,22 A. Ishikawa,46 H. Ishino,47 R. Itoh,8 M. Iwasaki,46 Y. Iwasaki,8 J. H. Kang,51 P. Kapusta,27 N. Katayama,8 H. Kawai,2 T. Kawasaki,29 H. Kichimi,8 H. J. Kim,17 Y. J. Kim,6 S. Korpar,20,14 P. Kriˇzan,19,14 P. Krokovny,8 R. Kulasiri,4 R. Kumar,33 C. C. Kuo,24 A. Kuzmin,1 Y.-J. Kwon,51 S. E. Lee,38 T. Lesiak,27 S.-W. Lin,26 Y. Liu,6 G. Majumder,42 7 F. Mandl,11 T. Matsumoto,48 S. McOnie,41 W. Mitaroff,11 K. Miyabayashi,23 H. Miyake,32 H. Miyata,29 0 Y. Miyazaki,22 R. Mizuk,13 G. R. Moloney,21 J. Mueller,35 Y. Nagasaka,9 E. Nakano,31 M. Nakao,8 Z. Natkaniec,27 0 S. Nishida,8 O. Nitoh,49 T. Ohshima,22 S. Okuno,15 S. L. Olsen,7 Y. Onuki,36 H. Ozaki,8 P. Pakhlov,13 2 G. Pakhlova,13 H. Park,17 L. S. Peak,41 R. Pestotnik,14 L. E. Piilonen,50 A. Poluektov,1 H. Sahoo,7 Y. Sakai,8 n N. Satoyama,39 T. Schietinger,18 O. Schneider,18 J. Schu¨mann,25 K. Senyo,22 M. Shapkin,12 H. Shibuya,43 a J B. Shwartz,1 V. Sidorov,1 A. Sokolov,12 A. Somov,4 S. Staniˇc,30 M. Stariˇc,14 H. Stoeck,41 K. Sumisawa,8 5 T. Sumiyoshi,48 S. Y. Suzuki,8 F. Takasaki,8 K. Tamai,8 M. Tanaka,8 G. N. Taylor,21 Y. Teramoto,31 X. C. Tian,34 2 K. Trabelsi,7 T. Tsuboyama,8 T. Tsukamoto,8 S. Uehara,8 T. Uglov,13 Y. Unno,3 S. Uno,8 P. Urquijo,21 Y. Usov,1 G. Varner,7 C. H. Wang,25 M.-Z. Wang,26 Y. Watanabe,47 R. Wedd,21 E. Won,16 A. Yamaguchi,45 2 v Y. Yamashita,28 M. Yamauchi,8 C. C. Zhang,10 L. M. Zhang,37 Z. P. Zhang,37 V. Zhilich,1 and A. Zupanc14 4 (The Belle Collaboration) 8 0 1Budker Institute of Nuclear Physics, Novosibirsk 0 2Chiba University, Chiba 1 3Chonnam National University, Kwangju 6 4University of Cincinnati, Cincinnati, Ohio 45221 0 5Department of Physics, Fu Jen Catholic University, Taipei / 6The Graduate University for Advanced Studies, Hayama, Japan x 7University of Hawaii, Honolulu, Hawaii 96822 e - 8High Energy Accelerator Research Organization (KEK), Tsukuba p 9Hiroshima Institute of Technology, Hiroshima e 10Institute of High Energy Physics, Chinese Academy of Sciences, Beijing h 11Institute of High Energy Physics, Vienna v: 12Institute of High Energy Physics, Protvino i 13Institute for Theoretical and Experimental Physics, Moscow X 14J. Stefan Institute, Ljubljana r 15Kanagawa University, Yokohama a 16Korea University, Seoul 17Kyungpook National University, Taegu 18Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne 19University of Ljubljana, Ljubljana 20University of Maribor, Maribor 21University of Melbourne, Victoria 22Nagoya University, Nagoya 23Nara Women’s University, Nara 24National Central University, Chung-li 25National United University, Miao Li 26Department of Physics, National Taiwan University, Taipei 27H. Niewodniczanski Institute of Nuclear Physics, Krakow 28Nippon Dental University, Niigata 29Niigata University, Niigata 30University of Nova Gorica, Nova Gorica 31Osaka City University, Osaka 32Osaka University, Osaka 33Panjab University, Chandigarh 34Peking University, Beijing 35University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Typeset by REVTEX 2 36RIKEN BNL Research Center, Upton, New York 11973 37University of Science and Technology of China, Hefei 38Seoul National University, Seoul 39Shinshu University, Nagano 40Sungkyunkwan University, Suwon 41University of Sydney, Sydney NSW 42Tata Institute of Fundamental Research, Bombay 43Toho University, Funabashi 44Tohoku Gakuin University, Tagajo 45Tohoku University, Sendai 46Department of Physics, University of Tokyo, Tokyo 47Tokyo Institute of Technology, Tokyo 48Tokyo Metropolitan University, Tokyo 49Tokyo University of Agriculture and Technology, Tokyo 50Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 51Yonsei University, Seoul (Dated: February 7, 2008) WereporttheresultsofsearchesforB+ →J/ψη′K+ andB0→J/ψη′KS0 decays,usingasample of 388 ×106 BB¯ pairs collected with the Belle detector at the Υ(4S) resonance. No statistically significant signal is found for either of the two decay modes and upper limits for the branching fractionsaredeterminedtobeB(B+ →J/ψη′K+)<8.8×10−5andB(B0 →J/ψη′KS0)<2.5×10−5 at 90% confidencelevel. PACSnumbers: 13.25.Hw,14.40.Gx,14.40.Nd Studies of exclusive B meson decays to charmonium andanelectromagneticcalorimetercomprisedofCsI(Tl) play an important role in exploring CP violation [1] crystals (ECL). These detectors are located inside a su- and in observations of new resonant states that include perconducting solenoid coil that provides a 1.5 T mag- ′ a (cc¯) pair [2] [3]. The decay B → J/ψη K proceeds netic field. An iron flux-return located outside of the via a Cabibbo-allowed and color-suppressed transition coilis instrumentedto detect K0 mesons andto identify L (b → cc¯s) with (ss¯) quark popping. A branching frac- muons. tion comparable to that of the decay B →J/ψφK [4] is Candidates for these two decay modes are recon- therefore expected. structed with the decay chains J/ψ → l+l− (l = e,µ), The B → J/ψη′K decay modes are of particular in- η′ →ηπ+π−, η →γγ and K0 →π+π−. S terest in the search for hybrid charmonium states, ψg, Events are required to pass a basic hadronic event which are excited gluonic (cc¯g) states, which may decay selection [11]. To suppress continuum background to J/ψ+(η(′),φ) [5]. These hybrid states are expected (e+e− → qq¯, where q = u,d,s,c), we require the ratio to be produced in B decays such as B →ψgK. A near- of the second to zeroth Fox-Wolframmoments [12] to be threshold ω J/ψ enhancement in B → KωJ/ψ decays less than 0.5 and the absolute value of the cosine of the observedbyBelle[3]hassomepropertiessimilartothose angle between the B meson and beam direction in the predictedforcc¯-gluonhybridstates[5]. Astate,Y(4260), center-of-mass system to be less than 0.85. recently observed by BaBar in e+e− → Y(4260)γ(ISR) The selectioncriteriafor the J/ψ decayingtol+l− are transitions [6], is alsoa candidate for sucha ψg state [7], identical to those used in our previous papers [11]. J/ψ where γ(ISR) denotes an initial state radiation photon. candidates are pairs of oppositely charged tracks that An enhanced decay rate to J/ψη(′) modes would be a originate from a region within 5 cm of the nominal in- supporting evidence for this assignment. teraction point (IP) along the beam direction and are In this paper, we reportresults on searchesfor the de- positively identified as leptons. In order to reduce the cay modes B+ →J/ψη′K+ and B0 →J/ψη′K0 [8] in a effect of bremsstrahlungor finalstate radiation,photons S sample of 357 fb−1 containing 388 ×106 BB¯ pairs accu- detected in the ECL within 0.05 radians of the original mulated at the Υ(4S) resonance with the Belle detector e− or e+ direction are included in the calculation of the [9] at the KEKB energy asymmetric e+e− collider [10]. e+e−(γ) invariant mass. Because of the radiative low- These are the first results ever presented for these decay masstail,theJ/ψcandidatesarerequiredtobewithinan modes. asymmetricinvariantmass window: −150(−60)MeV/c2 TheBelledetectorisalarge-solid-anglemagneticspec- <Me+e−(γ)(Mµ+µ−)−mJ/ψ <+36(+36)MeV/c2,where trometer that consists of a silicon vertex detector, a 50- m is the nominal J/ψ mass [13]. In order to improve J/ψ layer central drift chamber (CDC), an array of aero- themomentumresolutionoftheJ/ψ signal,avertexand gel threshold Cˇerenkovcounters (ACC), a barrel-like ar- massconstrainedfittothereconstructedJ/ψ candidates rangementof time-of-flight scintillation counters (TOF), isthenperformedandaloosecutonthevertexfitquality 3 is applied. mass (M ≡ E2 −P2) and the energy difference bc beam B In order to identify hadrons, a likelihood L for each (∆E ≡ E − E ), where E is the beam en- i B p beam beam hadron type i (i=π,K and p) is formed using informa- ergy, P and E are the reconstructed momentum and B B tion from the ACC, TOF and CDC (dE/dx). Charged energy of the B candidate. We select both B+ and tracks that were previously identified as electrons or B0 candidates within the range |∆E| < 0.20 GeV and muons are rejected in the hadron identification proce- M > 5.20 GeV/c2 for the final analysis. The signal bc dure. The kaonfromthe B meson andthe pions from η′ regions are defined to be 5.27 GeV/c2 < M < 5.29 bc are selected with the requirements of L /(L +L ) > GeV/c2 and|∆E|< 0.03 GeV for both B+ →J/ψη′K+ K K π 0.4 and L /(L +L ) > 0.1, which have efficiencies of and B0 → J/ψη′K0 modes, which corresponds to three π π K S 82.5% and 89.4%, respectively. standard deviations based on the MC simulation. The η from η′ decay is reconstructed by combining After all selection requirements, about 26.5% of the two photons that do not match to any charged track. B+ → J/ψη′K+ candidates have more than one entry The calorimetercluster energy,E , is requiredto exceed per event; this occurs for 30.0% of the B0 → J/ψη′K0 γ S 50 MeV for both photons. To veto photons from π0, candidates. For these events, the B candidate with the we combine each photon candidate with another pho- best vertex fit quality is used. From a study of MC sim- ton (with E > 50 MeV) and reject it if the invari- ulated events, we conclude that around 81.5% of multi- γ ant mass is consistent with a π0: |M − m | < 18 ple B+ → J/ψη′K+ candidates and 70.0% of multiple γγ π0 MeV/c2. For η candidates, cosθη is used to suppress B0 →J/ψη′K0 candidates are selected correctly by this hel S background, where θη is defined as the angle between procedure. hel the photonmomentumintheη restframe andthe boost The signalyields areextractedby maximizingthe two directionofηinthelaboratoryframe. Signaleventshave dimensional extended likelihood function, a uniform cosθη distribution, whereas random photon hel pairshaveadistributionthatpeaksnear±1. We require − Nk N T|choesθinhηevla|r<ian0t.9m4as(s0.o9f7)thfeorηcchaanrdgieddat(eneisutrreaqlu)irBeddteocabye. L= e NPk! " Nk×Pk(Mbic,∆Ei)#, i=1 k within 0.496 MeV/c2 <M <0.582 MeV/c2 (3σ of the Y X γγ nominal η mass). To improve the momentum resolution whereN isthe totalnumberofcandidateevents,iis the of the η, we apply a mass constrained fit to the recon- identifier of the i-th event, Nk and Pk are the yield and structed η. probability density function (PDF) of the component k, We reconstruct η′ candidates by combining the η and which corresponds to the signal and background. selectedπ+π− candidates. Werequiretheinvariantmass The signal PDFs for the two decay modes are mod- to be 0.940 MeV/c2 < Mηπ+π− < 0.975 MeV/c2. To eled using a sum of two Gaussians for Mbc and a sum of improve the momentum resolution, we apply a vertex two Gaussians plus a bifurcated Gaussian that describes and mass constrained fit on the η′ [14]. the tail of the distribution in ∆E. The PDF parame- For K0 candidates, we impose momentum-dependent ters are initially determined using signal MC and subse- S requirements on the impact parameters from the IP quently the primary Gaussian parameters are corrected for both K0 daughter tracks, the distance between the using a control data sample of B+ → J/ψK∗+ decays S daughter tracks along the beam axis at the K0 vertex, with K∗+ → π0K+. The signal shape parameters are S the difference of azimuthal angles between the K0 mo- kept fixed in the fits to the data. S mentum and the direction of the K0 vertex from the IP, Thedominantbackgroundcomesfromrandomcombi- S andtheflightlengthoftheK0. Theinvariantmassofthe nation of J/ψ, η′, and K candidates in BB¯ events. The S K0 candidateisrequiredtobewithin16MeV/c2 (3σ)of background from continuum is found to be small (a few S the K0 mass. We applyvertexandmassconstrainedfits %). A threshold function [15] is used for the M PDF. S bc forthe K0 candidatesto improvethe momentumresolu- For ∆E, we use a first-order polynomial function. The S tion. MC study shows that the background from the decays These criteria maximize Nsig/ Nsig+Nbkg, where with similar topologythat wouldmake a peak in Mbc or N is the number of expected signal events from sig- ∆E distributions is negligible. sig p nal Monte Carlo (MC) samples with assumed branching In the fit, the value of N and the parameters for k fractions of 1.0 × 10−5 for both B+ → J/ψη′K+ and the combinatoric background are allowed to float. Fig- B0 → J/ψη′K0 modes, and N is the number of ex- ures 1 and 2 show the (M , ∆E) scatterplots and their S bkg bc pected background events estimated from a MC sample projections for candidates after all selections are ap- of BB¯-pairs with a J/ψ in the final state. plied. The fit results are superimposed on the projec- B mesons are reconstructed by combining a J/ψ, an tions. There are 37 candidate events in the signalregion η′ and a K candidate. We identify B candidates us- for B+ →J/ψη′K+ and two for B0 →J/ψη′K0. S ing two widely used kinematic variables calculated in TableIsummarizesthemaximum-likelihoodfitresults the center-of-mass system: the beam-energy constrained forthesignal(Y)andsignal-regionbackground(b)yields 4 0.2 DE(GeV)000..01.155 (a) Evt./10.0 MeV11802 asblialgcnkaglround (b) 2vt./2.0 MeV/c1102 asblialgcnkaglround (c) E 8 0 6 6 -0.05 4 4 -0.1 -0.15 2 2 -0.2 0 0 5.2 5.22 5.24 5.26 5.28 5.3 -0.2-0.15-0.1-0.05 0 0.050.10.150.2 5.2 5.22 5.24 5.26 5.28 5.3 M (GeV/c2) D E(GeV) M (GeV/c2) bc bc FIG. 1: (a) The (Mbc, ∆E) scatterplot of B+ → J/ψη′K+ candidates and its projections onto (b) ∆E with 5.27 GeV/c2 <Mbc < 5.29 GeV/c2 and (c) Mbc with |∆E|<0.03 GeV. The dashed lines and solid boxes indicate the signal regions. The curvesare the result of thefit as described in the text. 0.2 5 DE(GeV)000..01.155 (a) Evt./10.0 MeV 456 asblialgcnkaglro(ubn)d 2Evt./2.0 MeV/c34..3455 asblialgcnkaglround (c) 0 2.5 3 -0.05 2 2 1.5 -0.1 1 1 -0.15 0.5 -0.2 0 0 5.2 5.22 5.24 5.26 5.28 5.3 -0.2-0.15-0.1-0.05 0 0.050.10.150.2 5.2 5.22 5.24 5.26 5.28 5.3 M (GeV/c2) D E(GeV) M (GeV/c2) bc bc FIG. 2: (a) The (Mbc, ∆E) scatterplot of B0 → J/ψη′KS0 candidates and its projections onto (b) ∆E with 5.27 GeV/c2 <Mbc<5.29GeV/c2 and(c)Mbc with|∆E|<0.03GeV.Thedashedlinesandthesolidboxindicatethesignal regions. The curvesare the result of thefit. TABLEI:Summaryoftheresults. Y andbarethesignalandexpectedtotalbackgroundyieldsinthesignalregion,Sig. isthe statistical significance, n0 is theobserved numberof candidate eventsin the signal region, Y90 is the upperlimit on the signal yield at 90% confidencelevel, ǫ (error includes systematic error) is thedetection efficiency and B is the branchingfraction. Mode Y b Sig. n0 Y90 ǫ(%) B B+ →J/ψη′K+ 6.0+4.5 22.0±0.7 1.8σ 37 28.1 3.9±0.6 <8.8×10−5 −3.9 B0 →J/ψη′KS0 1.1+−11..92 4.2±0.3 0.9σ 2 3.7 2.7+−00..67 <2.5×10−5 and their statistical errors. The statisticalsignificance is The branching fraction is determined with N /[ǫ × S definedas −2ln(L0/Lmax),whereLmax andL0 denote NBB¯ ×B(J/ψ →l+l−)×B(η′ →ηπ+π−)×B(η →γγ)] twhiethmtahxeimyipuemld lfiikxeeldihaotozderwoi,thresthpeecfititvteeldy.signal yield and flo+rl−B)×+ B→(η′J→/ψηηπ′+Kπ+−)a×ndB(NηS→/[ǫγγ×)×NBBB(¯K×0 →B(Jπ/+ψπ−→)] S No significant signal is found for either the B+ → for B0 → J/ψη′KS0. Here NS is the signal yield, NBB¯ J/ψη′K+ or B0 → J/ψη′K0 decay mode. We obtain is the number of BB¯ pairs. We use the world aver- upper limits on the yield atS90% confidence level (Y ) ages [13] for the branching fractions of B(J/ψ → l+l−), 90 from number of observed candidates in the signal region B(η′ → ηπ+π−), B(η → γγ) and B(KS0 → π+π−). The (n ) and b using the Feldman-Cousins method [16]. We efficiencies(ǫ)aredeterminedfromthesignalMCsample 0 account for systematic uncertainty due to uncertainties withthesameselectionasusedinthedata. Athree-body inthesignalreconstructionefficiencyandbackgroundes- phasespacemodelisemployedforallthreedecaymodes. timate using the method of Ref. [17]. ThefractionsofneutralandchargedB mesonsproduced 5 TABLE II: Summary of systematic uncertainties (%) of the denominator in branching fraction calculation. Source B+ →J/ψη′K+ B0 →J/ψη′KS0 Tracking error ±7.4 ±8.9 PID (π and K) ±2.7 ±1.4 Lepton ID ±3.8 ±3.8 π0 veto ±3.0 ±3.0 η reconstruction ±4.3 ±4.3 KS0 reconstruction - ±3.7 Branching fractions ±3.3 ±3.3 MC statistics ±0.2 ±0.3 3-body decay model +9.4/−11.3 +17.5/−22.8 NBB¯ ±1.4 ±1.4 Total +14.3/−15.6 +21.4/−25.9 in Υ(4S) decays are assumed to be equal. rea); KBN (contract No. 2P03B 01324, Poland); MIST The sources and sizes of systematic uncertainties in (Russia); MHEST (Slovenia); SNSF (Switzerland); NSC branching fraction calculation are summarized in Ta- and MOE (Taiwan); and DOE (USA). ble II. The dominant sources are uncertainties in the three-body decay model, tracking efficiency and particle identification. For the error due to uncertainty in de- caymodelingforB+ →J/ψη′K+ (B0 →J/ψη′K0), the S [1] Babar Collaboration, B. Aubert et al., Phys. Rev. Lett. distribution in phase space is unknown. We conserva- 87, 091801 (2001); Belle Collaboration, K. Abe et al., tively assign the maximum variation of efficiency among Phys. Rev.Lett. 87, 091802 (2001). ′ − ′ − the slices of M(J/ψ,η ), M(J/ψ,K ) and M(η ,K ) [2] Belle Collaboration, S.-K. Choi et al., Phys. Rev. Lett. [M(J/ψ,η′), M(J/ψ,KS0) and M(η′,KS0)] as a system- 89, 102001 (2002) [Erratum-ibid. 89, 129901 (2002)]; atic uncertainty. The uncertainties in the tracking effi- Belle Collaboration, S.-K. Choi et al., Phys. Rev. Lett. ciency are estimated by linearly adding the momentum- 91, 262001 (2003). dependent single track systematic errors. We assign un- [3] Belle Collaboration, S.-K. Choi et al., Phys. Rev. Lett. 94, 182002 (2005). certaintiesofabout1.3%per kaon,about0.7%perpion, [4] CLEO Collaboration, A. Anastassov et al., Phys. Rev. andabout1.9%perleptonforthe particleidentification. Lett. 84, 1393 (2000); Babar Collaboration, B. Aubert The η reconstruction uncertainty is determined by mea- et al.,Phys.Rev. Lett.91, 071801 (2003). suring the efficiency ratio between data and MC sam- [5] F.E. Close et al., Phys. Rev. D 57, 5653 (1998); ple in the inclusive η sample. The K0 reconstruction F.E.CloseandS.Godfrey,Phys.Lett.B574,210(2003). S is checked by comparing the ratio of D+ → K0π+ and [6] Babar Collaboration, B. Aubert et al., Phys. Rev. Lett. S D+ →K−π+π− yields. 95, 142001 (2005). [7] F.E.CloseandP.R.Page,Phys.Lett.B628,215(2005). The systematic errors for the background yield are [8] Inclusion of the charge conjugate state is implied evaluated by varying each of the PDF parameters by its throughout thispaper. statistical error from the fit. [9] Belle Collaboration, A.Abashian et al., Nucl. Instr. and In summary, we searched for B+ → J/ψη′K+ and Meth. A 479, 117 (2002). B0 →J/ψη′K0 decays. Nostatisticallysignificantsignal [10] S. Kurokawa and E. Kikutani, Nucl. Instr. and Meth. A S wasfoundforeitherofthetwodecaymodes;upperlimits 499, 1 (2003). forthebranchingfractionsaredeterminedtobeB(B+ → [11] Belle Collaboration, K. Abe et al., Phys. Rev. D 67, J/ψη′K+)<8.8×10−5 and B(B0 →J/ψη′K0)<2.5× 032003 (2003). 10−5 at 90% confidence level. S [12] G.C. Fox and S. Wolfram, Phys. Rev. Lett. 41, 1581 (1978). We thank the KEKB group for the excellent opera- [13] W.-M. Yao et al. (Particle Data Group), Journal of tionoftheaccelerator,theKEKcryogenicsgroupforthe Physics G 33, 1 (2006). efficient operation of the solenoid, and the KEK com- [14] Belle Collaboration, K. Abe et al., Phys. Lett. B 517, puter group and the NII for valuable computing and 309 (2001). Super-SINETnetworksupport. Weacknowledgesupport [15] ARGUSCollaboration, H.Albrecht et al.,Phys.Lett. B 241, 278 (1990). from MEXT and JSPS (Japan); ARC and DEST (Aus- [16] G.J. Feldman and R.D. Cousins, Phys. Rev.D 57, 3873 tralia); NSFC and KIP of CAS (contract No. 10575109 (1998). and IHEP-U-503, China); DST (India); the BK21 pro- [17] J. Conrad et al., Phys.Rev.D 67, 012002 (2003). gram of MOEHRD, and the CHEP SRC and BR (grant No. R01-2005-000-10089-0) programs of KOSEF (Ko-