Measurement of Branching Fraction and Search for CP Violation in B\to φφK
S. Mohanty, A. B. Kaliyar, V. Gaur, G. B. Mohanty, I. Adachi, K. Adamczyk, H. Aihara, S. Al Said, D. M. Asner, H. Atmacan, V. Aulchenko, T. Aushev, T. Aziz, V. Babu, S. Bahinipati, P. Behera, M. Bessner, V. Bhardwaj, T. Bilka, J. Biswal, A. Bobrov, A. Bozek, M. Bra?ko, T. E. Browder, M. Campajola, D. ?ervenkov, V. Chekelian, A. Chen, B. G. Cheon, K. Chilikin, K. Cho, S.-J. Cho, S.-K. Choi, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, S. Das, N. Dash, G. De Nardo, R. Dhamija, F. Di Capua, Z. Doležal, T. V. Dong, S. Eidelman, T. Ferber, B. G. Fulsom, N. Gabyshev, A. Garmash, A. Giri, P. Goldenzweig, B. Golob, O. Grzymkowska, Y. Guan, K. Gudkova, C. Hadjivasiliou, S. Halder, K. Hayasaka, H. Hayashii, W.-S. Hou, C.-L. Hsu, K. Inami, A. Ishikawa, R. Itoh, M. Iwasaki, W. W. Jacobs, H. B. Jeon, S. Jia, Y. Jin, K. K. Joo, K. H. Kang, G. Karyan, B. H. Kim, C. H. Kim, D. Y. Kim, S. H. Kim, Y.-K. Kim, K. Kinoshita, P. Kodyš, T. Konno, S. Korpar, D. Kotchetkov, P. Križan, P. Krokovny, R. Kulasiri, M. Kumar, R. Kumar, K. Kumara, Y.-J. Kwon, K. Lalwani, S. C. Lee, J. Li, L. K. Li, Y. B. Li, L. Li Gioi, J. Libby, Z. Liptak, D. Liventsev, C. MacQueen, M. Masuda, et al. (86 additional authors not shown)
aa r X i v : . [ h e p - e x ] J a n Belle Preprint
KEK Preprint
Measurement of Branching Fraction and Search for CP Violation in B → φφK S. Mohanty,
72, 80
A. B. Kaliyar, V. Gaur, G. B. Mohanty, I. Adachi,
15, 11
K. Adamczyk, H. Aihara, S. Al Said,
71, 34
D. M. Asner, H. Atmacan, V. Aulchenko,
4, 56
T. Aushev, T. Aziz, V. Babu, S. Bahinipati, P. Behera, M. Bessner, V. Bhardwaj, T. Bilka, J. Biswal, A. Bobrov,
A. Bozek, M. Braˇcko,
T. E. Browder, M. Campajola,
28, 49
D. ˇCervenkov, V. Chekelian, A. Chen, B. G. Cheon, K. Chilikin, K. Cho, S.-J. Cho, S.-K. Choi, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, S. Das, N. Dash, G. De Nardo,
28, 49
R. Dhamija, F. Di Capua,
28, 49
Z. Doleˇzal, T. V. Dong, S. Eidelman,
4, 56, 40
T. Ferber, B. G. Fulsom, N. Gabyshev,
4, 56
A. Garmash,
4, 56
A. Giri, P. Goldenzweig, B. Golob,
41, 31
O. Grzymkowska, Y. Guan, K. Gudkova,
4, 56
C. Hadjivasiliou, S. Halder, K. Hayasaka, H. Hayashii, W.-S. Hou, C.-L. Hsu, K. Inami, A. Ishikawa,
15, 11
R. Itoh,
15, 11
M. Iwasaki, W. W. Jacobs, H. B. Jeon, S. Jia, Y. Jin, K. K. Joo, K. H. Kang, G. Karyan, B. H. Kim, C. H. Kim, D. Y. Kim, S. H. Kim, Y.-K. Kim, K. Kinoshita, P. Kodyˇs, T. Konno, S. Korpar,
44, 31
D. Kotchetkov, P. Kriˇzan,
41, 31
P. Krokovny,
R. Kulasiri, M. Kumar, R. Kumar, K. Kumara, Y.-J. Kwon, K. Lalwani, S. C. Lee, J. Li, L. K. Li, Y. B. Li, L. Li Gioi, J. Libby, Z. Liptak, ∗ D. Liventsev,
82, 15
C. MacQueen, M. Masuda,
76, 62
T. Matsuda, M. Merola,
28, 49
K. Miyabayashi, R. Mizuk,
40, 17
T. J. Moon, R. Mussa, M. Nakao,
15, 11
A. Natochii, L. Nayak, M. Nayak, N. K. Nisar, S. Nishida,
15, 11
K. Ogawa, S. Ogawa, Y. Onuki, P. Oskin, G. Pakhlova,
17, 40
S. Pardi, C. W. Park, H. Park, S.-H. Park, S. Patra, T. K. Pedlar, R. Pestotnik, L. E. Piilonen, T. Podobnik,
41, 31
V. Popov, E. Prencipe, M. T. Prim, M. R¨ohrken, A. Rostomyan, N. Rout, G. Russo, D. Sahoo,
72, 80
Y. Sakai,
15, 11
S. Sandilya, A. Sangal, T. Sanuki, V. Savinov, G. Schnell,
1, 19
J. Schueler, C. Schwanda, A. J. Schwartz, Y. Seino, K. Senyo, M. E. Sevior, M. Shapkin, C. Sharma, J.-G. Shiu, B. Shwartz,
4, 56
F. Simon, E. Solovieva, M. Stariˇc, Z. S. Stottler, J. F. Strube, T. Sumiyoshi, M. Takizawa,
66, 16, 63
K. Tanida, Y. Tao, F. Tenchini, M. Uchida, Y. Unno, S. Uno,
15, 11
Y. Usov,
4, 56
S. E. Vahsen, R. Van Tonder, G. Varner, K. E. Varvell, A. Vinokurova,
4, 56
V. Vorobyev,
4, 56, 40
C. H. Wang, E. Wang, M.-Z. Wang, P. Wang, X. L. Wang, S. Watanuki, J. Wiechczynski, E. Won, X. Xu, B. D. Yabsley, W. Yan, H. Ye, J. H. Yin, Z. P. Zhang, V. Zhilich,
4, 56 and V. Zhukova (The Belle Collaboration) University of the Basque Country UPV/EHU, 48080 Bilbao University of Bonn, 53115 Bonn Brookhaven National Laboratory, Upton, New York 11973 Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090 Faculty of Mathematics and Physics, Charles University, 121 16 Prague Chonnam National University, Gwangju 61186 University of Cincinnati, Cincinnati, Ohio 45221 Deutsches Elektronen–Synchrotron, 22607 Hamburg University of Florida, Gainesville, Florida 32611 Key Laboratory of Nuclear Physics and Ion-beam Application (MOE)and Institute of Modern Physics, Fudan University, Shanghai 200443 SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193 Gyeongsang National University, Jinju 52828 Department of Physics and Institute of Natural Sciences, Hanyang University, Seoul 04763 University of Hawaii, Honolulu, Hawaii 96822 High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 J-PARC Branch, KEK Theory Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 Higher School of Economics (HSE), Moscow 101000 Forschungszentrum J¨ulich, 52425 J¨ulich IKERBASQUE, Basque Foundation for Science, 48013 Bilbao Indian Institute of Science Education and Research Mohali, SAS Nagar, 140306 Indian Institute of Technology Bhubaneswar, Satya Nagar 751007 Indian Institute of Technology Hyderabad, Telangana 502285 Indian Institute of Technology Madras, Chennai 600036 Indiana University, Bloomington, Indiana 47408 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 Institute of High Energy Physics, Vienna 1050 Institute for High Energy Physics, Protvino 142281 INFN - Sezione di Napoli, 80126 Napoli INFN - Sezione di Torino, 10125 Torino Advanced Science Research Center, Japan Atomic Energy Agency, Naka 319-1195 J. Stefan Institute, 1000 Ljubljana Institut f¨ur Experimentelle Teilchenphysik, Karlsruher Institut f¨ur Technologie, 76131 Karlsruhe Kennesaw State University, Kennesaw, Georgia 30144 Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah 21589 Kitasato University, Sagamihara 252-0373 Korea Institute of Science and Technology Information, Daejeon 34141 Korea University, Seoul 02841 Kyungpook National University, Daegu 41566 Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991 Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana Luther College, Decorah, Iowa 52101 Malaviya National Institute of Technology Jaipur, Jaipur 302017 University of Maribor, 2000 Maribor Max-Planck-Institut f¨ur Physik, 80805 M¨unchen School of Physics, University of Melbourne, Victoria 3010 University of Miyazaki, Miyazaki 889-2192 Graduate School of Science, Nagoya University, Nagoya 464-8602 Universit`a di Napoli Federico II, 80126 Napoli Nara Women’s University, Nara 630-8506 National Central University, Chung-li 32054 National United University, Miao Li 36003 Department of Physics, National Taiwan University, Taipei 10617 H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342 Niigata University, Niigata 950-2181 Novosibirsk State University, Novosibirsk 630090 Osaka City University, Osaka 558-8585 Pacific Northwest National Laboratory, Richland, Washington 99352 Peking University, Beijing 100871 University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Punjab Agricultural University, Ludhiana 141004 Research Center for Nuclear Physics, Osaka University, Osaka 567-0047 Meson Science Laboratory, Cluster for Pioneering Research, RIKEN, Saitama 351-0198 Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics,University of Science and Technology of China, Hefei 230026 Seoul National University, Seoul 08826 Showa Pharmaceutical University, Tokyo 194-8543 Soochow University, Suzhou 215006 Soongsil University, Seoul 06978 Sungkyunkwan University, Suwon 16419 School of Physics, University of Sydney, New South Wales 2006 Department of Physics, Faculty of Science, University of Tabuk, Tabuk 71451 Tata Institute of Fundamental Research, Mumbai 400005 School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978 Toho University, Funabashi 274-8510 Department of Physics, Tohoku University, Sendai 980-8578 Earthquake Research Institute, University of Tokyo, Tokyo 113-0032 Department of Physics, University of Tokyo, Tokyo 113-0033 Tokyo Institute of Technology, Tokyo 152-8550 Tokyo Metropolitan University, Tokyo 192-0397 Utkal University, Bhubaneswar 751004 Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Wayne State University, Detroit, Michigan 48202 Yamagata University, Yamagata 990-8560 Yonsei University, Seoul 03722
We report the measurement of branching fractions and CP -violation asymmetries in B → φφK decays based on a 711 fb − data sample containing 772 × BB events. The data were recordedat the Υ (4 S ) resonance with the Belle detector at the KEKB asymmetric-energy e + e − collider. For B + → φφK + , the branching fraction and CP -violation asymmetry measured below the η c threshold( m φφ < .
85 GeV /c ) are [3 . + 0 . − . (stat) ± . × − and − . ± . ± . B → φφK below the η c threshold is[3 . + 0 . − . (stat) ± . × − . We also measure the CP -violation asymmetry for B + → φφK + within the η c region ( m φφ ∈ [2 . , .
02] GeV /c ) to be +0 . ± . ± . PACS numbers: 13.25.Hw, 14.40.Nd B -meson decays to three-body φφK final states pro-ceed via a b → sss loop (penguin) transition, which re-quires the creation of an additional ss pair. The samefinal state can also originate from the tree-level process B → η c ( → φφ ) K . Figure 1 shows the dominant Feyn-man diagrams that contribute to these decays. The in-terference between penguin and tree amplitudes is max-imal when the φφ invariant mass lies close to the η c mass ( m φφ ∈ [2 . , .
02] GeV /c ). No CP violation is ex-pected from this interference, as the relative weak phasebetween the two amplitudes is arg( V tb V ∗ ts /V cb V ∗ cs ) ≈ V ij denote CKM matrix elements [1]. A poten-tial new physics (NP) contribution to the loop, however,can introduce a nonzero CP -violating phase. In partic-ular, the CP asymmetry can be as large as 40% in thepresence of NP [2]. Thus, an observation of large CP violation in B → φφK would indicate the presence ofphysics beyond the Standard Model. In addition to be-ing an NP probe, the decay is sensitive to the possibleproduction of a glueball candidate near 2 . /c thatcan subsequently decay to φφ [3]. We can also search fora structure at 2 .
35 GeV /c observed in the m φφ distribu-tion in two-photon collisions [4] and dubbed the X (2350). + B b s φ u u + Kssss φ + W )t,c,u( + B b c c η u u + Kcs + W FIG. 1. Dominant Feynman diagrams that contribute to thedecays (left) B + → φφK + and (right) B + → η c K + . Replace-ment of the spectator u quark with a d quark will lead to thecorresponding diagrams for B → φφK and B → η c K . Based on a 78 fb − data sample, Belle reported the firstevidence for the decay with a branching fraction B ( B + → φφK + ) = [2 . + 1 . − . (stat) ± . × − [5] belowthe η c threshold ( m φφ < .
85 GeV /c ) [6]. The resultwas consistent with the corresponding theory prediction,which lies in the range (1 . . × − [7, 8]. The BaBarexperiment performed a measurement of this decay usingtheir full dataset of 464 × BB events [9]. The branch-ing fraction obtained with the same m φφ requirement was B ( B + → φφK + ) = (5 . ± . ± . × − , about threestandard deviations above Belle’s result and larger thantheoretical estimates. The B → φφK channel was ob- served with a branching fraction of (4 . ± . ± . × − .BaBar also reported CP asymmetries for charged B de-cays as − . ± . ± .
02 below the η c threshold and+0 . ± . ± .
02 within the η c region.In this paper, we update our earlier result [5] with asignificantly larger data sample containing 772 × BB events. The data were collected at the Υ (4 S ) resonancewith the Belle detector [10] at the KEKB asymmetric-energy e + e − collider [11]. The subdetectors relevant forour study are a silicon vertex detector (SVD), a cen-tral drift chamber (CDC), an array of aerogel thresholdCherenkov counters (ACC), and time-of-flight scintilla-tion counters (TOF). All these are located inside a 1 . B + → φφK + and B → φφK decaycandidates, we combine a pair of φ mesons with a chargedkaon and K S , respectively. All charged tracks except forthose from the K S must have a distance of closest ap-proach with respect to the interaction point (IP) of lessthan 0 . r – φ plane, and less than5 . z axis. The z axis is defined as the direc-tion opposite that of the e + beam. We identify chargedkaons based on a likelihood ratio R K/π = L K / ( L K + L π ),where L K and L π denote the individual likelihood forkaons and pions, respectively. These are calculated usingspecific ionization in the CDC and information from theACC and the TOF. A requirement R K/π > . φ candidates from pairs of oppo-sitely charged kaons with an invariant mass in the range1 . .
04 GeV /c , corresponding to ± σ ( σ is the widthof the mass distribution) around the nominal φ mass [12].This is referred to as the M KK signal region in the fol-lowing discussion. The K S candidates are reconstructedfrom two oppositely charged tracks, assumed to be pi-ons, and are further required to satisfy a criterion on theoutput of a neural network (NN) algorithm [13]. Thealgorithm uses the following input variables: the K S mo-mentum in the lab frame; the distance of closest approachalong the z axis between the two pion tracks; the flightlength in the r – φ plane; the angle between the K S mo-mentum and the vector joining the IP to the K S decayvertex; the angle between the K S momentum in the labframe and the pion momentum in the K S rest frame; thedistances of closest approach in the r – φ plane betweenthe IP and the two pion tracks; the number of CDC hitsfor each pion track; and the presence or absence of SVDhits for each pion track. We require that the invariantmass lie between 491 MeV /c and 504 MeV /c , which cor-responds to a ± σ window in resolution around the nom-inal K S mass [12]. B -meson candidates are identified with two kinematicvariables: the beam-energy-constrained mass M bc ≡ q E /c − | P i ~p i /c | , and the energy difference ∆ E ≡ P i E i − E b , where E b is the beam energy, and ~p i and E i are the momentum and energy, respectively, of the i -thdecay product of the B candidate. All these quantitiesare evaluated in the e + e − center-of-mass (CM) frame.We perform a fit for each B candidate, constrainingits decay products to originate from a common vertex.Candidate events with M bc ∈ [5 . , . /c and | ∆ E | < . M bc requirement corresponds to approximately ( − σ , +3 σ )in resolution around the nominal B mass [12], and the∆ E requirement denotes a ± σ window around zero.We apply such loose requirements on M bc and ∆ E asthese are used in a maximum-likelihood fit to obtain thesignal yield (described later). We define a signal regionas M bc ∈ [5 . , . /c and | ∆ E | < .
05 GeV.After application of the above selection criteria, the av-erage number of B candidates found per event selected indata are 1 . . B + → φφK + and B → φφK ,respectively. In the case of multiple B candidates, wechoose the candidate with the lowest χ value for theaforementioned B -vertex fit. From Monte Carlo (MC)simulation the best candidate selection method is foundto have an efficiency of 68% (65%) to correctly identifythe B -meson candidate in B + → φφK + ( B → φφK )decays. In only about 6% of the total signal events, the B candidate is misreconstructed due to swapping of kaonsbetween the two φ candidates, or of one daughter trackwith that from the rest of the event. Such misrecon-structed events are treated as a part of the signal.The dominant background is from the e + e − → qq ( q = u, d, s, c ) continuum process. To suppress this back-ground, observables based on event topology are used.The event shape in the CM frame is expected to be spher-ical for BB events and jet-like for continuum events. Weuse an NN [13] to combine the following six variables:a Fisher discriminant formed out of 16 modified Fox-Wolfram moments [14]; the cosine of the angle betweenthe B momentum and the z axis; the cosine of the an-gle between the B thrust axis [15] and the z axis; thecosine of the angle between the thrust axis of the B can-didate and that of the rest of the event; the ratio of thesecond- to the zeroth-order Fox-Wolfram moments (allquantities are calculated in the CM frame); and the ver-tex separation along the z axis between the B candidateand the remaining tracks. The NN training and vali-dation are performed with signal and qq MC simulatedevents. The signal sample is generated with the
EvtGen program [16], assuming a uniform distribution over thethree-body phase space of the final state.The neural network output ( O NN ) ranges between − . .
0, where events near − . .
0) are morecontinuum- (signal-) like. We apply a loose criterion O NN > − . B + → φφK + ( B → φφK ) decays,whereas the fraction of continuum events rejected is 76%(66%). As the remainder of the O NN distribution stronglypeaks near 1 . O ′ NN = log (cid:20) O NN − O NN , min O NN , max − O NN (cid:21) , (1)where O NN , min = − . O NN , max ≃ .
0, has aGaussian-like distribution that is easier to model. Thus,we use this transformed variable in our signal fit.Backgrounds due to B decays, mediated by the dom-inant b → c transition, are studied with MC samples ofsuch decays. For both B + → φφK + and B → φφK channels, the M bc and ∆ E distributions are found topeak in the signal region. To investigate the sourceof these contributions, we inspect the m φφ distribution,which displays several peaks corresponding to the η c andother charmonium resonances. To suppress these peak-ing backgrounds, we exclude candidates for which the m φφ value is greater than 2 .
85 GeV /c . This requirementalso allows us to compare our results with the earlier onesfrom Belle [5] and BaBar [9]. We calculate the detectionefficiencies for candidate events below the η c threshold tobe 12 .
4% and 12 .
0% for B + → φφK + and B → φφK ,respectively.Charmless backgrounds that do not produce onlykaons in the final state may still contribute to the M bc –∆ E signal region when a final-state particle is misidenti-fied. These are studied with a BB MC sample in whichone of the B mesons decays via b → u, d, s transitionswith known or estimated branching fractions [12]. Only40 events survive from an MC sample equivalent to 50times the size of the data sample. This small componentis combined with the events surviving from b → c transi-tions to form an overall BB background component. Inaddition to this BB background that does not peak in M bc or ∆ E , we can have contributions from B → φKKK and B → KKKKK decays (described later), which havethe same final-state particles as the signal.The signal yield is obtained with an unbinned extendedmaximum-likelihood fit to the three variables M bc , ∆ E ,and O ′ NN . We define a probability density function (PDF)for each event category, i.e., signal, qq , and BB back-grounds: P ij ≡ (1 − q i A CP,j ) P j ( M i bc ) P j (∆ E i ) P j ( O ′ i NN ) , (2)where i denotes the event index, q i is the charge of the B candidate ( q i = ± B ± ), and P j and A CP,j arethe PDF and CP asymmetry, respectively, for the eventcategory j . The latter is defined as A CP = N B − − N B + N B − + N B + , (3)where N B + ( N B − ) is the number of B + ( B − ) events. Wefind equal detection efficiencies for the B + (12 . ± . B − (12 . ± . B decays, wereplace the factor (1 − q i A CP,j ) by 1 in Eq. (2). Wealso do not perform a CP -violation study in this case,since we would need to tag the recoiling B candidate forthat, causing further loss in efficiency on top of the smallsignal yield. As the correlations among M bc , ∆ E , and O ′ NN are found to be small ( . L = e − P j n j N ! Y i h X j n j P ij i , (4)where n j is the yield of event category j , and N is thetotal number of candidate events. From the fitted signalyield ( n sig ), we calculate the branching fraction as B ( B → φφK ) = n sig εN BB [ B ( φ → K + K − )] , (5)where ε and N BB are the detection efficiency and thenumber of BB events, respectively. In case of B → φφK , we multiply the denominator by a factor of to account for K → K S , as well as by the subdecaybranching fraction B ( K S → π + π − ) [12].As the expected yield of the nonpeaking BB back-ground is small, and it is distributed similarly to qq in M bc and ∆ E , we merge qq and BB backgrounds into asingle component. We find that the difference in the O ′ NN distribution between the two backgrounds contributes anegligible systematic uncertainty. Table I lists the PDFshapes used to model M bc , ∆ E , and O ′ NN distributionsfor various event categories of B → φφK candidates.The yield and PDF shape parameters of the combinedbackground are floated in B + → φφK + . For the neu-tral channel, however, the background PDF shapes arefixed to their MC values after correcting for small dif-ferences between data and simulation, as obtained fromthe charged decay. Similarly, for the signal components,we fix the M bc , ∆ E , and O ′ NN shapes to MC values andcorrect for small data-MC differences according to valuesobtained from a control sample of B + → D + s D decays,where D + s → φ ( → K + K − ) π + and D → K + π − .We apply the above 3D fit to B + → φφK + and B → φφK candidate events to determine the signalyield (and A CP in the first case). Figures 2 and 3 show M bc , ∆ E , and O ′ NN projections of the fits. The fit resultsare listed in Table II. We find signal yields of 85 . + 10 . − . for B + → φφK + and 26 . + 5 . − . for B → φφK , and an A CP value of − . ± .
11 for the first case. We also apply the 3D fit to B + → φφK + candidate events with m φφ within the η c region to calculate the signal yield and A CP value. The corresponding M bc and ∆ E projectionsare shown in Fig. 4, with the fit results listed in Table II.We obtain a signal yield of 73 . + 9 . − . and an A CP value of+0 . ± .
12 in the η c region. The signal significance iscalculated as p − L / L max ), where L and L max arethe likelihood values with the signal yield fixed to zeroand for the nominal fit, respectively. We include system-atic uncertainties that impact only the signal yield intothe likelihood curve via a Gaussian convolution beforecalculating the final significance. TABLE I. List of PDFs used to model the M bc , ∆ E , and, O ′ NN distributions for various event categories for B → φφK .The notation G, AG, 2G, ARG, and Poly1 denote Gaussian,asymmetric Gaussian, sum of two Gaussians, ARGUS [17]function, and first-order polynomial, respectively.Event category M bc ∆ E O ′ NN Signal G+ARG 2G+Poly1 G+AG qq + BB ARG Poly1 G
To estimate the contribution of B → φKKK and B → KKKKK decays in the M KK signal region (SR),we repeat the 3D fit in the following two sidebands: SB1is denoted by the sum of ( M K K ∈ [1 . , .
2] GeV /c and M K K ∈ [1 . , .
04] GeV /c ) and ( M K K ∈ [1 . , .
04] GeV /c and M K K ∈ [1 . , .
2] GeV /c ), andSB2 is denoted by M K K ∈ [1 . , .
2] GeV /c and M K K ∈ [1 . , .
2] GeV /c . In Fig. 5 we plot the dis-tribution of data events in the M K K vs M K K planeshowing SR, SB1, and SB2. The resonant B → φφK yield in SR is obtained by solving the following threelinear equations: N = n s + r a × n a + r b × n b , (6) N = r s × n s + n a + r b × n b , (7) N = r s × n s + r a × n a + n b , (8)where N , N , and N are the yields obtained in SR,SB1, and SB2, respectively; n s , n a , and n b are the B → φφK yield in SR, B → φKKK yield in SB1, and B → KKKKK yield in SB2, respectively. Lastly, r s and r s are the ratios of B → φφK yields in SB1 and SB2 tothat in SR; r a and r a are the ratios of B → φKKK yields in SR and SB2 to that in SB1; and r b and r b are the ratios of B → KKKKK yields in SR and SB1to that in SB2. All these ratios are obtained from anMC study. We obtain the resonant B → φφK yield inSR ( n s ) as 81 . + 10 . − . and 23 . + 5 . − . for the charged andneutral mode, respectively. These n s values are used inthe branching fraction calculation of Eq. (5).The background-subtracted distributions [18] of m φφ and m φK obtained for B ± → φφK ± below the η c thresh-old are shown in Fig. 6. These are broadly compatiblewith the predictions of a three-body phase space MC ) (GeV/c bc M ) E v en t s / ( . M e V / c + K φφ → + B ) (GeV/c bc M ) E v en t s / ( . M e V / c - K φφ → - B − − E (GeV) ∆ E v en t s / ( M e V ) + K φφ → + B − − E (GeV) ∆ E v en t s / ( M e V ) - K φφ → - B /NN O − − − − E v en t s / . + K φφ → + B /NN O − − − − E v en t s / . - K φφ → - B FIG. 2. Projections of B ± → φφK ± candidate events onto(top) M bc , (middle) ∆ E , and (bottom) O ′ NN . Black pointswith error bars are the data, solid blue curves are the to-tal PDF, dashed green curves are the signal component, anddotted red curves are the combined qq and BB backgroundcomponents. sample. In particular, we do not find any enhancementin the m φφ spectrum, including the 2 . /c region [3]where a glueball and X (2350) candidates are predicted.Systematic uncertainties in the branching fraction arelisted in Table III. The uncertainties due to PDF shapesare estimated by varying all the fixed shape parame-ters by their errors. In particular, for fixed signal shapeparameters, we vary the data-MC corrections by theiruncertainties as determined using the control sample of ) (GeV/c bc M ) E v en t s / ( . M e V / c − − E (GeV) ∆ E v en t s / ( M e V ) /NN O − − − − E v en t s / . FIG. 3. Projections of B → φφK candidate events onto(top left) M bc , (top right) ∆ E , and (bottom) O ′ NN . The leg-ends of the plots are defined in the same manner as in Fig. 2.TABLE II. Number of candidate events ( n cand ), detection effi-ciency ( ε ), total and resonant signal yield ( n sig ), significance,branching fraction ( B ) and CP asymmetry ( A CP ) obtainedfrom a fit to data for B → φφK decays below and within the η c region. Quoted uncertainties are statistical only, and sig-nificances defined in the text are given in terms of standarddeviations. B + → φφK + B → φφK B + → φφ ( η c ) K + n cand
207 51 84 ε (%) 12 . . . n sig . + 10 . − . . + 5 . − . . + 9 . − . Significance 14 . . . n sig . + 10 . − . . + 5 . − . – B (10 − ) 3 . + 0 . − . . + 0 . − . – A CP − . ± .
11 – +0 . ± . B + → D + s D decays. Potential fit bias is checked byperforming an ensemble test comprising 1000 pseudo-experiments, where signal is taken from the correspond-ing MC sample, and the PDF shapes are used to gen-erate background events. We obtain a Gaussian nor-malized residual distribution of unit width, and add itsmean and uncertainty in width in quadrature to cal-culate the systematic error. Uncertainty due to con-tinuum suppression is obtained with the B + → D + s D ) (GeV/c bc M ) E v en t s / ( . M e V / c + )K c η ( φφ → + B ) (GeV/c bc M ) E v en t s / ( . M e V / c - )K c η ( φφ → - B − − E (GeV) ∆ E v en t s / ( M e V ) + )K c η ( φφ → + B − − E (GeV) ∆ E v en t s / ( M e V ) - )K c η ( φφ → - B FIG. 4. Projections of B ± → φφK ± candidate events withinthe η c region onto (top) M bc and (bottom) ∆ E . The legendsof the plots are defined in the same manner as in Fig. 2. ) (GeV/c K K M1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 ) ( G e V / c K K M
21 34
FIG. 5. Distribution of data events in the M K K vs M K K plane which shows the M KK signal region (region 1) and twosidebands SB1 (region 2 and 3) and SB2 (region 4). control sample by comparing, between data and simu-lation, fit results obtained with and without the O NN requirement. A D ∗ + → D ( K − π + ) π + control sampleis used to determine the systematic uncertainty due tothe R K/π requirement. We use partially reconstructed D ∗ + → D ( K S π + π − ) π + decays to assign the systematic ) (GeV/c φφ m ) E v en t s / ( M e V / c ) (GeV/c K φ m ) E v en t s / ( M e V / c FIG. 6. Background-subtracted signal yield as a function of m φφ (left) and m φ K (right) for B ± → φφK ± . Black pointswith error bars are data and solid blue histograms denote theexpectation from a phase-space MC sample. uncertainty due to charged-track reconstruction (0 . K S reconstructionis estimated from D → K S K S decays [19]. We esti-mate the uncertainty due to efficiency variation acrossthe Dalitz plot by weighting phase-space-generated sig-nal MC events according to the measured distributionin data (Fig. 6) and taking the difference between theweighted and nominal efficiency. The total systematicuncertainty is obtained by adding all the above contribu-tions in quadrature. TABLE III. Systematic uncertainties (in %) in the branchingfractions. Values listed in the top three rows impact the signalyield and are included in the calculation of signal significance.Source B ± → φφK ± B → φφK Signal PDF + 1 . − . . − . Background PDF – + 3 . − . Fit bias ± . ± . ± . ± . R K/π requirement ± . ± . qq suppression ± . ± . ± . ± . K S reconstruction – ± . BB events ± . ± . ± . + 6 . − . We consider two possible sources of systematic un-certainties contributing to A CP , as listed in Table IV.The first is due to the intrinsic detector bias on chargedkaon detection and is estimated using D + s → φπ + and D → K − π + decays [20]. The second arises due to thepotential variation of the PDF shapes. We calculate itscontribution by following a procedure similar to that usedin estimating the PDF shape uncertainties in the branch-ing fractions.In summary, we have measured the branching fractionsand CP -violation asymmetries in B → φφK decays basedon the full Υ (4 S ) data sample of 772 × BB events TABLE IV. Systematic uncertainties in A CP .Source B ± → φφK ± B ± → φφ ( η c ) K ± Detection asymmetry ± . ± . + 0 . − . ± . ± . ± . collected by the Belle detector at the KEKB asymmetric-energy e + e − collider. We obtain the branching fractionand CP asymmetry for B ± → φφK ± below the η c thresh-old ( m φφ < .
85 GeV /c ) as(3 . + 0 . − . ± . × − (9)and − . ± . ± . , (10)respectively. We also report the CP -violation asym-metry for B ± → φφK ± in the η c region ( m φφ ∈ [2 . , .
02] GeV /c ) to be+0 . ± . ± . , (11)consistent with no CP violation. The obtained value ofthe branching fraction of B ± → φφK ± decay is consis-tent with and supersedes our previous result [5]. Themeasured branching fraction for B → φφK below the η c threshold is (3 . + 0 . − . ± . × − . (12)We find no evidence for glueball production in these de-cays.SM acknowledges fruitful discussions with S. Mahap-atra (Utkal University). We thank the KEKB group forexcellent operation of the accelerator; the KEK cryogen-ics group for efficient solenoid operations; and the KEKcomputer group, the NII, and PNNL/EMSL for valu-able computing and SINET5 network support. We ac-knowledge support from MEXT, JSPS and Nagoya’s TL-PRC (Japan); ARC (Australia); FWF (Austria); NSFCand CCEPP (China); MSMT (Czechia); CZF, DFG,EXC153, and VS (Germany); DAE, Project Identifica-tion No. RTI 4002, and DST (India); INFN (Italy);MOE, MSIP, NRF, RSRI, FLRFAS project, GSDC ofKISTI and KREONET/GLORIAD (Korea); MNiSWand NCN (Poland); MSHE, Agreement 14.W03.31.0026 (Russia); University of Tabuk (Saudi Arabia); ARRS(Slovenia); IKERBASQUE (Spain); SNSF (Switzerland);MOE and MOST (Taiwan); and DOE and NSF (USA). ∗ now at Hiroshima University[1] N. Cabibbo, Phys. Rev. Lett. , 531 (1963); M.Kobayashi and T. Maskawa, Prog. Theor. Phys. , 652(1973).[2] M. Hazumi, Phys. Lett. B , 285 (2004).[3] C. K. Chua, W.-S. Hou, and S.-Y. Tsai, Phys. Lett. B , 139 (2002).[4] Z. Q. Liu et al. (Belle Collaboration), Phys. Rev. Lett. , 232001 (2012).[5] H. C. Huang et al. (Belle Collaboration), Phys. Rev. Lett. , 241802 (2003).[6] Inclusion of charge-conjugate reactions is implied unlessstated otherwise.[7] S. Fajfer, T. N. Pham, and A. Prapotnik, Phys. Rev. D , 114020 (2004).[8] C.-H. Chen and H.-N. Li, Phys. Rev. D , 054006(2004).[9] J. P. Lees et al. (BaBar Collaboration), Phys. Rev. D ,012001 (2011).[10] A. Abashian et al. (Belle Collaboration), Nucl. Instrum.Methods Phys. Res., Sect. A , 117 (2002); also seethe detector section in J. Brodzicka et al. , Prog. Theor.Exp. Phys. , 04D001 (2012).[11] S. Kurokawa and E. Kikutani, Nucl. Instrum. MethodsPhys. Res., Sect. A , 1 (2003), and other papers in-cluded in this Volume; T. Abe et al. , Prog. Theor. Exp.Phys. , 03A001 (2013) and references therein.[12] P. A. Zyla et al. (Particle Data Group), Prog. Theor.Exp. Phys. , 083C01 (2020).[13] M. Feindt and U. Kerzel, Nucl. Instrum. Methods Phys.Res., Sect. A , 190 (2006).[14] S. H. Lee et al. (Belle Collaboration), Phys. Rev. Lett. , 261801 (2003).[15] S. Brandt, C. Peyrou, R. Sosnowski, and A. Wroblewski,Phys. Lett. , 57 (1964); E. Farhi, Phys. Rev. Lett. ,1587 (1977).[16] D. J. Lange, Nucl. Instrum. Methods Phys. Res., Sect. A , 152 (2001).[17] H. Albrecht et al. (ARGUS Collaboration), Phys. Lett.B , 278 (1990).[18] M. Pivk and F. R. Le Diberder, Nucl. Instrum. MethodsPhys. Res., Sect. A , 356 (2005).[19] N. Dash et al. (Belle Collaboration), Phys. Rev. Lett. , 171801 (2017).[20] M. Staric et al. (Belle Collaboration), Phys. Rev. Lett.108