Search for B0 → K∗0K∗0, B0 → K∗0K∗0 and B0 → K+π−K∓π± Decays C.-C. Chiang,25 H. Aihara,42 K. Arinstein,1,30 V. Aulchenko,1,30 T. Aushev,17,11 A. M. Bakich,36 V. Balagura,11 0 E. Barberio,20 K. Belous,9 V. Bhardwaj,32 M. Bischofberger,22 A. Bondar,1,30 A. Bozek,26 M. Braˇcko,18,12 1 T.E.Browder,6 P.Chang,25 Y.Chao,25 A.Chen,23 P.Chen,25 B.G.Cheon,5 I.-S.Cho,45 Y.Choi,35 J.Dalseno,19,38 0 A. Das,37 Z. Doleˇzal,2 A. Drutskoy,3 S. Eidelman,1,30 M. Feindt,14 N. Gabyshev,1,30 P. Goldenzweig,3 H. Ha,15 2 T. Hara,7 K. Hayasaka,21 H. Hayashii,22 Y. Horii,41 Y. Hoshi,40 Y. B. Hsiung,25 T. Iijima,21 K. Inami,21 n R. Itoh,7 M. Iwasaki,42 N. J. Joshi,37 J. H. Kang,45 P. Kapusta,26 T. Kawasaki,28 C. Kiesling,19 H. J. Kim,16 a J H. O. Kim,16 K. Kinoshita,3 B. R. Ko,15 S. Korpar,18,12 M. Kreps,14 P. Kriˇzan,46,12 P. Krokovny,7 Y.-J. Kwon,45 6 S.-H. Kyeong,45 J. S. Lange,4 M. J. Lee,34 S.-H. Lee,15 J. Li,6 A. Limosani,20 C. Liu,33 Y. Liu,25 D. Liventsev,11 2 R. Louvot,17 A. Matyja,26 S. McOnie,36 K. Miyabayashi,22 H. Miyata,28 Y. Miyazaki,21 E. Nakano,31 M. Nakao,7 Z. Natkaniec,26 S. Neubauer,14 S. Nishida,7 K. Nishimura,6 O. Nitoh,43 S. Ogawa,39 S. Okuno,13 S. L. Olsen,34,6 ] x W. Ostrowicz,26 G. Pakhlova,11 C. W. Park,35 H. Park,16 H. K. Park,16 K. S. Park,35 R. Pestotnik,12 M. Petriˇc,12 e L. E. Piilonen,44 M. Ro¨hrken,14 S. Ryu,34 H. Sahoo,6 Y. Sakai,7 O. Schneider,17 C. Schwanda,8 A. J. Schwartz,3 - p K. Senyo,21 M. E. Sevior,20 J.-G. Shiu,25 R. Sinha,10 P. Smerkol,12 A. Sokolov,9 S. Staniˇc,29 M. Stariˇc,12 e h J. Stypula,26 K. Sumisawa,7 M. Tanaka,7 Y. Teramoto,31 K. Trabelsi,7 Y. Unno,5 P. Urquijo,20 Y. Usov,1,30 [ G. Varner,6 K. E. Varvell,36 K. Vervink,17 C. H. Wang,24 M.-Z. Wang,25 M. Watanabe,28 Y. Watanabe,13 E. Won,15 B. D. Yabsley,36 Y. Yamashita,27 Z. P. Zhang,33 T. Zivko,12 A. Zupanc,14 and O. Zyukova1,30 1 v (The Belle Collaboration) 5 1Budker Institute of Nuclear Physics, Novosibirsk 9 2Faculty of Mathematics and Physics, Charles University, Prague 5 3University of Cincinnati, Cincinnati, Ohio 45221 4 4Justus-Liebig-Universit¨at Gießen, Gießen . 1 5Hanyang University, Seoul 0 6University of Hawaii, Honolulu, Hawaii 96822 0 7High Energy Accelerator Research Organization (KEK), Tsukuba 1 8Institute of High Energy Physics, Vienna v: 9Institute of High Energy Physics, Protvino i 10Institute of Mathematical Sciences, Chennai X 11Institute for Theoretical and Experimental Physics, Moscow r 12J. Stefan Institute, Ljubljana a 13Kanagawa University, Yokohama 14Institut fu¨r Experimentelle Kernphysik, Karlsruhe Institut fu¨r Technologie, Karlsruhe 15Korea University, Seoul 16Kyungpook National University, Taegu 17E´cole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne 18University of Maribor, Maribor 19Max-Planck-Institut fu¨r Physik, Mu¨nchen 20University of Melbourne, School of Physics, Victoria 3010 21Nagoya University, Nagoya 22Nara Women’s University, Nara 23National Central University, Chung-li 24National United University, Miao Li 25Department of Physics, National Taiwan University, Taipei 26H. Niewodniczanski Institute of Nuclear Physics, Krakow 27Nippon Dental University, Niigata 28Niigata University, Niigata 29University of Nova Gorica, Nova Gorica 30Novosibirsk State University, Novosibirsk 31Osaka City University, Osaka 32Panjab University, Chandigarh 33University of Science and Technology of China, Hefei 34Seoul National University, Seoul 35Sungkyunkwan University, Suwon 36School of Physics, University of Sydney, NSW 2006 2 37Tata Institute of Fundamental Research, Mumbai 38Excellence Cluster Universe, Technische Universita¨t Mu¨nchen, Garching 39Toho University, Funabashi 40Tohoku Gakuin University, Tagajo 41Tohoku University, Sendai 42Department of Physics, University of Tokyo, Tokyo 43Tokyo University of Agriculture and Technology, Tokyo 44IPNAS, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 45Yonsei University, Seoul 46Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana We report a search for the decays B0 → K∗0K∗0 and B0 → K∗0K∗0. We also measure other charmless decay modes with K+π−K−π+ and K+π−K+π− final states. The results are obtained from a data sample containing 657×106 BB pairs collected with the Belle detector at the KEKB asymmetric-energye+e− collider. WesetupperlimitsonthebranchingfractionsforB0 →K∗0K∗0 and B0 →K∗0K∗0 of 0.81×10−6 and 0.20×10−6, respectively,at the 90% confidencelevel. PACSnumbers: 11.30.Er,12.15.Hh,13.25.Hw,14.40.Nd The charmless decay B0 → K∗0K∗0 [1] proceeds a K+π−K−π+ or K+π−K+π− final state using a data through electroweak and gluonic b → d “penguin” loop sample 1.7 times larger than that of BaBar. The data diagrams. It provides an opportunity to probe the dy- sample used in the analysis contains 657 × 106 BB namics of both weak and strong interactions,which play pairs collected with the Belle detector [12, 13] at the an important role in CP violation phenomena. For a B KEKB asymmetric-energy e+e− (3.5 GeV and 8 GeV) meson decaying to two vector particles, B → VV, the- collider[14]operatingattheΥ(4S)resonance. TheBelle oretical models based on the frameworks of either QCD detectorincludesasiliconvertexdetector,a50-layercen- factorization or perturbative QCD predict the fraction tral drift chamber (CDC), an array of aerogel threshold of longitudinal polarization (f ) to be ∼ 0.9 for tree- Cherenkov counters (ACC), and a barrel-like arrange- L dominateddecaysand∼0.75forpenguin-dominatedde- ment of time-of-flight scintillation counters (TOF). Sig- cays [2, 3]. However, the measured polarization fraction nal Monte Carlo (MC) events are generated with EVT- in the pure penguin decay B → φK∗ has a somewhat GEN [15], and final-state radiationis taken into account lower value of f ∼ 0.5 [4]. This unexpected result has with the PHOTOS package [16]. Generated events are L motivated further studies [5]. processed through a full detector simulation program OneresolutiontothispuzzleisasmallerB →K∗ form based on GEANT3 [17]. factor that could reduce f significantly [6]. If this ex- We reconstruct signal decays from neutral combina- L planationiscorrect,thepenguin-dominateddecayB0 → tions of four charged tracks fitted to a common vertex. K∗0K∗0 shouldexhibitasimilarpolarizationfraction. A Neutral K∗ mesons are reconstructed via K∗0 →K+π− time-dependent angular analysis of B0 →K∗0K∗0 could and K∗0 → K−π+. Charged track candidates are re- distinguish between penguin annihilation and rescatter- quired to have a distance of closest approach to the in- ing as mechanisms for the f observed in B → φK∗ de- teractionpoint of less than 2.0 cm in the directionalong L cays [7]. The B0 → K∗0K∗0 mode can also be used the positron beam (z axis), and less than 0.1 cm in the to extract the branching fraction corresponding to the transverse plane. Tracks are also required to have a lab- longitudinal helicity final state, determine hadronic pa- oratorymomentumintherange[0.5,4.0]GeV/c,apolar rameters for the b → s decay B → K∗0K∗0, and help angleintherange[32.2,127.2]◦,andatransversemomen- s constrain the angles φ (α) and φ (γ) of the Cabibbo- tum p >0.1GeV/c. Chargedpions are identified using 2 3 T Kobayashi-Maskawaunitarity triangle [8]. The topologi- informationfromthe CDC (dE/dx), ACC,andTOFde- cally similar decay B0 →K∗0K∗0 is strongly suppressed tectors [18]. We distinguish charged kaons from pions in the Standard Model (SM); its observationwouldindi- using a likelihood ratio R = L /(L + L ), where K K K π cate new physics. L (L ) is the likelihood value for the pion (kaon) hy- π K Theoretical calculations predict the branching frac- pothesis. We require RK < 0.4 (RK > 0.6) for the two tionsforB0 →K∗0K∗0 andB0 →K∗0K∗0 tobe(0.17− chargedpions (kaons). The kaon(pion) identificationef- 0.92)×10−6 [9]and(2.9±0.2)×10−15[10],respectively. ficiency is 83% (90%), and 6% (12%) of pions (kaons) The BaBar collaboration [11] has reported a branching are misidentified as kaons (pions). We also use the lep- fraction B(B0 → K∗0K∗0) = (1.28+−00..3350±0.11)×10−6 ton identification likelihood Rx (x denotes either µ or and has set an upper limit B(B0 → K∗0K∗0) < 0.41× e) described in Ref. [18]: charged particles identified as 10−6 at the 90% confidence level (C.L.). In this pa- electrons (Re >0.9) or muons (Rµ >0.9) are removed. per, we report a search for the decays B0 → K∗0K∗0, We veto B → D(∗)±X, B → D±X, B → D0X, and s B0 → K∗0K∗0, and other charmless decay modes with B0 → φX decays that result in the K+π−K−π+ final 3 state, and we veto B → D(∗)±X and B → D0X de- events that is obtained from the signal MC simulation cays that result in the K+π−K+π− final state. For the (events in the sideband regionM <5.26 GeV/c2). For bc B → D(∗)±X and B → D±X vetos, we remove can- additionalsuppression,wealsouseaflavortaggingqual- s didates that satisfy either |M(K±K∓π∓) − m | < ityvariablerprovidedbytheBelletaggingalgorithm[20] D∓ 13 MeV/c2, |M(K±π∓π∓) − m | < 13 Me(Vs)/c2, that identifies the flavor of the accompanying B0 meson D(∓s) intheΥ(4S)→B0B0 decay. The variabler rangesfrom |M(K±h∓π∓)−m |<13MeV/c2,or|M(K±h∓π∓)− K D∓ π r =0fornoflavordiscriminationtor =1forunambigu- m | < 13 MeV/c2, where m are the masses of the D∓ D∓ ous flavor assignment, and it is used to divide the data (s) D∓ mesons, and h∓ (h∓) is the kaon (pion) mass as- sample into six r bins. As the discrimination between (s) K π signal and continuum events depends on the r-bin, we signed to a pion (kaon) candidate track [i.e., a kaon impose different requirements on R for each bin. The (pion) was misidentified as a pion (kaon)]. For the B → D0X veto, we remove candidates satisfying ei- requirements are determined by maximizing a figure-of- ther |M(K±K∓)−m |<13 MeV/c2 or |M(K±h∓)− merit Ns/ Ns+Nqq, where Ns (Nqq) is the expected D0 K m | < 13 MeV/c2, where m is the mass of the D0 number ofpsignal(continuum) events in the signalregion D0 D0 ∆E ∈[−0.045, 0.045] GeV, M ∈[5.27, 5.29] GeV/c2, meson. For the B → φX veto, we remove candidates bc satisfying |M(K±h∓K)−mφ|<20 MeV/c2, where mφ is anIdnMa1b,2o(uKtπ1)7∈%[0o.f82e6v,en0.t9s66th]eGreeVa/rce2.multiple B0 → the mass of the φ meson. These vetos together remove 9.7% (3.6%) of longitudinally polarized B0 → K∗0K∗0 K∗0K∗0 or B0 → K∗0K∗0 candidates. For these events (B0 →K∗0K∗0) signal, according to MC simulation. we select the candidate with the smallest χ2 value for the B0 decay vertex reconstruction. This selects the Signal event candidates are characterized by two correct combination 87% (97%) of the time for longi- kinematic variables: the beam-energy-constrained mass, tudinally (transversely) polarized B0 → K∗0K∗0 and Mbc = Eb2eam−PB∗2, and the energy difference, ∆E = B0 → K∗0K∗0 decays. The overall reconstruction ef- EB∗ −Ebpeam,whereEbeam istherun-dependentbeamen- ficiency for B0 → K∗0K∗0 as obtained from MC sim- ergy, and P∗ and E∗ are the momentum and energy of B B ulation is 4.43% (5.23%) for longitudinal (transverse) theBcandidateintheΥ(4S)center-of-mass(CM)frame. polarization. The overall reconstruction efficiency for We distinguish nonresonant B0 → KKππ decays from B0 → K∗0K∗0 is 5.74% (5.92%) for longitudinal (trans- our signal modes by fitting the two-dimensional mass verse)polarization. Theefficiencyforlongitudinalpolar- distributions M(K+π−) vs. M(K−π+) or M(K+π−) izationislower,asinthiscasetheK∗0daughtersproduce vs. M(K+π−). There are two possible combina- lower momentum kaons and pions. tions in B0 → K∗0K∗0 reconstruction for M(K+π−) The signal yields for B0 → K∗0K∗0 and other B0 → vs. M(K+π−): (K1+π1−)(K2+π2−) and (K1+π2−)(K2+π1−), K+π−K−π+ decays are extracted by performing an ex- where the subscripts label the momentum ordering, i.e., tended unbinned maximum likelihood (ML) fit to the sKid1+e(rπb1−o)thha(Ks h1+iπgh1−e)r(Km2+omπ2−en)taunmd(tKha1+nπK2−)2+(K(π2+2−π).1−W)ceomcobni-- vaanrdiaMble2sM≡bMc,∆(KE−,πM+1),.anTdhMis2,fowuhr-edreimMen1s≡ionMal(Kfit+πd−is)- nations and select candidate events if either one of the criminatesamongK∗0K∗0, K∗0Kπ, K∗(1430)K∗(1430), 0 0 combined masses lies within the signal window of [0.7, K∗(1430)K∗0, K∗(1430)Kπ,andnonresonantKKππ fi- 1.7] GeV/c2. If both combinations fall within the signal 0 0 nal states. Since there are large overlaps between these window,weselectthe(K+π−)(K+π−)combination. Ac- 1 2 2 1 states, we distinguish them by fitting a large (M1,M2) cording to MC simulation, this choice selects the correct region: M ∈ [0.7, 1.7] GeV/c2. We use a likelihood 1,2 combination for signal decays 99% of the time. For fit- function ting,wesymmetrizetheM2(K+π−)vs.M2(K+π−)plot by plotting M2(K+π−) [M2(K+π−)] on the horizontal Ncand 1 2 L=exp − n n Pi , (1) axis for events with an even [odd] event number. This (cid:18) j(cid:19) (cid:18) j j(cid:19) number denotes the location of the event in the data set Xj iY=1 Xj (i.e., n =1,2,3...N ). event total where i is the event identifier, j indicates one of the The dominant source of background is continuum event type categories for signals and backgrounds, nj e+e− → qq¯ (q = u,d,s and c) events. To distinguish denotes the yield of category j, and Pi is the prob- j signal from the jet-like continuum background, we use ability density function (PDF) of event i for cate- modified Fox-Wolfram moments [19] that are combined gory j. The PDF is a product of two smoothed into a Fisher discriminant. This discriminant is subse- two-dimensional functions: Pji = Pj(Mbic,∆Ei) × quently combined with the probabilities for the cosineof P (Mi,Mi) ≡ P (Mi ,∆Ei,Mi,Mi). The signal yields j 1 2 j bc 1 2 the B flight direction in the CM frame and the distance for B0 →K∗0K∗0 and other B0 →K+π−K+π− decays alongthe z axisbetweenthe twoB mesondecayvertices areextractedbyanotherfour-dimensionalfitinthesame to form a likelihood ratio R = L /(L + L ). Here, way, except that for this fit M ≡M(K+π−). s s qq 2 L (L ) is a likelihood function for signal (continuum) For the B signal components, the smoothed functions s qq 4 P(M ,∆E)andP(M ,M )areobtainedfromMCsim- where x corresponds to the number of signal events. We bc 1 2 ulation. For the M and ∆E PDFs, possible differences include the systematic uncertainty in the upper limit bc between data and the MC modeling are calibrated using (UL) by smearing the statistical likelihood function by a large control sample of B0 → D−(K+π−π−)π+ de- a bifurcated Gaussian whose width is equal to the to- cays. The signal mode PDF is divided into two parts: tal systematic error. We also smear L when calculating oneiscorrectlyreconstructedevents(CR),andtheother the signalsignificance,except thatonly the additive sys- is “self-cross-feed” events (SCF) in which at least one tematic errors related to signal yield are included in the track from the signal decay is replaced by one from the convolved Gaussian width. Our upper limits correspond accompanying B decay. We use different PDFs for CR to a longitudinal polarization fraction f = 1; as the ef- L and SCF events and fix the SCF fraction (f ) to that ficiency for f < 1 is higher than that for f = 1, our SCF L L obtained from MC simulation, i.e., limits are conservative. To check our reconstruction efficiencies, we mea- PSiignal = (1−fSCF)×PCR(Mbic,∆Ei,M1i,M2i) sure the yields of control samples B0 → D−π+ → + f ×P (Mi ,∆Ei,Mi,Mi). (2) (K+K−π−)π+ and B0 → D0K∗0 → (K+π−)(K+π−). SCF SCF bc 1 2 Thesemodeshaveasimilartopologytothesignalmodes For the continuum and b → c decay backgrounds, we and are selected using the same selection criteria ex- use the product of a linear function for ∆E, an ARGUS cept that, instead of D vetos, we require |M(KKπ)− function [21] for Mbc, and a two-dimensional smoothed mD±|<13MeV/c2, |M(Kπ)−mD0|<13MeV/c2, and function for M1-M2. The shape parameters of the linear 826 MeV/c2 < M(Kπ) < 966 MeV/c2. The efficiencies and ARGUS functions for the continuum (b→c) events are 19% for B0 → D−π+ and 11% for B0 → D0K∗0. arefloated(fixed)inthefit;theshapeoftheM -M func- Thedifferenceinsignalyieldsbetweenthemeasuredand 1 2 tions for the continuum and b → c events are obtained expected values are (5.8±5.8)% and (5.6±27.8)% for from MC simulation and fixed in the fit. The yields of B0 → D−π+ and B0 → D0K∗0, respectively. These the continuum and b→c decay backgrounds are floated differences are consistent with zero. in the fit. For the charmless B decay backgrounds, we The systematic errors (in units of events) are sum- use separate PDFs for B0 → K+K−K0, nonresonant marized in Tables II and III. For systematic uncer- B0 →Kπππ,andothercharmlessBmodes;allthePDFs tainties due to fixed yields, e.g., that of charmless B areobtainedfromMCsimulation. Note thatthe nonres- background, we vary the yields by their uncertainties onant B0 → Kπππ decay will enter the sample if one (±1σ). For the systematic uncertainties due to B0 → of the pions is misidentified as a kaon; in this case the K∗(1430)X decays, including B0 →K∗(1430)K∗(1430), 2 2 2 mean of the ∆E distribution shifts by about +75 MeV, B0 → K∗(1430)K∗(1430), B0 → K∗(1430)K∗0, and 2 0 2 since assigning a kaon mass instead of a pion mass in- B0 → K∗(1430)Kπ, we float their yields in the four- 2 creases the B candidate energy. In the fit, we fix the dimensionalML fit; the differencesbetween these results yield of B0 → K+K−K0 to 32 events, corresponding to and the nominal fit values are taken as systematic er- a branching fraction of 24.7×10−6 [22], and the yield of rors. Systematic uncertainties for the ∆E-M PDFs bc other known charmless B decays to that expected based are estimated by varying the signal peak positions and on world average branching fractions [23]. We set the resolutions by ±1σ and repeating the fits. Systematic branchingfractionforB0 →K∗(1430)X tozeroandonly uncertainties for the M -M PDFs are estimated in a 2 1 2 consider it in the systematics, as this mode has a large similar way; we vary the mean and width of K∗0 and correlationwith B0 →K∗(1430)X. The yield of nonres- K∗(1430) mass shapes according to the uncertainties in 0 0 onant B0 →Kπππ is floated. For the fully nonresonant the worldaveragevalues [22]. A systematic error for the modes,weassumethefinal-stateparticlesaredistributed longitudinal polarization fraction is obtained by chang- uniformly in three- and four-body phase space. ing the fraction from the nominal value f = 1 to the L The fit results are listed in Table I, and projec- lowest possible value f =0 when evaluating the recon- L tions of the fit superimposed to the data are shown in struction efficiency. According to MC simulation, the Figs. 1 and 2. The statistical significance is calculated signal SCF fractions are 13.4% for (longitudinally polar- as −2ln(L0/Lmax), where L0 and Lmax are the val- ized) B0 → K∗0K∗0, 7.9% for B0 → K∗0Kπ, 6.7% for uespof the likelihood function when the signal yield is B0 →K∗(1430)K∗(1430),6.7%forB0 →K∗(1430)K∗0, 0 0 0 fixed to zero andwhen it is allowedto vary,respectively. 7.6% for B0 → K∗(1430)Kπ, and 9.2% for nonresonant 0 We do not find significant signals for B0 → K∗0K∗0, B0 →KKππ. Weestimateasystematicuncertaintydue B0 → K∗0K∗0, and other charmless decay modes with to these fractions by varying them by ±50%. K+π−K∓π± finalstates,anddetermine90%C.L.upper A high-statistics MC study indicates that there are limits for the yields (N). These limits are calculated via small fit biases; these are listed in Table I. We find that fit biases occur due to the correlations between the two N L(x)dx sets of variables (∆E, M ) and (M , M ), which are 0 = 0.90, (3) bc 1 2 R∞L(x)dx not taken into account in our fit. We correct the fitted 0 R 5 TABLE I: Fit results for decay modes with final states K+π−K−π+ and K+π−K+π−. The fit bias (in units of events) is obtainedfrom MCsimulation; theyield includesthebiascorrection; theefficiency εincludesthePIDefficiency correction and branching fractions for K∗0 → K+π− and K∗(1430) → K+π− (66.5% and 66.7%, respectively); and the significance S is in 0 unitsof σ. The first (second) error listed is statistical (systematic). Mode Fit bias Yield ε (%) S B×106 UL ×106 B0 →K∗0K∗0 1.5±0.7 7.7+9.7+2.8 4.43 (f =1.0) 0.9 0.26+0.33+0.10 <0.8 −8.5−2.2 L −0.29−0.08 B0 →K∗0K−π+ −5.4±2.9 18.2+48.4+41.7 1.31 0.3 2.11+5.63+4.85 <13.9 −45.3−40.9 −5.26−4.75 B0 →K∗(1430)K∗(1430) 2.1±5.1 78.5+70.6+56.4 3.72 0.8 3.21+2.89+2.31 <8.4 0 0 −69.6−56.8 −2.85−2.32 B0 →K∗(1430)K∗0 13.3±2.3 19.6+31.1+40.0 4.38 0.4 0.68±1.08+1.39 <3.3 0 −31.0−43.0 −1.49 B0 →K∗(1430)K−π+ 14.6±9.8 −222.8+171.5+159.8 1.34 — — <31.8 0 −170.8−168.6 Nonresonant B0 →K+π−K−π+ −10.8±7.3 158.4+120.6+104.1 0.82 1.0 29.41+22.39+19.32 <71.7 −117.8−105.0 −21.87−19.49 B0 →K∗0K∗0 1.0±0.5 −3.7±3.3+2.5 5.74 (f =1.0) — — <0.2 −2.7 L B0 →K∗0K+π− −2.5±2.7 0.5±32.3+43.5 1.93 0.0 0.04±2.55+3.43 <7.6 −40.1 −3.16 B0 →K∗(1430)K∗(1430) 3.4±1.3 −28.4±16.1+87.7 4.28 — — <4.7 0 0 −21.1 B0 →K∗(1430)K∗0 8.2±1.6 8.0±18.7+23.9 5.14 0.3 0.24±0.55+0.71 <1.7 0 −30.3 −0.90 Nonresonant B0 →K+π−K+π− 7.7±2.2 10.8±28.3+31.4 1.98 0.3 0.83±2.17+2.42 <6.0 −101.5 −7.80 50 50 20 (a) 20 (b) 45 (c) 45 (d) 17.5 17.5 40 40 Events/ 10 MeV17211..50555 Events/ 2 MeV17211..50555 Events/ 50 MeV 112233050505 Events/ 50 MeV 112233050505 2.5 2.5 5 5 0 0 0 0 -0.1 -0.05 0 0.05 0.1 5.255.265.275.285.29 5.3 0.7 0.9 1.1 1.3 1.5 1.7 0.7 0.9 1.1 1.3 1.5 1.7 D E (GeV) M (GeV/c2) M(K+p -) (GeV) M(K-p +) (GeV) bc 1 2 FIG. 1: Projections of the four-dimensional fit onto (a) ∆E, (b) M , (c) M(K+π−), and (d) M(K−π+) for candidates bc satisfying (except for the variable plotted) ∆E ∈ [−0.045, 0.045] GeV, Mbc ∈ [5.27, 5.29] GeV/c2, and M1,2(Kπ) ∈ [0.826, 0.966] GeV/c2. Thethick solid curveshows theoverall fitresult; thesolid shaded region represents theB0→K∗0K∗0 signal component; and the dotted, dot-dashed and dashed curves represent continuum background, b → c background, and charmless B decay background,respectively. 12 (a) 14 (b) 22.5 (c) 22.5 (d) Events/ 10 MeV 14680 Events/ 2 MeV 1146802 Events/ 50 MeV11727112...5050555 Events/ 50 MeV11727112...5050555 2 2 2.5 2.5 0 0 0 0 -0.1 -0.05 0 0.05 0.1 5.255.265.275.285.29 5.3 0.7 0.9 1.1 1.3 1.5 1.7 0.7 0.9 1.1 1.3 1.5 1.7 D E (GeV) M (GeV/c2) M(K+p -) (GeV) M(K+p -) (GeV) bc 1 2 FIG. 2: Same as for Fig. 1 but for the B0 →K∗0K∗0 →(K+π−)(K+π−) study: (a) ∆E, (b) M , (c) M (K+π−), and (d) bc 1 M (K+π−). 2 6 yields for these biases. To take into accountpossible dif- Phys. Rev.Lett. 98 051801 (2007). ferences between MC simulation and data, we take both [5] A. Kagan, Phys. Lett. B 601, 151 (2004); C. Bauer et themagnitudeofthebiascorrectionsandtheuncertainty al.,Phys. Rev.D70, 054015 (2004); P. Colangelo et al., Phys. Lett. B 597, 291 (2004); M. Ladisa et al., Phys. in the corrections as systematic errors. The systematic Rev.D70,114025(2004);H.-n.LiandS.Mishima,Phys. errorsforthe efficiency arisefromthe trackingefficiency, Rev. D 71, 054025 (2005); M. Beneke et al., Phys. Rev. PID, and the R requirement. The systematic error on Lett. 96, 141801 (2006). the track-finding efficiency is estimated to be 1.2% per [6] H-n.Li, Phys. Lett. B 622, 63 (2005). track using partially reconstructed D∗ events. The sys- [7] A. Datta et al.,Phys. Rev.D 76, 034051 (2007). tematic error due to the PID is 1.0% per track as esti- [8] D.AtwoodandA.Soni,Phys.Rev.D65,073018(2002); mated using an inclusive D∗ control sample. The sys- S.Descotes-Genon,J.MatiasandJ.Virto,Phys.Rev.D 76, 074005 (2007). tematic error for the R requirement is determined from [9] W. Zou and Z. Xiao, Phys. Rev. D 72, 094026 (2005); theefficiencydifferencebetweendataandMCsamplesof M. Beneke, J. Rohrer, and D. Yang, Nucl. Phys. B774, B0 →D−(K+π−π−)π+ decays. 64 (2007). H.-Y. Cheng and K.-C. Yang, Phys. Rev. D In summary, we have used a data sample correspond- 78, 094001 (2008). ing to 657×106 BB pairs to search for B0 → K∗0K∗0, [10] D. Pirjol and J. Zupan,arXiv:0908.3150 [hep-ph]. B0 → K∗0K∗0, and other charmless decay modes with [11] B.Aubert(BaBarCollaboration), Phys.Rev.Lett.100, a K+π−K∓π± final state. We do not find significant 081801 (2008). signals for any of these modes. Our measured branching [12] A. Abashian et al. (Belle Collaboration), Nucl. Instrum. fraction for B0 → K∗0K∗0 is (0.26+0.33+0.10) × 10−6, and Methods Phys.Res. Sect. A 479, 117 (2002). −0.29−0.07 [13] Z. Natkaniec et al. (Belle SVD2 Group), Nucl. Instrum. which is lower than that obtained by BaBar [11] by and Methods Phys.Res. Sect. A 560, 1 (2006). 2.2σ. Our 90% C.L. upper limits are 0.8 × 10−6 for [14] S.KurokawaandE.Kikutani,Nucl.Instrum.andMeth- B(B0 →K∗0K∗0) and 0.2×10−6 for B(B0 →K∗0K∗0); ods Phys. Res. Sect. 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Theparameters NB0→K∗(1430)X and Nb→u,d,s (the other known charmless B decays) correspond to branching fraction uncertainties for these 2 charmlessB decays. Valuesforf andf aretheuncertaintiesfor longitudinalpolarization andself-cross-feed, respectively. L SCF Source K∗0K∗0 K∗0K−π+ K∗(1430)K∗(1430) K∗(1430)K∗0 K∗(1430)K−π+ Nonresonant K+π−K−π+ 0 0 0 0 Fitting PDF ±1.8 ±40.3 ±55.6 ±37.7 ±158.0 ±102.4 NB0→K∗(1430)X +1.1 +10.2 −7.1 −20.4 −52.8 −10.5 2 Nb→u,d,s ±0.0 ±0.1 ±0.2 ±0.1 ±0.7 ±1.0 f −0.1 — — — — — L f ±0.7 ±1.4 ±5.6 ±2.2 ±17.2 ±14.6 SCF Fit Bias +1.5 +2.9 ±5.1 +13.3 +8.9 +7.3 −0.7 −5.4 −2.3 −14.7 −10.8 Tracking ±0.4 ±0.8 ±3.5 ±0.9 ±9.6 ±6.8 PID ±0.4 ±0.7 ±2.9 ±0.7 ±8.2 ±6.0 R requirement ±0.2 ±0.4 ±1.6 ±0.4 ±4.5 ±3.2 N ±0.1 ±0.3 ±1.1 ±0.3 ±3.1 ±2.2 BB Sum +2.8 +41.7 +56.3 +40.0 +159.7 +104.1 −2.1 −40.7 −56.8 −43.0 −168.6 −104.9 TABLE III: Same as for Table II but for decay modes with a final state K+π−K+π−. Source K∗0K∗0 K∗0K+π− K∗(1430)K∗(1430) K∗(1430)K∗0 Nonresonant K+π−K+π− 0 0 0 Fitting PDF ±2.4 ±40.0 ±20.7 ±22.5 ±30.5 NB0→K∗(1430)X,K∗(1430)Kπ −0.3 +16.8 +85.1 −20.2 −96.8 2 0 Nb→u,d,s ±0.0 ±0.4 ±0.1 ±0.3 ±0.3 f −0.7 — — — — L f ±0.1 ±0.2 ±0.8 ±0.5 ±0.2 SCF Fit Bias +0.5 ±2.7 +1.3 +8.2 +7.7 −1.0 −3.4 −1.6 −2.2 Tracking ±0.2 ±0.0 ±1.2 ±0.4 ±0.5 PID ±0.2 ±0.0 ±1.0 ±0.3 ±0.4 Rrequirement ±0.1 ±0.0 ±0.6 ±0.2 ±0.2 N ±0.1 ±0.0 ±0.4 ±0.1 ±0.2 BB Sum +2.5 +43.5 +87.7 +23.9 +31.4 −2.7 −40.1 −21.1 −30.3 −101.5