Search for charmonium and charmonium-like states in Υ(2S) radiative decays
X. L. Wang, C. P. Shen, C. Z. Yuan, P. Wang, Belle Collaboration
aa r X i v : . [ h e p - e x ] A ug Search for charmonium and charmonium-like states in
Υ(2 S ) radiative decays X. L. Wang, C. P. Shen, C. Z. Yuan, P. Wang, I. Adachi, H. Aihara, D. M. Asner, T. Aushev, A. M. Bakich, E. Barberio, K. Belous, B. Bhuyan, A. Bozek, M. Braˇcko,
T. E. Browder, M.-C. Chang, A. Chen, B. G. Cheon, K. Chilikin, I.-S. Cho, K. Cho, Y. Choi, J. Dalseno,
28, 47
M. Danilov, Z. Doleˇzal, S. Eidelman, J. E. Fast, M. Feindt, V. Gaur, Y. M. Goh, J. Haba, K. Hayasaka, H. Hayashii, Y. Hoshi, Y. B. Hsiung, H. J. Hyun, T. Iijima, A. Ishikawa, R. Itoh, M. Iwabuchi, Y. Iwasaki, T. Iwashita, T. Julius, J. H. Kang, N. Katayama, T. Kawasaki, H. Kichimi, H. J. Kim, H. O. Kim, J. B. Kim, J. H. Kim, K. T. Kim, M. J. Kim, Y. J. Kim, K. Kinoshita, B. R. Ko, N. Kobayashi,
41, 52
S. Koblitz, P. Kriˇzan,
A. Kuzmin, Y.-J. Kwon, J. S. Lange, S.-H. Lee, J. Li, X. R. Li, Y. Li, J. Libby, C.-L. Lim, C. Liu, D. Liventsev, R. Louvot, D. Matvienko, S. McOnie, K. Miyabayashi, H. Miyata, Y. Miyazaki, G. B. Mohanty, R. Mussa, Y. Nagasaka, M. Nakao, H. Nakazawa, Z. Natkaniec, S. Neubauer, S. Nishida, K. Nishimura, O. Nitoh, S. Ogawa, T. Ohshima, S. Okuno, S. L. Olsen,
43, 8
Y. Onuki, P. Pakhlov, G. Pakhlova, H. Park, H. K. Park, T. K. Pedlar, R. Pestotnik, M. Petriˇc, L. E. Piilonen, M. Ritter, S. Ryu, H. Sahoo, Y. Sakai, T. Sanuki, O. Schneider, C. Schwanda, K. Senyo, O. Seon, M. E. Sevior, M. Shapkin, T.-A. Shibata,
41, 52
J.-G. Shiu, B. Shwartz, F. Simon,
28, 47
P. Smerkol, Y.-S. Sohn, E. Solovieva, S. Staniˇc, M. Stariˇc, M. Sumihama,
41, 6
G. Tatishvili, Y. Teramoto, K. Trabelsi, M. Uchida,
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S. Uehara, Y. Unno, S. Uno, Y. Usov, G. Varner, C. H. Wang, M.-Z. Wang, Y. Watanabe, E. Won, B. D. Yabsley, Y. Yamashita, M. Yamauchi, Z. P. Zhang, and V. Zhilich (The Belle Collaboration) Budker Institute of Nuclear Physics SB RAS and Novosibirsk State University, Novosibirsk 630090 Faculty of Mathematics and Physics, Charles University, Prague University of Cincinnati, Cincinnati, Ohio 45221 Department of Physics, Fu Jen Catholic University, Taipei Justus-Liebig-Universit¨at Gießen, Gießen Gifu University, Gifu Hanyang University, Seoul University of Hawaii, Honolulu, Hawaii 96822 High Energy Accelerator Research Organization (KEK), Tsukuba Hiroshima Institute of Technology, Hiroshima Indian Institute of Technology Guwahati, Guwahati Indian Institute of Technology Madras, Madras Institute of High Energy Physics, Chinese Academy of Sciences, Beijing Institute of High Energy Physics, Vienna Institute of High Energy Physics, Protvino INFN - Sezione di Torino, Torino Institute for Theoretical and Experimental Physics, Moscow J. Stefan Institute, Ljubljana Kanagawa University, Yokohama Institut f¨ur Experimentelle Kernphysik, Karlsruher Institut f¨ur Technologie, Karlsruhe Korea Institute of Science and Technology Information, Daejeon Korea University, Seoul Kyungpook National University, Taegu ´Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana Luther College, Decorah, Iowa 52101 University of Maribor, Maribor Max-Planck-Institut f¨ur Physik, M¨unchen University of Melbourne, School of Physics, Victoria 3010 Nagoya University, Nagoya Nara Women’s University, Nara National Central University, Chung-li National United University, Miao Li Department of Physics, National Taiwan University, Taipei H. Niewodniczanski Institute of Nuclear Physics, Krakow Nippon Dental University, Niigata Niigata University, Niigata University of Nova Gorica, Nova Gorica Osaka City University, Osaka Pacific Northwest National Laboratory, Richland, Washington 99352 Research Center for Nuclear Physics, Osaka University of Science and Technology of China, Hefei Seoul National University, Seoul Sungkyunkwan University, Suwon School of Physics, University of Sydney, NSW 2006 Tata Institute of Fundamental Research, Mumbai Excellence Cluster Universe, Technische Universit¨at M¨unchen, Garching Toho University, Funabashi Tohoku Gakuin University, Tagajo Tohoku University, Sendai Department of Physics, University of Tokyo, Tokyo Tokyo Institute of Technology, Tokyo Tokyo University of Agriculture and Technology, Tokyo CNP, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Yonsei University, Seoul (Dated: December 3, 2017)Using a sample of 158 million Υ(2 S ) events collected with the Belle detector, charmonium andcharmonium-like states with even charge parity are searched for in Υ(2 S ) radiative decays. Nosignificant χ cJ or η c signal is observed and the following upper limits at 90% confidence level (C.L.)are obtained: B (Υ(2 S ) → γχ c ) < . × − , B (Υ(2 S ) → γχ c ) < . × − , B (Υ(2 S ) → γχ c ) < . × − , and B (Υ(2 S ) → γη c ) < . × − . No significant signal of any charmonium-like state isobserved, and we obtain the limits B (Υ(2 S ) → γX (3872)) × B ( X (3872) → π + π − J/ψ ) < . × − , B (Υ(2 S ) → γX (3872)) × B ( X (3872) → π + π − π J/ψ ) < . × − , B (Υ(2 S ) → γX (3915)) ×B ( X (3915) → ωJ/ψ ) < . × − , B (Υ(2 S ) → γY (4140)) × B ( Y (4140) → φJ/ψ )) < . × − ,and B (Υ(2 S ) → γX (4350)) × B ( X (4350) → φJ/ψ )) < . × − at 90% C.L. PACS numbers: 14.40.Pq, 14.40.Rt, 13.20.Gd
The data samples of the B factories have provided awealth of experimental information on charmonium spec-troscopy [1]. Below open charm threshold agreementbetween experimental mass measurements and predic-tions based upon potential models was recently demon-strated with high accuracy for the h c [2, 3]. However, inthe region above the open charm threshold, in additionto many conventional charmonium states, a number ofcharmonium-like states (the so-called “ XY Z particles”)have been discovered with unusual properties. These mayinclude exotic states, such as quark-gluon hybrids, mesonmolecules, and multi-quark states [1]. Many of these newstates are established in a single production mechanismor in a single decay mode only. To better understandthem, it is necessary to search for such states in moreproduction processes and/or decay modes. States with J P C = 1 −− can be studied via initial state radiation(ISR) with the large Υ(4 S ) data samples at BaBar orBelle, or via e + e − collisions directly at the peak energyat, for example, BESIII. For charge-parity-even charmo-nium states, radiative decays of the narrow Υ states be-low the open bottom threshold can be examined.The production rates of the P -wave spin-triplet χ cJ ( J =0, 1, 2) and S -wave spin-singlet η c states inΥ(1 S ) radiative decays have been calculated by Gao etal. ; the rates in Υ(2 S ) decays are estimated to be at thesame level [4]. However, there are no such calculationsor estimations for “ XY Z particles” due to the limitedknowledge of their nature. In this paper, with the world largest data sample takenat the Υ(2 S ) peak, we report a search for the χ cJ , η c , X (3872) [5], X (3915) [6], and Y (4140) [7] in Υ(2 S ) ra-diative decays, extending our previous work on the Υ(1 S )sample [8]. In addition, the new structure X (4350) [9],which was observed as a 3.2 standard deviation ( σ ) signalin γγ → φJ/ψ is also searched for. As any charmoniumstate above ψ (2 S ) is expected to have a larger branch-ing fraction for the E1/M1 transition to ψ (2 S ) than to J/ψ [10], we also search for states decaying into γψ (2 S ).The data used in this analysis include a 24.7 fb − data sample collected at the Υ(2 S ) peak and a 1.7 fb − data sample collected at √ s = 9 .
993 GeV (off-resonancedata) with the Belle detector [11] operating at the KEKBasymmetric-energy e + e − collider [12]. The number ofthe Υ(2 S ) events is determined by counting the hadronicevents in the data taken at the Υ(2 S ) peak after sub-tracting the scaled continuum background from the datasample collected at √ s = 9 .
993 GeV. The selectioncriteria for hadronic events are validated with the off-resonance data by comparing the measured R value ( R = σ ( e + e − → hadrons ) σ ( e + e − → µ + µ − ) ) with CLEO’s result [13]. The numberof Υ(2 S ) events is determined to be (158 ± × , withthe error dominated by the MC simulation of the Υ(2 S )decay dynamics using pythia [14].Well measured charged tracks and photon candidatesare first selected. For a charged track, the impact pa-rameters perpendicular to and along the beam directionwith respect to the interaction point (IP) are requiredto be less than 0.5 cm and 4 cm, respectively, and thetransverse momentum should exceed 0.1 GeV/ c in thelaboratory frame. Information from different detectorsubsystems is combined to form a likelihood L i for eachparticle species [15]. A track with R K = L K L K + L π > . R K < . R e = L e L e + L x , where L e and L x are the likelihoods forelectron and non-electron, respectively, determined usingthe ratio of the energy deposited in the electromagneticcalorimeter (ECL) to the momentum measured in the sili-con vertex detector and central drift chamber (CDC), theshower shape in the ECL, the matching between the po-sition of charged track trajectory and the cluster positionin the ECL, the hit information from the aerogel thresh-old Cherenkov counters and the dE/dx measurements inthe CDC [16]. For muon identification, the likelihood ra-tio is defined as R µ = L µ L µ + L π + L K , where L µ , L π and L K are the likelihoods for muon, pion and kaon hypotheses,respectively, based on the matching quality and pene-tration depth of associated hits in the iron flux return(KLM) [17]. A good neutral cluster is reconstructed as aphoton if its ECL shower does not match the extrapola-tion of any charged track and its energy is greater than40 MeV. In the e + e − center-of-mass (C.M.) frame, thephoton candidate with the maximum energy is taken tobe the Υ(2 S ) radiative decay photon (denoted as γ R ),and its energy is required to be greater than 3 . . . /c produced in Υ(2 S ) radiative decays.We reconstruct J/ψ signals from e + e − or µ + µ − candi-dates. In order to reduce the effect of bremsstrahlungor final-state radiation, photons detected in the ECLwithin 0.05 radians of the original e + or e − directionare included in the calculation of the e + /e − momen-tum. For the lepton pair used to reconstruct J/ψ ,at least one track should have R e > .
95 while theother should satisfy R e > .
05 in the e + e − mode; orone track should have R µ > .
95 (in the χ cJ analy-sis, the other track should have associated hits in theKLM detector that agree with the extrapolated trajec-tory of a charged track provided by the drift chamber)in the µ + µ − mode. The lepton pair identification ef-ficiency is about 97% for J/ψ → e + e − and 87% for J/ψ → µ + µ − . In order to improve the J/ψ momen-tum resolution, a mass-constrainted fit is then performedfor
J/ψ signals in the γJ/ψ , π + π − J/ψ , π + π − π J/ψ ,and φJ/ψ modes. Different modes have similar
J/ψ mass resolutions. The
J/ψ signal region is defined as | M ℓ + ℓ − − m J/ψ | <
30 MeV /c ( ≈ . σ ), where m J/ψ isthe nominal mass of
J/ψ . The
J/ψ mass sidebands aredefined as 2 .
959 GeV /c < M ℓ + ℓ − < .
019 GeV /c and3 .
175 GeV /c < M ℓ + ℓ − < .
235 GeV /c , and are twiceas wide as the signal region. For the γψ (2 S ) channel, the ψ (2 S ) is reconstructed from the π + π − J/ψ final state, with a mass constrained to the nominal ψ (2 S ) mass toimprove its momentum resolution. To estimate the dif-ference in the ψ (2 S ) mass resolution between MC simula-tion and data, the process e + e − → γ ISR ψ (2 S ) is selectedas a reference sample, and the mass resolution is foundto be 3 . ± . /c from data, and 2 . /c fromMC simulation. The difference in the mass resolution isincluded when extracting the signal yields in the analysesbelow.We search for the χ cJ in the γJ/ψ mode. The en-ergy deposited by the χ cJ photon (denoted as γ l , sinceits energy is much lower than that of γ R ) is required tobe greater than 150 MeV to reduce the large backgroundfrom mis-reconstructed photons, and the total number ofphotons is required to be exactly two to suppress multi-photon backgrounds. The angle between the γ R and γ l should be larger than 18 ◦ to remove the background fromsplit-off fake photons. To remove the ISR background e + e − → γ ISR ψ (2 S ) → γ ISR γχ cJ , where a photon is miss-ing, we require the square of the “mass recoiling againstthe γ l and J/ψ ” ( M = ( P e + e − − P f ) , here P e + e − isthe 4-momentum of the e + e − collision system, and P f is the sum of the 4-momenta of the observed final stateparticles) to be within − . /c and 0.5 GeV /c .This M requirement is effective since this backgroundhas at least two missing photons and M ( γ l J/ψ ) tendsto be large. Bhabha and dimuon background events withfinal-state radiative photons are further suppressed by re-moving events in which a photon is detected within a 18 ◦ cone around each charged track direction.The µ + µ − mode shows a clear J/ψ signal, while the e + e − mode has some residual radiative Bhabha back-ground. Figure 1 shows the γ l J/ψ invariant mass distri-bution together with the background estimated from the
J/ψ mass sidebands (normalized to the width of the
J/ψ signal range) for the combined e + e − and µ + µ − modesafter the above selection criteria are applied. Some ISRbackgrounds with a correctly reconstructed J/ψ remainin the data. No χ cJ signal is observed.A simultaneous fit to the signal region is performedwith Breit-Wigner (BW) functions convolved with Gaus-sian resolution functions for the resonances and a second-order polynomial background term. The width of theGaussian resolution function is fixed at 7 . c ,which is obtained by increasing the MC-simulated valueby 10% to account for the difference between data andMC simulation. The masses and widths of the χ cJ res-onances are fixed to their PDG values [19]. In the si-multaneous fit, the ratio of the yields in the two J/ψ decay channels is fixed to B i ε i , where B i is the J/ψ de-cay branching fraction for the e + e − mode or µ + µ − modereported by the PDG [19], and ε i is the MC-determinedefficiency for this mode. The upper limit on the number( n up ) of signal events at the 90% C.L. is calculated bysolving the equation R n up0 L ( x ) dx R + ∞ L ( x ) dx = 0 .
9, where x is thenumber of signal events, and L ( x ) is the likelihood func-tion depending on x from the fit to the data. The valuesof n up are found to be 2 .
8, 3 . . χ c , χ c and χ c , respectively, when requiring the signal yields to benon-negative in the fit. We do not observe any structureat high masses, where excited χ cJ states are expected. ) ) (GeV/c y J/ g M( E ve n t s / M e V / c ) ) (GeV/c y J/ g M( E ve n t s / M e V / c FIG. 1: The γ l J/ψ invariant mass distribution in the Υ(2 S )data sample. There is no χ c , χ c , or χ c signal observed. Thesolid curve is the best fit, the dashed curve is the background,and the shaded histogram is from the normalized J/ψ masssidebands. The signal yield is required to be non-negative inthe fit.
To search for a possible excited charmonium statein the γ l ψ (2 S ) final state, a J/ψ candidate and twooppositely charged pion candidates are reconstructed.The ψ (2 S ) signal region is defined as 3 .
67 GeV /c 70 GeV /c , and the ψ (2 S ) mass side-bands are defined as 3 . 63 GeV /c < M π + π − J/ψ < . 66 GeV /c and 3 . 71 GeV /c < M π + π − J/ψ < . 74 GeV /c . To suppress backgrounds with miscon-structed photons, we require the energy of the γ l to behigher than 75 MeV. To suppress the ISR background e + e − → γ ISR ψ (2 S ) → γ ISR π + π − J/ψ , we require thesquare of the mass recoiling against the γ l and ψ (2 S ) tobe within − . /c and 1.5 GeV /c since M forthe ISR background tends to be shifted towards negativevalues.The γ l ψ (2 S ) invariant mass distribution after theabove selection is shown in Fig. 2. There is no signifi-cant signal. However, a few events accumulate around3 . 82 GeV /c , where the γψ (2 S ) decays of the χ c (2 P )and η c (1 D ) [10] are expected. A fit between 3 . 75 GeV /c and 3 . 90 GeV /c with a Gaussian to parameterize thesignal shape yields a mass of (3 . ± . /c anda signal yield of 5 . ± . . σ . The signal significance isdetermined by comparing the value of − L /L max )from the fit, with values from fits to 10,000 pseudo-experiments. Here L and L max are the likelihoods ofthe fits without and with the signal, respectively. The up-per limit on the product branching fraction B (Υ(2 S ) → γX ) × B ( X → γψ (2 S )) < . × − at the 90% C.L. isdetermined following the procedure described below.To search for the η c signal in Υ(2 S ) radiative decays,we reconstruct η c candidates from the K S K + π − + c.c. , π + π − K + K − , 2( K + K − ), 2( π + π − ), and 3( π + π − ) modes.Well measured charged tracks should be identified as pi-ons or kaons, and the number of charged tracks is six ) (2S)) (GeV/c yg M( E ve n t s / M e V / c FIG. 2: The γ l ψ (2 S ) invariant mass distribution. The openhistogram is from the ψ (2 S ) signal mass region, the shadedhistogram is from the normalized ψ (2 S ) mass sidebands. Inthe inset, the solid curve is the best fit between 3 . 75 GeV /c and 3 . 90 GeV /c , and the dashed curve is a fit with only asecond-order polynomial to describe the background. for the 3( π + π − ) final state and four for the other finalstates. In the K S K + π − + c.c. mode, K S candidates arereconstructed from π + π − pairs with an invariant mass M π + π − within 30 MeV/ c of the K S nominal mass. A K S candidate should have a displaced vertex and flightdirection consistent with a K S originating from the IP;the same selection method is used in Ref. [18]. Eventswith leptons misidentified as pions in the π + π − K + K − and 2( π + π − ) modes are removed by requiring R e < . R µ < . M for the hadronic daughters of the η c candidate is requiredto be within − /c and 1 GeV /c .After the selection described above, Fig. 3 shows thecombined mass distribution of the hadronic final statesfor the five η c decay modes. The large J/ψ signal is dueto the ISR process e + e − → γ ISR J/ψ , while the accumu-lation of events within the η c mass region is small. Theshaded histogram in Fig. 3 is the same distribution forthe off-resonance data and is not normalized. ) M(hadrons) (GeV/c E ve n t s / M e V / c ) M(hadrons) (GeV/c E ve n t s / M e V / c FIG. 3: The mass distribution for a sum of the five η c de-cay modes. The solid curve is a sum of the correspondingfunctions obtained from a simultaneous fit to all the η c de-cay modes, and the dashed curve is a sum of the backgroundfunctions from the fit. The shaded histogram is a sum of theoff-resonance events (not normalized). The J/ψ signal is pro-duced via ISR rather than from a radiative decay of an Υ( nS )resonance. A simultaneous fit is performed to the five final states.The ratios of the η c ( J/ψ ) yields in all the channels arefixed to B i ε i , where each B i is the η c ( J/ψ ) decay branch-ing fraction for the i -th mode reported by the PDG [19],and ε i is the MC-determined efficiency for this mode.The fit function contains a BW function convolved witha Gaussian resolution function (its resolution is fixed to7.9 MeV /c from MC simulation) describing the η c sig-nal shape, another Gaussian function describing the J/ψ signal shape, and a second-order polynomial describingthe background shape. The mass and width of the BWfunction are fixed to the PDG values [19] for the η c . Theresults of the fit are shown in Fig. 3, where the solidcurve is the sum of all the fit functions, and the dashedcurve is the sum of the background functions. The fityields 14 ± η c signal events corresponding to an upperlimit n up of 44 at the 90% C.L. In addition, we obtain370 ± J/ψ signal events from the fit (in agreement with338 ± 16 expected from γ ISR J/ψ production according toMC simulation), giving a mass of 3098 . ± . /c ,which is consistent with the PDG value [19].The selection criteria for Υ(2 S ) → γ R X (3872), X (3872) → π + π − J/ψ are similar to those used for ISR π + π − J/ψ events in Υ(4 S ) data [20]. We require thatone J/ψ candidate be reconstructed, two well-identified π ’s have an invariant mass greater than 0.35 GeV/ c ,and that M ( π + π − J/ψ ) be within the range between − /c and 1 GeV /c . To suppress the ISR π + π − J/ψ background, we require that the polar angle ofthe γ R candidate satisfy | cos θ | < . e + e − C.M.frame. Except for a few residual ISR produced ψ (2 S )signal events, only a small number of events appear inthe π + π − J/ψ invariant mass distribution, as shown inFig. 4(a). There is no accumulation of events in the X (3872) mass region. Fitting using a signal shape fromthe MC sample and a first-order polynomial function asthe background shape, the upper limit n up for the num-ber of signal events is determined to be 3.6 at the 90%C.L.We also search for the X (3872) and X (3915) in the π + π − π J/ψ mode. We select π + , π − , and J/ψ can-didates in the X (3872) → π + π − J/ψ mode (with therequirement on the π + π − invariant mass greater than0.35 GeV/ c removed) and a π candidate from a pairof photons with invariant mass within 10 MeV /c of the π nominal mass. Here the π mass resolution is about4 MeV/ c from MC simulation. Figure 4(b) shows the π + π − π J/ψ invariant mass distribution, where the openhistogram is the MC expectation for the X (3872) sig-nal plotted with an arbitrary normalization. Using thesame fit method as in X (3872) → π + π − J/ψ , we deter-mine n up for the number of X (3872) signal events to be4.2 at the 90% C.L. Figure 4(c) shows the scatter plotof m ( π + π − π J/ψ ) versus m ( π + π − π ) from data, wherethe region indicated by the ellipse corresponds to the ± σ mass regions of m ( π + π − π J/ψ ) and m ( π + π − π )from the X (3915) → ωJ/ψ decay. There is one eventwith m ( π + π − π J/ψ ) at 3.923 GeV/ c and m ( π + π − π ) M( p + p - J/ y ) (GeV/c ) E n t r i e s / M e V / c M( p + p - p J/ y ) (GeV/c ) E n t r i e s / M e V / c M( p + p - p J/ y ) (GeV/c ) M ( p + p - p ) ( G e V / c ) FIG. 4: (a) Distribution of the π + π − J/ψ invariant massfor Υ(2 S ) → γ R π + π − J/ψ candidates. (b) Distribution ofthe π + π − π J/ψ invariant mass for Υ(2 S ) → γ R π + π − π J/ψ candidates. (c) Scatter plots of m ( π + π − π J/ψ ) versus m ( π + π − π ), where the region indicated by the ellipse cor-responds to the ± σ mass regions of m ( π + π − π J/ψ ) and m ( π + π − π ) from the X (3915) → ωJ/ψ decay. Points witherror bars are data, open histograms are the MC expectationfor the X (3872) signal (arbitrary normalization). The peakat 3 . 686 GeV/ c in (a) is due to ψ (2 S ) production via ISR. at 0.790 GeV/ c from Υ(2 S ) data, as shown in the el-lipse. Assuming that the number of background eventsis zero, the upper limit n up for the number of X (3915)signal events is 4.4 at the 90% C.L.We search for the Y (4140) and the X (4350) in the φJ/ψ mode. The selection criteria are very similar tothose in the analysis of X (3872) → π + π − J/ψ describedabove and the φ is reconstructed from a K + K − pair.According to MC simulation, the φ signal region is de-fined as 1 . 01 GeV /c < M K + K − < . 03 GeV/ c . Thenumber of well measured charged tracks is required to beexactly four. After applying all of the above event selec-tion criteria, there is no clear J/ψ or φ signal. Nor arethere candidate events in the Y (4140) or X (4350) massregions. The upper limits on the number of Y (4140) and X (4350) signal events are both 2.3 at the 90% C.L.Several sources of systematic uncertainties are con-sidered. The uncertainty due to particle identificationefficiency is 2.4%-3.4% and depends on the final stateparticles. The uncertainty in the tracking efficiency fortracks with angles and momenta characteristic of signalevents is about 0.35% per track, and is additive. Thephoton reconstruction contributes an additional 2.0% perphoton. Errors on the branching fractions of the inter-mediate states are taken from the PDG [19]; they are6.9% for the χ c mode, 4.5% for the χ c mode, 4.2%for the χ c mode, 1.7% for the γψ (2 S ) mode, 17% forthe η c mode, 1.0% for the X (3872) mode, 1.3% for the X (3915) mode, and 1.6% for the φJ/ψ mode. By using aphase space distribution and including possible interme-diate resonant states, the largest difference of efficiencyis determined to be 2.1% for the η c decay modes. Thedifference in the overall efficiency for a flat angular distri-bution of radiative photons and a 1 ± cos θ distribution isless than 3.0%. Therefore, we quote an additional errorof 5.0% due to the limited knowledge of the decay dy-namics for all the states studied, except for the χ c modeand η c mode, which are known to follow a 1 + cos θ distribution. According to MC simulation, the triggerefficiency is 89% for the χ cJ mode, rather high for othermodes ( ≥ χ cJ modeand 1.0% error for other modes as a conservative esti-mate of the corresponding uncertainties. With the pure e + e − → γ ISR ψ (2 S ) , ψ (2 S ) → π + π − J/ψ or J/ψη ( → γγ )samples obtained from Belle data, the uncertainty due tothe recoil mass squared requirement is 1.0% for the chan-nels with a single photon and 4.7% for channels with twophotons. By changing the order of the background poly-nomial, the range of the fit, and the values of the massesand widths of the resonances, uncertainties on the χ cJ and η c signal yields are estimated to be 1.1% and 16%,respectively. In the Υ(2 S ) → γ R χ cJ mode, the uncer-tainty associated with the requirement on the number ofphotons is 2.0% after applying a correction factor of 0.94to the MC efficiency, which is determined from a studyof a very pure Υ(2 S ) → µ + µ − event sample. In the η c → K S K + π − + c.c. mode, the uncertainty in the K S selection efficiency is determined by a study on a largesample of high momentum K S → π + π − decays; the ef-ficiency difference between data and MC simulation isless than 4.9% [21]. Finally, the uncertainty on the totalnumber of Υ(2 S ) events is 2.3%. Assuming that all ofthese systematic error sources are independent, we addthem in quadrature to obtain a total systematic error asshown in Table I. Since there is no evidence for signals in the modes stud-ied, we determine upper limits on the branching fractionsof Υ(2 S ) radiative decays. Table I lists the upper limits n up for the number of signal events, detection efficien-cies, systematic errors, and final results for the upperlimits on the branching fractions. In order to calculateconservative upper limits on these branching fractions,the efficiencies are lowered by a factor of 1 − σ sys in thecalculation. TABLE I: Summary of the limits on Υ(2 S ) radiative decays tocharmonium and charmonium-like states R . Here n up is theupper limit on the number of signal events, ε is the efficiencywith the secondary decay branching fractions excluded andtrigger efficiency included, σ sys is the total systematic error,and B (Υ(2 S ) → γR ) up ( B R ) is the upper limit at the 90%C.L. on the decay branching fraction in the charmonium statecase, and on the product branching fraction in the case of acharmonium-like state.State ( R ) n up ε (%) σ sys (%) B R χ c . × − χ c . × − χ c . × − η c 44 26.3 24 2 . × − X (3872) → π + π − J/ψ . × − X (3872) → π + π − π J/ψ . × − X (3915) → ωJ/ψ . × − Y (4140) → φJ/ψ . × − X (4350) → φJ/ψ . × − To summarize, we find no significant signals for the χ cJ or η c , as well as for the X (3872), X (3915), Y (4140), or X (4350) in Υ(2 S ) radiative decays. 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