Search for B_{s}^{0} \rightarrow η^{\prime} X_{s\bar{s}} at Belle using a semi-inclusive method
Belle Collaboration, S. Dubey, T. E. Browder, H. Aihara, S. Al Said, D. M. Asner, T. Aushev, R. Ayad, V. Babu, S. Bahinipati, P. Behera, J. Bennett, M. Bessner, B. Bhuyan, S. Bilokin, J. Biswal, A. Bobrov, G. Bonvicini, A. Bozek, M. Bra?ko, M. Campajola, D. ?ervenkov, B. G. Cheon, K. Chilikin, H. E. Cho, K. Cho, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, S. Das, R. Dhamija, F. Di Capua, Z. Doležal, D. Dossett, S. Eidelman, D. Epifanov, T. Ferber, B. G. Fulsom, R. Garg, V. Gaur, N. Gabyshev, A. Garmash, A. Giri, P. Goldenzweig, B. Golob, D. Greenwald, Y. Guan, K. Gudkova, C. Hadjivasiliou, K. Hayasaka, H. Hayashii, M. T. Hedges, W.-S. Hou, C.-L. Hsu, K. Inami, A. Ishikawa, R. Itoh, M. Iwasaki, Y. Iwasaki, E.-J. Jang, Y. Jin, C. W. Joo, K. K. Joo, A. B. Kaliyar, T. Kawasaki, H. Kichimi, C. H. Kim, D. Y. Kim, S. H. Kim, Y.-K. Kim, T. D. Kimmel, K. Kinoshita, S. Korpar, P. Križan, R. Kroeger, P. Krokovny, T. Kuhr, R. Kulasiri, R. Kumar, K. Kumara, Y.-J. Kwon, K. Lalwani, J. S. Lange, S. C. Lee, C. H. Li, J. Li, L. K. Li, Y. B. Li, L. Li Gioi, J. Libby, D. Liventsev, C. MacQueen, M. Masuda, T. Matsuda, M. Merola, F. Metzner, K. Miyabayashi, R. Mizuk, G. B. Mohanty, et al. (74 additional authors not shown)
BBelle Preprint 2021-01KEK Preprint 2020-40
Search for B s → η (cid:48) X s ¯ s at Belle Using a Semi-Inclusive Method S. Dubey, T. E. Browder, H. Aihara, S. Al Said,
75, 34
D. M. Asner, T. Aushev, R. Ayad, V. Babu, S. Bahinipati, P. Behera, J. Bennett, M. Bessner, B. Bhuyan, S. Bilokin, J. Biswal, A. Bobrov,
4, 59
G. Bonvicini, A. Bozek, M. Braˇcko,
46, 30
M. Campajola,
27, 52
D. ˇCervenkov, B. G. Cheon, K. Chilikin, H. E. Cho, K. Cho, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, S. Das, R. Dhamija, F. Di Capua,
27, 52
Z. Doleˇzal, D. Dossett, S. Eidelman,
4, 59, 40
D. Epifanov,
4, 59
T. Ferber, B. G. Fulsom, R. Garg, V. Gaur, N. Gabyshev,
4, 59
A. Garmash,
4, 59
A. Giri, P. Goldenzweig, B. Golob,
42, 30
D. Greenwald, Y. Guan, K. Gudkova,
4, 59
C. Hadjivasiliou, K. Hayasaka, H. Hayashii, M. T. Hedges, W.-S. Hou, C.-L. Hsu, K. Inami, A. Ishikawa,
15, 11
R. Itoh,
15, 11
M. Iwasaki, Y. Iwasaki, E.-J. Jang, Y. Jin, C. W. Joo, K. K. Joo, A. B. Kaliyar, T. Kawasaki, H. Kichimi, C. H. Kim, D. Y. Kim, S. H. Kim, Y.-K. Kim, T. D. Kimmel, K. Kinoshita, S. Korpar,
46, 30
P. Kriˇzan,
42, 30
R. Kroeger, P. Krokovny,
4, 59
T. Kuhr, R. Kulasiri, R. Kumar, K. Kumara, Y.-J. Kwon, K. Lalwani, J. S. Lange, S. C. Lee, C. H. Li, J. Li, L. K. Li, Y. B. Li, L. Li Gioi, J. Libby, D. Liventsev,
86, 15
C. MacQueen, M. Masuda,
81, 66
T. Matsuda, M. Merola,
27, 52
F. Metzner, K. Miyabayashi, R. Mizuk,
40, 17
G. B. Mohanty, S. Mohanty,
76, 84
T. J. Moon, M. Nakao,
15, 11
A. Natochii, L. Nayak, M. Nayak, N. K. Nisar, S. Nishida,
15, 11
K. Nishimura, S. Ogawa, H. Ono,
57, 58
Y. Onuki, P. Oskin, G. Pakhlova,
17, 40
S. Pardi, S.-H. Park, T. K. Pedlar, R. Pestotnik, L. E. Piilonen, T. Podobnik,
42, 30
E. Prencipe, M. T. Prim, A. Rostomyan, N. Rout, G. Russo, D. Sahoo, Y. Sakai,
15, 11
S. Sandilya, A. Sangal, L. Santelj,
42, 30
T. Sanuki, V. Savinov, G. Schnell,
1, 19
C. Schwanda, Y. Seino, K. Senyo, M. E. Sevior, M. Shapkin, C. Sharma, J.-G. Shiu, B. Shwartz,
4, 59
E. Solovieva, M. Stariˇc, Z. S. Stottler, J. F. Strube, K. Sumisawa,
15, 11
M. Takizawa,
70, 16, 67
U. Tamponi, K. Tanida, Y. Tao, F. Tenchini, K. Trabelsi, M. Uchida, Y. Unno, S. Uno,
15, 11
Y. Ushiroda,
15, 11
Y. Usov,
4, 59
S. E. Vahsen, R. Van Tonder, G. Varner, C. H. Wang, E. Wang, P. Wang, M. Watanabe, S. Watanuki, X. Xu, B. D. Yabsley, W. Yan, S. B. Yang, H. Ye, J. H. Yin, Z. P. Zhang, V. Zhilich,
4, 59 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 Justus-Liebig-Universit¨at Gießen, 35392 Gießen 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 Technology Bhubaneswar, Satya Nagar 751007 Indian Institute of Technology Guwahati, Assam 781039 Indian Institute of Technology Hyderabad, Telangana 502285 Indian Institute of Technology Madras, Chennai 600036 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 a r X i v : . [ h e p - e x ] F e b Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583 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 Liaoning Normal University, Dalian 116029 Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana Ludwig Maximilians University, 80539 Munich 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 Mississippi, University, Mississippi 38677 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 United University, Miao Li 36003 Department of Physics, National Taiwan University, Taipei 10617 H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342 Nippon Dental University, Niigata 951-8580 Niigata University, Niigata 950-2181 Novosibirsk State University, Novosibirsk 630090 Osaka City University, Osaka 558-8585 Pacific Northwest National Laboratory, Richland, Washington 99352 Panjab University, Chandigarh 160014 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 Department of Physics, Technische Universit¨at M¨unchen, 85748 Garching 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 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 (Dated: February 23, 2021)
We report the first search for the penguin-dominated process B s → η (cid:48) X s ¯ s using a semi-inclusivemethod. A 121.4 fb − integrated luminosity Υ(5 S ) data set collected by the Belle experiment, atthe KEKB asymmetric-energy e + e − collider, is used. We observe no statistically significant signaland including all uncertainties, we set a 90% confidence level upper limit on the partial branchingfraction at 1.4 × − for M ( X s ¯ s ) ≤ c . The study of the decay of B mesons — bound states ofa b antiquark and either a u , d , s , or c quark — has beenfruitful for the interrogation of rare processes, elucidatingthe strong and weak interactions of the Standard Model(SM) of particle physics. According to the SM flavor-changing neutral currents are forbidden in B decays atleading-order, but may effectively occur at higher-orderin so-called “penguin” processes [1].The CLEO collaboration measured a larger than ex-pected branching fraction (BF) for the charmless de-cay (decays whose primary decay products lack a charmquark) B → η (cid:48) X s as B ( B → η (cid:48) X s ) = [4.6 ± ± ± × − , with M ( X s ) < c , where the third uncertainty is due to the back-ground subtraction [2, 3]. BaBar measured B ( B → η (cid:48) X s )= [3.9 ± ± ± × − ,for the same M ( X s ) requirement [4]. Belle previouslymeasured the BF for the related process B → ηX s as B ( B → ηX s ) = [26.1 ± +1 . − . (syst.) +4 . − . (model)] × − [5]. While the η (cid:48) meson itself is interest-ing [6] as its mass is higher than is expected from symme-try considerations, it is the unexpected BF enhancementseen in these measurements that has generated consider-able interest. In Ref. [7], for example, the predicted BFfor B → η (cid:48) X is 1.3 × − . Explanations for this appar-ent enhancement focus on processes such as the b → sg transition, which is modified to an anomalous b → sg ∗ process, where g ∗ → gη (cid:48) , with the gluon coupling to the η (cid:48) singlet [8–14]. Hence, glueball coupling may providean explanation for these decays involving the η (cid:48) . Inclusive b → sg processes have not yet been in-vestigated using the B s meson. In this letter we re-port the first search for the decay B s → η (cid:48) X s ¯ s usinga semi-inclusive method [15] with data collected at theΥ(5 S ) resonance by the Belle detector at the KEKBasymmetric-energy e + e − collider in Japan [16].To lowest order, the amplitude for B s → η (cid:48) X s ¯ s con-tains contributions from QCD penguin diagrams, theanomalous gη (cid:48) coupling, the tree-level color-suppressed b → u diagram, and the b → s ( γ, Z ) electroweak penguindiagrams, shown in Fig. 1 [17].The Belle detector is a large-solid-angle magnetic spec-trometer that consists of a silicon vertex detector (SVD),a 50-layer central drift chamber (CDC), an array of aero-gel threshold Cherenkov counters (ACC), a barrel-like ar-rangement of time-of-flight scintillation counters (TOF),and an electromagnetic calorimeter comprised of CsI(Tl)crystals (ECL) located inside a superconducting solenoidcoil that provides a 1.5 T magnetic field. An iron flux-return located outside of the coil is instrumented to de- (a) QCD Penguin (b) QCD Penguin(c) g − η (cid:48) Coupling (d) Color-Suppressed Tree(e) Electroweak Penguin (f) Electroweak Penguin
FIG. 1. Lowest-order diagrams contributing to B s → η (cid:48) X s ¯ s tect K L mesons and to identify muons. The Υ(5 S ) datasample used a 1.5 cm radius beampipe, a 4-layer SVD,and a small-inner-cell CDC [18].We use the 121.4 fb − data sample recorded by Belle,taken at the center-of-mass (CM) energy √ s = 10 . ± × B s ¯ B s pairs, the world’s largest Υ(5 S ) sample in e + e − collisions[19]. A blind analysis is performed, whereby the selectioncriteria are first optimized on Monte Carlo (MC) simula-tions before being applied to the data. A signal MC sam-ple for B s → η (cid:48) X s ¯ s is generated using EvtGen [20] andthe detector response is simulated using GEANT3 [21],with PHOTOS describing final-state radiation [22]. TheMC-generated mass of the X s ¯ s system is bounded belowby the two-(charged) kaon mass 0.987 GeV/ c and hasan upper bound of 3.0 GeV/ c . The X s ¯ s mass is gener-ated as a flat distribution and is fragmented by PYTHIA6 [23].The B s (¯ bs ) and ¯ B s ( b ¯ s ) candidates are reconstructedusing a semi-inclusive method in which the X s ¯ s is re-constructed as a system of two kaons, either K + K − or K ± K S ( → π + π − ), and up to four pions with at most one π , where the π decays via the channel π → γγ . The η (cid:48) is reconstructed in the channel η (cid:48) → η ( → γγ ) π + π − .The experimental signature is divided into two classes ofdecay modes: without ( B s → η (cid:48) K + K − + nπ ) and with( B s → η (cid:48) K ± K S + nπ ) a K S . These classes are analyzedseparately, with the weighted average BFs taken at theend. Charge-conjugate decays are included unless explic-itly stated otherwise.Well-constrained charged tracks are required to have atransverse momentum p T greater than 50 MeV/ c . Sepa-ration of the charged kaons and charged pions is providedby the CDC [24], ACC [25], and the TOF [26] systems.Information from these subdetectors is combined to forma likelihood ratio for the charged kaon hypothesis: P K ± = L K ± /( L K ± + L π ± ). For this analysis, the selections P K ± > K ± and P K ± < π ± are applied.The efficiency to correctly identify a pion (kaon) is 98%(88)%, with a misidentification rate of 4% (12)% [5].The π candidate mass range is M ( γγ ) ∈ [0.089, 0.180]GeV/ c ( ± σ window). The π candidates are kinemat-ically constrained to the nominal mass [27]. In the ECL,the photons constituting the π are required to have en-ergies greater than 50 MeV in the barrel region, greaterthan 100 MeV in the endcaps, and the ratio of their en-ergy depositions in a 3 × × π laboratory-framemomentum to be greater than 0.2 GeV/ c is imposed.The η is reconstructed in a two-photon asymmetric in-variant mass window M η ∈ [0.476, 0.617] GeV/ c (5.3 σ L ,10 σ R ). The asymmetry is due to energy leakage in theECL, causing the η mass distribution to be asymmet-ric. Each photon is required to have E γ > | E γ − E γ | / ( E γ + E γ ) < η (cid:48) mesons are reconstructed ina fully efficient mass window M η (cid:48) ∈ [0.933, 0.982] GeV/ c ( ± σ ). The η and η (cid:48) masses are kinematically fit to theworld average [27]. The mass range of the K S is M K S ∈ [0.487, 0.508] GeV/ c ( ± σ window).The X s ¯ s system is reconstructed as a system of kaonsand pions, which is in turn combined with the η (cid:48) toform B s candidates. Two variables important in extract-ing the signal are the energy difference ∆ E , defined as∆ E = E B s − E beam and the beam-energy-constrainedmass, defined as M bc = (cid:113) E /c − p B s /c , where E beam = √ s/ E B s is the energy of the B s , and p B s is the magnitude of the B s three-momentum in the CMframe.An initial reduction in continuum background( e + e − → q ¯ q , q = u , d , s , c ) is done with a selection on theratio of the second to the zeroth order Fox-Wolfram mo-ments R ≤ O NN describes, effec-tively, the probability that a B s candidate came from anevent whose topology is spherical or jet-like.To obtain a specific O NN selection, the figure-of-merit(FOM) S/ √ S + B is optimized as a function of O NN ,where S and B are the fitted signal and background yieldsfrom an MC sample that is passed through the trainednetwork. This MC contains an approximately data-equivalent background and an enhanced signal. Thiswas done assuming B ( B s → η (cid:48) X s ¯ s ) = 2 × − ; this is1.6 standard deviations below the BaBar central valuefor B → η (cid:48) X s . The value of O NN corresponding to themaximum value of the FOM is selected. Events hav-ing O NN values below this selection are rejected. Sep-arate optimizations are done for B s → η (cid:48) K + K − + nπ and B s → η (cid:48) K ± K S + nπ . The NN requirement re-duces continuum background by more than 97% in bothcases, while preserving 39% and 53% of signal events for B s → η (cid:48) K + K − + nπ and B s → η (cid:48) K ± K S + nπ , respec-tively. The two experimental signatures have differentbackground levels and efficiencies, and hence their NNsare optimized separately.After an initial requirement of M bc > .
30 GeV/ c , | ∆ E | < .
35 GeV, and M ( X s ¯ s ) ≤ c , and afterall final selections are applied, there are an average of 6.4candidates per event for B s → η (cid:48) K + K − + nπ and 26.0for B s → η (cid:48) K ± K S + nπ . To select the best candidateper event, the candidate with the smallest χ given by χ = χ /ndf +(∆ E − µ ∆ E ) /σ E is selected, where ∆ E is calculated on a candidate-by-candidate basis, and µ ∆ E is the mean energy difference obtained through studiesof signal MC of individual exclusive B s → η (cid:48) X s ¯ s decaymodes. Here χ /ndf is the reduced χ from a successfulvertex fit of the primary charged daughter particles of the X s ¯ s . From signal MC, the efficiency of the best candidateselection is 85.5% for B s → η (cid:48) K + K − + nπ and 43.2% for B s → η (cid:48) K ± K S + nπ , in the signal region. The fraction of B s candidates passing best candidate selection that arecorrectly reconstructed is 94.0% for B s → η (cid:48) K + K − + nπ and 60.4% for B s → η (cid:48) K ± K S + nπ . These numbers areobtained after all final selections are applied.Other backgrounds were studied as sources of poten-tial peaking background. Due to the signal final state,it is difficult to have backgrounds that will be equiva-lent in topology and strangeness, and that are not highlysuppressed. However, one such unmeasured mode is B s → η (cid:48) D s π . Reconstruction efficiency is estimated us-ing MC events and an expected number of peaking eventsis determined. For B s → η (cid:48) D s π the BF is assumed to besimilar to B → D − π + ρ , for which the world average is[1.1 ± × − [27]. After applying all final selections,the total number of expected peaking events is less thanone. There is a negligible amount of peaking backgroundbased on studies of B s ) ¯ B s ) MC samples.The decay B → η (cid:48) K ∗ can contribute to peaking back-ground if the pion from K ∗ → K − π + is misidentified.The world average BF is [2.8 ± × − [27]. Fromthis and the pion misidentification rate, we expect thebackground contribution from this mode to be negligi-ble.The color-suppressed, tree-level process B s → ¯ D η (cid:48) ,with D → K + K − could potentially contribute to thepeaking background. However, B → ¯ D η (cid:48) has a mea-sured BF of B ( B → ¯ D η (cid:48) ) = [1.38 ± × − . Theprocess D → K + K − is Cabibbo-suppressed and has ameasured BF of B ( D → K + K − ) = [4.08 ± × − [27]. Assuming SU (3) symmetry, we expect there to beless than one event from B s → ¯ D η (cid:48) , for this analysis.For signal extraction, fitting is done in 0.2 GeV/ c bins of X s ¯ s mass, up to 2.4 GeV/ c , using unbinnedmaximum-likelihood fits. All submodes are combined forfitting. Signal extraction is done by fitting the M bc distri-bution in the region M bc > .
30 GeV/ c , − ≤ ∆ E ≤ S ) decays to B s pairs with a fraction of 0.172 ± S ) has threechannels for the B s decays: Υ(5 S ) → B ∗ s ¯ B ∗ s , Υ(5 S ) → B s ¯ B ∗ s and B ∗ s ¯ B s , and Υ(5 S ) → B s ¯ B s . The rates are87.0%, 7.3%, and 5.7%, respectively [19]. The low-energyphoton from B ∗ s → B s γ is not reconstructed. This hasthe effect of shifting the mean of the ∆ E distribution toa value of approximately −
50 MeV.The signal is modeled as the sum of three Gaussianprobability density functions (PDFs) that correspond tothe three Υ(5 S ) decays described in the previous para-graph. For analysis of the Υ(5 S ) data, their shape pa-rameters are empirically derived from a B s → D − s ρ + data control sample. The means and widths of the sig-nal Gaussians are fixed from this. The dominant non-peaking background is from continuum with others com-ing from generic B ∗ ) s ¯ B ∗ ) s and B ¯ BX decays. The non-peaking background fit component is an ARGUS PDF[31] with a fixed shape parameter, determined from fitsto Υ(5 S ) data NN sidebands. The ARGUS endpoint isfixed at 5.434 GeV/ c , the kinematic limit of M bc . Thefull model is the sum of the signal and background PDFs,with the signal and background yields allowed to float.The signal reconstruction efficiency, defined as (cid:15) i = N rec i /N gen i , is determined from fitting signal MC sample,in each X s ¯ s mass bin i after all selections are applied.Here, N gen i = N B s → η (cid:48) K + K − + nπi + N B s → η (cid:48) K ± K S + nπi + N other i , is the number of generated B s mesons in thesignal MC sample. The quantity N other i is the numberof generated B s mesons that do not belong to either ofthe two classes of signal modes: B s → η (cid:48) K + K − + nπ and B s → η (cid:48) K ± K S + nπ [32]. The quantity N rec i is thenumber of events found from the Gaussian signal fit in the i -th X s ¯ s mass bin.The BF is calculated as B ( B s → η (cid:48) X s ¯ s ) i = N sig i / (2 × N B ∗ ) s ¯ B ∗ ) s ) (cid:15) (cid:48) i [ B ( η → γγ ) B ( η (cid:48) → π + π − η )], where i de-notes the mass bins of X s ¯ s , the (cid:15) (cid:48) i are the bin-by-bin MCsignal reconstruction efficiencies (cid:15) i , corrected for data-MC discrepancies in NN selection, best candidate selec-tion, particle identification, tracking efficiency, η → γγ reconstruction, π → γγ reconstruction, and K S → π + π − reconstruction. The quantity N sig i is the numberof fitted signal events and the quantity N B ∗ ) s ¯ B ∗ ) s is thenumber of produced B ∗ ) s ¯ B ∗ ) s pairs.Figures 2 and 3 show the sum of the fits, whose resultsare listed in Tables I and II, respectively, overlaid on thedata. The central value for B ( B s → η (cid:48) X s ¯ s ) is estimatedby taking the weighted average of the total BF centralvalues for B s → η (cid:48) K + K − + nπ and B s → η (cid:48) K ± K + nπ .These are obtained by summing the BFs listed in Tables Iand II, for B s → η (cid:48) K + K − + nπ and B s → η (cid:48) K ± K + nπ ,respectively. The weights for the average central valueare obtained from the statistical uncertainties. System-atic uncertainties are added in quadrature; fragmenta-tion model (FM) uncertainties are added linearly withina class and for the final weighted average, these classsums are added in quadrature.The statistical significance in each X s ¯ s mass bin is cal-culated as S = (cid:112) − L / L max ), where L is the like-lihood at zero signal yield and L max is the maximumlikelihood. No statistically significant excess of events isobserved in any X s ¯ s mass bin. We set an upper limiton the partial BF (a BF with the requirement M ( X s ¯ s ) ≤ c ) at 90% confidence level by integrating aGaussian likelihood function whose standard deviation isestimated by the sum in quadrature of the positive sta-tistical and systematic uncertainties [33]. The standarddeviation, σ , is approximately 8.6 × − . The integralis restricted to the physically allowed region above zero,giving an upper limit on B ( B s → η (cid:48) X s ¯ s ). As a result,1.68 σ is added to the weighted average central value toobtain the 90% confidence level upper limit.The central value of the BF is B ( B s → η (cid:48) X s ¯ s ) = [ − ± ± +3 . − . (FM) ± B ∗ ) s ¯ B ∗ ) s )] × − . The FM uncertainty is obtained by consider-ing alternate sets of X s ¯ s fragmentation parameter valuesin PYTHIA and redetermining the signal reconstructionefficiency [34].The corresponding upper limit at 90% confidence levelon the partial BF, including all uncertainties, is 1.4 × − for M ( X s ¯ s ) ≤ c . If SU (3) symmetryholds, then the BFs of B → η (cid:48) X s and B s → η (cid:48) X s ¯ s would be equivalent and their ratio, R ( η (cid:48) ) = B ( B s → η (cid:48) X s ¯ s )/ B ( B → η (cid:48) X s ) would be close to 1 [17]. Themeasured BF for the decay B → η (cid:48) X s is [3.9 ± ± ± × − [4].Using this and the weighted average BF given previ-ously for B s → η (cid:48) X s ¯ s , R ( η (cid:48) ) is approximately − FIG. 2. Sum of the fits to all M ( X s ¯ s ) bins overlaid on the M bc distribution, for the decay B s → η (cid:48) ( → ηπ + π − ) X s ¯ s for B s → η (cid:48) K + K − + nπ submodes and M ( X s ¯ s ) ≤ c and with all selections applied. The light blue shaded regionis the sum of the background fits, the red shaded region is thesum of the signal fits, and the black dashed curve is the sumof the two.FIG. 3. Sum of the fits to all M ( X s ¯ s ) bins overlaid on the M bc distribution, for the decay B s → η (cid:48) ( → ηπ + π − ) X s ¯ s for B s → η (cid:48) K ± K S + nπ submodes and M ( X s ¯ s ) ≤ c and with all selections applied. The light blue shaded regionis the sum of the background fits, the red shaded region is thesum of the signal fits, and the black dashed curve is the sumof the two. ± . . ) ± . . ) +0 . − . (FM) ± . N B ∗ ) s ¯ B ∗ ) s ). Ap-plying the same method as used to calculate the upperlimit on B ( B s → η (cid:48) X s ¯ s ), the 90% confidence level upperlimit on R ( η (cid:48) ) is 3.5.As a byproduct of the preceding measurement, we TABLE I. Results for the B s → η (cid:48) K + K − + nπ submodes,from the 121.4 fb − Υ(5 S ) data set; the table contains the M ( X s ¯ s ) bin in units of GeV/ c , corrected reconstruction ef-ficiency ( (cid:15) (cid:48) ), number of fitted signal events N sig , and B , thecentral value of the partial BF. M ( X s ¯ s ) (cid:15) (cid:48) (%) N sig B ( B s → η (cid:48) X s ¯ s ) (10 − )1.0 - 1.2 3.6 ± +2 . − . +0 . − . (stat.) +0 . − . (syst.)1.2 - 1.4 2.8 ± +2 . − . +0 . − . (stat.) +0 . − . (syst.)1.4 - 1.6 0.9 ± +2 . − . +1 . − . (stat.) +0 . − . (syst.)1.6 - 1.8 0.5 ± +2 . − . +1 . − . (stat.) +0 . − . syst.)1.8 - 2.0 0.3 ± +2 . − . +3 . − . (stat.) +0 . − . (syst.)2.0 - 2.2 0.2 ± +3 . − . +7 . − . (stat.) +0 . − . (syst.)2.2 - 2.4 0.1 ± − +3 . − . − +11 . − . (stat.) +1 . − . (syst.) TABLE II. Results for the B s → η (cid:48) K ± K S + nπ submodes,from the 121.4 fb − Υ(5 S ) data set; rows with dashes indicatebins where no events, background or signal, were found; thetable contains the M ( X s ¯ s ) bin in units of GeV/ c , correctedreconstruction efficiency ( (cid:15) (cid:48) ), number of fitted signal events N sig , and B , the central value of the partial BF. M ( X s ¯ s ) (cid:15) (cid:48) (%) N sig B ( B s → η (cid:48) X s ¯ s ) (10 − )1.0 - 1.2 0.02 ± ± +1 . − . +2 . − . (stat.) +0 . − . (syst.)1.4 - 1.6 0.9 ± +3 . − . +1 . − . (stat.) +0 . − . (syst.)1.6 - 1.8 0.6 ± +3 . − . +2 . − . (stat.) +0 . − . (syst.)1.8 - 2.0 0.4 ± +4 . − . +3 . − . (stat.) +0 . − . (syst.)2.0 - 2.2 0.4 ± − +3 . − . − +4 . − . (stat.) +0 . − . (syst.)2.2 - 2.4 0.2 ± − +3 . − . − +8 . − . (stat.) +0 . − . (syst.) searched for the decay B s → η (cid:48) φ , with φ → K + K − . Thisdecay was searched for in the X s ¯ s mass subrange M ( X s ¯ s ) ∈ [1.006, 1.03] GeV/ c ( ± σ window). From MC simu-lations, the reconstruction efficiency is determined to be7.90 ± × − . The result from fitting is shown in Fig.4. LHCb determines the upper limit at 90% confidencelevel to be 8.2 × − [35].To conclude, we set an upper limit on the partial BFfor the decay B s → η (cid:48) X s ¯ s , for M ( X s ¯ s ) ≤ c .Including all uncertainties, the upper limit at 90% confi-dence level is determined to be 1.4 × − . This is thefirst result for the decay B s → η (cid:48) X s ¯ s . Future measure-ments may help elucidate SU (3) symmetries and enhancethe understanding of different penguin contributions tothe amplitude of b → sg decays. This and future anal-yses should also help to motivate further studies, bothexperimental and theoretical, of inclusive B s processesas there is a dearth of research of the B s relative to B d and B ± u .We thank the KEKB group for excellent operation FIG. 4. B s → φ ( → K + K − ) η (cid:48) decay results for M( X s ¯ s ) ∈± σ φ mass range of the accelerator; the KEK cryogenics group for ef-ficient solenoid operations; and the KEK computergroup, the NII, and PNNL/EMSL for valuable comput-ing and SINET5 network support. 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