Measurement of neutral pion pair production in two-photon collisions
aa r X i v : . [ h e p - e x ] N ov BELLE-CONF-0768
Measurement of neutral pion pair productionin two-photon collisions
K. Abe, I. Adachi, H. Aihara, K. Arinstein, T. Aso, V. Aulchenko, T. Aushev,
22, 16
T. Aziz, S. Bahinipati, A. M. Bakich, V. Balagura, Y. Ban, S. Banerjee, E. Barberio, A. Bay, I. Bedny, K. Belous, V. Bhardwaj, U. Bitenc, S. Blyth, A. Bondar, A. Bozek, M. Braˇcko,
24, 17
J. Brodzicka, T. E. Browder, M.-C. Chang, P. Chang, Y. Chao, A. Chen, K.-F. Chen, W. T. Chen, B. G. Cheon, C.-C. Chiang, R. Chistov, I.-S. Cho, S.-K. Choi, Y. Choi, Y. K. Choi, S. Cole, J. Dalseno, M. Danilov, A. Das, M. Dash, J. Dragic, A. Drutskoy, S. Eidelman, D. Epifanov, S. Fratina, H. Fujii, M. Fujikawa, N. Gabyshev, A. Garmash, A. Go, G. Gokhroo, P. Goldenzweig, B. Golob,
23, 17
M. Grosse Perdekamp,
12, 41
H. Guler, H. Ha, J. Haba, K. Hara, T. Hara, Y. Hasegawa, N. C. Hastings, K. Hayasaka, H. Hayashii, M. Hazumi, D. Heffernan, T. Higuchi, L. Hinz, H. Hoedlmoser, T. Hokuue, Y. Horii, Y. Hoshi, K. Hoshina, S. Hou, W.-S. Hou, Y. B. Hsiung, H. J. Hyun, Y. Igarashi, T. Iijima, K. Ikado, K. Inami, A. Ishikawa, H. Ishino, R. Itoh, M. Iwabuchi, M. Iwasaki, Y. Iwasaki, C. Jacoby, N. J. Joshi, M. Kaga, D. H. Kah, H. Kaji, S. Kajiwara, H. Kakuno, J. H. Kang, P. Kapusta, S. U. Kataoka, N. Katayama, H. Kawai, T. Kawasaki, A. Kibayashi, H. Kichimi, H. J. Kim, H. O. Kim, J. H. Kim, S. K. Kim, Y. J. Kim, K. Kinoshita, S. Korpar,
24, 17
Y. Kozakai, P. Kriˇzan,
23, 17
P. Krokovny, R. Kumar, E. Kurihara, A. Kusaka, A. Kuzmin, Y.-J. Kwon, J. S. Lange, G. Leder, J. Lee, J. S. Lee, M. J. Lee, S. E. Lee, T. Lesiak, J. Li, A. Limosani, S.-W. Lin, Y. Liu, D. Liventsev, J. MacNaughton, G. Majumder, F. Mandl, D. Marlow, T. Matsumura, A. Matyja, S. McOnie, T. Medvedeva, Y. Mikami, W. Mitaroff, K. Miyabayashi, H. Miyake, H. Miyata, Y. Miyazaki, R. Mizuk, G. R. Moloney, T. Mori, J. Mueller, A. Murakami, T. Nagamine, Y. Nagasaka, Y. Nakahama, I. Nakamura, E. Nakano, M. Nakao, H. Nakayama, H. Nakazawa, Z. Natkaniec, K. Neichi, S. Nishida, K. Nishimura, Y. Nishio, I. Nishizawa, O. Nitoh, S. Noguchi, T. Nozaki, A. Ogawa, S. Ogawa, T. Ohshima, S. Okuno, S. L. Olsen, S. Ono, W. Ostrowicz, H. Ozaki, P. Pakhlov, G. Pakhlova, H. Palka, C. W. Park, H. Park, K. S. Park, N. Parslow, L. S. Peak, M. Pernicka, R. Pestotnik, M. Peters, L. E. Piilonen, A. Poluektov, J. Rorie, M. Rozanska, H. Sahoo, Y. Sakai, H. Sakaue, N. Sasao, T. R. Sarangi, N. Satoyama, K. Sayeed, T. Schietinger, O. Schneider, P. Sch¨onmeier, J. Sch¨umann, C. Schwanda, A. J. Schwartz, R. Seidl,
12, 41
A. Sekiya, K. Senyo, M. E. Sevior, L. Shang, M. Shapkin, C. P. Shen, H. Shibuya, S. Shinomiya, J.-G. Shiu, B. Shwartz, J. B. Singh, A. Sokolov, E. Solovieva, A. Somov, S. Staniˇc, M. Stariˇc, J. Stypula, A. Sugiyama, K. Sumisawa, T. Sumiyoshi, S. Suzuki, S. Y. Suzuki, O. Tajima, F. Takasaki, K. Tamai, N. Tamura, M. Tanaka, N. Taniguchi, G. N. Taylor, Y. Teramoto, I. Tikhomirov, K. Trabelsi, Y. F. Tse, T. Tsuboyama, K. Uchida,
1. Uchida, S. Uehara, K. Ueno, T. Uglov, Y. Unno, S. Uno, P. Urquijo, Y. Ushiroda, Y. Usov, G. Varner, K. E. Varvell, K. Vervink, S. Villa, A. Vinokurova, C. C. Wang, C. H. Wang, J. Wang, M.-Z. Wang, P. Wang, X. L. Wang, M. Watanabe, Y. Watanabe, R. Wedd, J. Wicht, L. Widhalm, J. Wiechczynski, E. Won, B. D. Yabsley, A. Yamaguchi, H. Yamamoto, M. Yamaoka, Y. Yamashita, M. Yamauchi, C. Z. Yuan, Y. Yusa, C. C. Zhang, L. M. Zhang, Z. P. Zhang, V. Zhilich, V. Zhulanov, A. Zupanc, and N. Zwahlen (The Belle Collaboration) Budker Institute of Nuclear Physics, Novosibirsk Chiba University, Chiba University of Cincinnati, Cincinnati, Ohio 45221 Department of Physics, Fu Jen Catholic University, Taipei Justus-Liebig-Universit¨at Gießen, Gießen The Graduate University for Advanced Studies, Hayama Gyeongsang National University, Chinju Hanyang University, Seoul University of Hawaii, Honolulu, Hawaii 96822 High Energy Accelerator Research Organization (KEK), Tsukuba Hiroshima Institute of Technology, Hiroshima University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 Institute of High Energy Physics,Chinese Academy of Sciences, Beijing Institute of High Energy Physics, Vienna Institute of High Energy Physics, Protvino Institute for Theoretical and Experimental Physics, Moscow J. Stefan Institute, Ljubljana Kanagawa University, Yokohama Korea University, Seoul Kyoto University, Kyoto Kyungpook National University, Taegu ´Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne University of Ljubljana, Ljubljana University of Maribor, Maribor 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 Osaka University, Osaka Panjab University, Chandigarh Peking University, Beijing University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Princeton University, Princeton, New Jersey 08544 RIKEN BNL Research Center, Upton, New York 11973 Saga University, Saga University of Science and Technology of China, Hefei Seoul National University, Seoul Shinshu University, Nagano Sungkyunkwan University, Suwon University of Sydney, Sydney, New South Wales Tata Institute of Fundamental Research, Mumbai Toho University, Funabashi Tohoku Gakuin University, Tagajo Tohoku University, Sendai Department of Physics, University of Tokyo, Tokyo Tokyo Institute of Technology, Tokyo Tokyo Metropolitan University, Tokyo Tokyo University of Agriculture and Technology, Tokyo Toyama National College of Maritime Technology, Toyama Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Yonsei University, Seoul
Abstract
The differential cross section of the process γγ → π π has been measured in the kinematicalrange 0.6 GeV < W < . | cos θ ∗ | < . γγ center-of-mass system. We find at least four resonant structures including a peak from f (980). In addition, there is evidence for χ c production. We also make a preliminary discussionof the angular dependence and cross section ratio to γγ → π + π − . PACS numbers: 13.20.Gd, 13.60.Le, 13.66.Bc, 14.40.Cs,14.40.Gx . INTRODUCTION Measurements of exclusive hadronic final states in two-photon collisions provide valuableinformation concerning the physics of light and heavy-quark resonances, perturbative andnon-perturbative QCD and hadron-production mechanisms. So far, we have measured theproduction cross sections of charged-pion pairs [1, 2], charged and neutral-kaon pairs [2, 3],and proton-antiproton pairs [4]. We have also analyzed D -meson-pair production to searchfor a new charmonium state [5].In this report, we show an analysis of neutral-pion pair production in two-photon pro-cesses. The motivation for this study is essentially the same as that for the charged-pionpair case. But the two processes are physically different and independent; we cannot predictvery precisely what happens in one by measuring only the other.In the low energy region ( W < . π + π − and π π crosssections. The predictions are not easy because of non-perturbative effects. In the interme-diate energy range (1 . < W < . ππ is the dominant contribution. For ordinary q ¯ q mesons conserving isospin in decays to ππ , the only allowed I G J P C states produced by two photons are 0 + (even) ++ , that is, f J =even mesons. The ratio of the f -meson’s branching fractions, B ( f → π π ) / B ( f → π + π − ) is 1/2from isospin invariance. But, interference of the resonance with the continuum componentwhich cannot be precisely calculated distorts the ratio even near the resonant peaks. The π π channel has an advantage in the study of resonances, since a smaller contribution fromthe continuum is expected in it than in the π + π − channel.For higher energies, we can invoke a quark model. In the leading order calculations [6, 7]which take into account spin correlation between quarks, the π π cross section is predictedto be much smaller than that of π + π − , and the cross section ratio of π π to π + π − is around0.03-0.06. However, higher-order or non-perturbative QCD effects can modify the ratio.For example, the handbag model which considers soft hadron exchange predicts the sameamplitude for the two processes, and this ratio becomes 0.5 [8]. Analyses of energy andangular distributions of the cross sections are essential for determining properties of theobserved resonances and for testing the validity of QCD models.We present preliminary results of the measurement of the differential cross section, dσ/d | cos θ ∗ | , for the process γγ → π π in a wide two-photon center-of-mass (c.m.) en-ergy ( W ) range from 0.6 to 4.0 GeV, and a c.m. angular range, | cos θ ∗ | < .
8. (Althoughwe do not need to put the absolute-value symbol for cos θ ∗ for the present channel where theidentical particle pairs appear in both initial and final states, we follow the usual conven-tion of the two-photon differential cross section to avoid unnecessary confusion.) Our datasample is by several hundred times larger than in previous experiments [9, 10]. II. EXPERIMENTAL APPARATUS AND TRIGGER
We use a data sample that corresponds to an integrated luminosity of 95 fb − recordedwith the Belle detector at the KEKB asymmetric-energy e + e − collider [11]. The energy ofthe accelerator was set at 10.58 GeV (83 fb − ), 10.52 GeV(9 fb − ), 10.36 GeV(Υ(3 S ) runs,2.9 fb − ) and 10.30 GeV(0.3 fb − ), in the c.m. energy of the e + e − beams. The difference ofthe two-photon flux (luminosity function) in the measured W regions due to the differentbeam energies is very small (a few percent at maximum), and the fraction of integrated4uminosity of the runs with the lower beam energies is very small. We therefore combine theresults for different beam energies. The effect on the cross section deviation is less than 0.5%.The analysis is made in the “zero-tag” mode, where neither the recoil electron nor positronis detected. We restrict the virtuality of the incident photons to be small by imposing stricttransverse-momentum balance with respect to the beam axis for the final-state hadronicsystem.A comprehensive description of the Belle detector is given elsewhere [12]. We mention hereonly those detector components which are essential for the present measurement. Chargedtracks are reconstructed from hit information in a central drift chamber (CDC) located ina uniform 1.5 T solenoidal magnetic field. The detector solenoid is along the z axis whichpoints in the direction opposite to that of the positron beam. The CDC and a siliconvertex detector measure the longitudinal and transverse momentum components (along the z axis and in the rϕ plane, respectively). Photon detection and energy measurements areperformed with a CsI(Tl) electromagnetic calorimeter (ECL).In the present measurement, we require that there be no reconstructed tracks coming fromthe vicinity of the nominal collision point. Therefore, the CDC is used for vetoing eventswith track(s). Photons from decays of two neutral pions are detected and their momentumvectors are measured by the ECL.Signals from the ECL are used to trigger the signal events. The conditions of the ECLtrigger are as follows: The ECL total energy deposit in the triggerable acceptance region(see the next subsection) is greater than 1.15 GeV (the ’HiE’ trigger), or, the number ofthe ECL clusters counted according to the energy threshold at 110 MeV for segments of theECL is four or greater (the ’Clst4’ trigger). The above energy thresholds are determinedfrom the experimental data from a study of the correlations between the two triggers. Nosoftware filterings are applied for triggering events by either or both of the two ECL triggers. III. EVENT SELECTION
The selection conditions for signal candidates of γγ → π π are as follows: All thevariables in the criteria (1)-(5) are measured in the laboratory frame; (1) there is no goodtrack that satisfies dr < | dz | < p t > . c , where dr and dz are theradial and axial distances, respectively, of the closest approach (as seen in the rϕ plane)to the nominal collision point, and the p t is the transverse momentum measured in thelaboratory frame with respect to the z axis; (2) the events are triggered by the HiE or Clst4triggers; (3) there are two or more photons whose energy is greater than 100 MeV; (4) thereare just two π ’s, each having transverse momentum greater than 0.15 GeV/ c , and each ofthe decay-product photons has energy greater than 70 MeV, where the π is reconstructedfrom two photons and is selected with a χ value of a mass constraint fit; (5) the total energydeposit in ECL is smaller than 5.7 GeV.Then, the transverse momentum in the e + e − c.m. frame ( | Σ p ∗ t | ) of the two-pion systemis calculated. For further analysis, (6) we use events with | Σ p ∗ t | <
50 MeV/ c as the signalcandidates.In order to reduce uncertainty from the efficiency of the hardware ECL triggers, we setoffline selection criteria which emulate the hardware trigger conditions as follows: (7) theECL energy sum within the triggerable region is greater than 1.25 GeV, or all the fourphotons composing the two π are contained in the triggerable acceptance region. Here, wedefine the triggerable acceptance region as the polar-angle range in the laboratory system57 . ◦ < θ < . ◦ . IV. SIGNAL CANDIDATES AND BACKGROUNDSA. Yield distribution of the signal candidates
We derive the c.m. energy W of the two-photon collision from the invariant mass of thetwo neutral pion system. We calculate cosine of the scattering angle of π in the γγ c.m.frame, | cos θ ∗ | for each event. We use the e + e − collision axis in the e + e − c.m. frame asthe reference of the polar angle as an approximation, because we do not know the exact γγ collision axis.The two-dimensional yield distribution of the selected events is shown by the lego plot inFig. 1. The W distribution with | cos θ ∗ | < . f (980) near 0.98 GeV and f (1270) near 1.25 GeV,and broad structures near 1.65 GeV and near 1.95 GeV. Figure 2(b) is an enlarged view of thecharmonium region for | cos θ ∗ | < .
4, where we see some hints of charmonium contributionsin the χ c ( ∼ .
40 GeV) and χ c ( ∼ .
55 GeV) mass region.
B. Background subtraction
We study the p t -balance distribution, i.e., the event distribution in | Σ p ∗ t | to separate thesignal and background components. The signal Monte Carlo (MC) events show that thesignal component peaks around 10-20 MeV/ c in this distribution. In the experimental data,however, in addition to such a signal component, we find some contribution from the p t -unbalanced components in the low- W region. The source of such p t -unbalanced components,in general, is considered to be non-exclusive processes such as π π π etc. But, in the presentcase, the background found in the experimental data is very large only in the low W regionwhere the π π π contribution is expected to be much smaller than π π in two-photoncollisions. (Note that a C -parity odd system cannot go to π π .) We believe that thebackgrounds are dominated by beam-background photons (or neutral pions from secondaryinteractions) or spurious hits in the detector.Figures 3 (a) and (b) show the p t -balance distributions in the low W region. Withthe fit described below, we separate the signal components from the background. In theintermediate or higher energy regions, the backgrounds are less than 1%, buried under the f (1270) peak (Fig. 3(c)), or we do not see any detectable p t -unbalanced components withinthe statistical errors (as shown in Fig. 3(d)). Even at the highest energy 3.6 GeV < W < . | cos θ ∗ | < .
4, we find no visible contamination from the background.A fit to the p t -balance distribution is made to separate the signal and background com-ponents for the W region below 1.2 GeV. The fit function is a sum of the signal componentand the background component. The signal component is taken as an empirical functionreproducing the shape of the signal MC, y = Ax/ ( x . + B + Cx ), where ( x ≡ | Σ p ∗ t | , A , B and C are the fitting parameters, and y is the distribution). This function has a peak at x = ( B . ) . and vanishes at x = 0 and infinite x . The shape of the background is taken asa linear function y = ax for x < .
05 GeV/ c which is smoothly connected to a quadraticfunction above x > .
05 GeV/ c . 6 ( G e V ) | c o s (cid:84) * || c o s (cid:84) * | W ( G e V ) N u m be r o f e v en t s FIG. 1: The two-dimensional distribution of the experimental π π candidates. The same distri-bution is viewed from two different directions. The background yields obtained from the fits are fitted to a smooth two-dimensionalfunction of ( W , | cos θ ∗ | ) in order to minimize statistical fluctuations. Then, the backgroundsare subtracted from the experimental yield distribution. The background yields integratedover the angle is shown in Fig. 2(a). We omit the data points in the small-angle ( | cos θ ∗ | > .
6) region in
W < .
72 GeV, because there the background dominates the yield.
C. Unfolding the W distributions We estimate the invariant-mass resolutions from studies of the signal-MC and experi-mental events. We find that the MC events show a relative invariant-mass resolution of1.4%, which is almost constant in the whole W region of the present measurement. Themomentum resolution of π is known to be worse by about 15% in the experimental datathan in MC from a study of the p t -balance distributions (described in Sect. V). Moreover,the distribution of the MC is asymmetric; it has a longer tail on the lower mass side.An asymmetric Gaussian function with standard deviations of 1.9% W and 1.3% W onthe lower and higher sides of the peak, respectively, is used and approximates the smearingreasonably well.We calibrate the experimental energy scale and invariant-mass distribution using the γγ invariant mass from experimental samples of η ′ → γγ from two-photon processes. The peakposition is consistent with the nominal mass of η ′ with an accuracy better than 0.2%.This invariant-mass resolution is comparable to or larger than the W bin width (20 MeV)used in Figs. (1) and (2). We made an unfolding of the invariant-mass distribution in each | cos θ ∗ | bin separately, to correct for migrations of signal yields between different W bins,based on the smearing function of the above asymmetric Gaussian shape. The migration inthe | cos θ ∗ | direction is expected to be small and is neglected.The unfolding is made using the Singular Value Decomposition (SVD) algorithm [13] inthe yield level, and is applied so as to reproduce the corrected W distribution in the 0.9 -2.4 GeV region, using data at observed W between 0.72 and 3.0 GeV. For lower energies, W < . W > . (GeV) N u m be r o f e v en t s (a)0 1 2 3 4 W(GeV) N u m be r o f e v en t s FIG. 2: The W distribution of the candidate events. (a) | cos θ ∗ | < .
8. The curve is an estimateof backgrounds from events with p t imbalance. (b) | cos θ ∗ | < .
4, near the charmonium region.The curve is the fit described in Sect. VIII.
Distributions before and after the unfolding for a typical angular bin ( | cos θ ∗ | = 0 . V. DETERMINATION OF EFFICIENCY
We determine the trigger efficiency for signal events using the detector and trigger simu-lators applied to the signal MC events.The signal MC events for e + e − → e + e − π π are generated using TREPS code [14] forthe trigger efficiency study at 27 fixed W points between 0.5 and 4.1 GeV, isotropic in | cos θ ∗ | . The angular distribution at the generator level does not play a role for the efficiencydetermination, because we calculate the efficiencies separately in each | cos θ ∗ | bin with width0.05. 5 × events are generated at each W point.8 (cid:54) p t*| (GeV/c)(a) (b)(c) (d) N u m be r o f e v en t s FIG. 3: The distribution of imbalance in p t for candidate events. (a) In the bin centered at W = 0 .
90 GeV and | cos θ ∗ | = 0 .
05 (The bin width is 0.04 GeV and 0.1 in the W and | cos θ ∗ | directions, respectively, in (a)-(c).), the experimental distribution (histogram) is fitted with the sumof signal and background components (curves). The grey region shows the estimated backgroundcontamination in the signal region. (b) W = 0 .
66 GeV, same as in (a) for the others. (c) In the binof W = 1 .
18 GeV, | cos θ ∗ | = 0 .
65, the experimental distribution (dots with error bars) is comparedwith the signal MC (histogram). The grey region shows the estimated background contaminatingthe signal region obtained from the fit. (d) For 3 . < W < . | cos θ ∗ | < .
4, theexperimental distribution (dots with error bars) is compared with the signal MC (histogram).
To minimize statistical fluctuation in the MC, we fit the numerical results of the triggerefficiency to a two-dimensional empirical function in ( W, | cos θ ∗ | ). The W dependences areshown in Fig. 5 for two typical angular bins. We find that the trigger efficiency is almostflat and close to 100% for the region W above 1.3 GeV. The angular dependence is rathersmall.Separately, we generated signal MC events at 48 W points in the same W region with 10 events at each value of W , for the acceptance calculations. Here we call the efficiency of theselections not including the hardware trigger “acceptance”; the net efficiency is a product ofthe trigger efficiency and the acceptance. The determined acceptance from the MC eventsis fitted by a smooth two-dimensional function of ( W , | cos θ ∗ | ) (Fig. 6). It is about 11% atmaximum and gets smaller (down to around 1%) at lower W or smaller c.m. angle (larger | cos θ ∗ | ).The acceptance calculated using the signal MC events is corrected for a systematic dif-ference found between the peak widths in the p t -balance distributions of the experimental9 W(GeV) N u m be r o f y i e l d / b i n FIG. 4: Invariant mass distributions of the yield in each bin before(orange colored triangles) andafter (dark-blue diamonds) the unfolding, at | cos θ ∗ | = 0 . W below and above 2.0 GeV. |cos q *|=0.02500.20.40.60.811.2 0 1 2 3 4 5 t r i gge r e ff i c i en cy t r i gge r e ff i c i en cy |cos q *|=0.725 FIG. 5: The W dependence of the trigger efficiency for two angular bins. The curves are the fit toparameterize it. data and the MC, which could affect the acceptance through the | Σ p ∗ t | cut. It originatesfrom a difference in the momentum resolution for π between data and MC. We find thatthe peak position of the experimental data in the distribution is 10% to 20% higher thanthe MC expectation, depending on W and | cos θ ∗ | . The correction factor ranges from 0.90to 0.95. 10 |cos q *|=0.725|cos q *|=0.025W (GeV) A cc ep t an c e FIG. 6: The W dependence of the acceptance for two angular bins. The curves are the fit toparameterize it. No correction for the π momentum resolution is included. VI. CROSS SECTION CALCULATION
The differential cross section for each ( W , | cos θ ∗ | ) point is derived by the followingformula: dσd | cos θ ∗ | = ∆ Y − ∆ B ∆ W ∆ | cos θ ∗ | R L dtL γγ ( W ) η trg η acc where ∆ Y and ∆ B are the signal yield and the estimated p t -unbalanced background in thebin, ∆ W and ∆ | cos θ ∗ | are the bin widths, R L dt and L γγ ( W ) are the integrated luminosityand two-photon luminosity function calculated by TREPS, respectively, and η trg and η acc are the trigger efficiency and the acceptance, respectively, the latter including the correctiondescribed in the previous section.Figures 7(a) and (b) show the W dependence of the cross section integrated over | cos θ ∗ | < . | cos θ ∗ | < .
6, respectively. They are obtained by simply adding dσ/d | cos θ ∗ | · ∆ | cos θ ∗ | over the corresponding angular bins.The data points for 0.9 GeV < W < W = 0 .
02 GeV (0.04 GeV) for W above (below) 2.0 GeV. For the data pointsabove 2.4 GeV, we average five data points each with a bin width of 0.02 GeV and getresults for every 0.1 GeV at W . We have removed the bins in the range 3.3 GeV < W < . χ c , χ c and the continuum ina model-independent way due to a finite mass resolution and insufficient statistics in themeasurement.We show the angular dependence of the differential cross section at several W points inFig. 8.It is noted that the cross section results after the unfolding are no longer independent ofeach other in the neighboring bins, in both central values and size of errors.11 .010.111010010000.5 1.5 2.5 3.5 (a) (b)W (GeV)W (GeV) s ( gg p p ) ( nb ) |cos q *| < 0.6|cos q *| < 0.8 FIG. 7: The cross section results integrated in the angular regions (a) | cos θ ∗ | < . | cos θ ∗ | < . W = 0.97 GeV W = 1.27 GeV W = 1.95 GeVW = 2.45 GeV W = 3.15 GeV d s / d | c o s q * | ( nb ) FIG. 8: The differential cross sections for five selected W points, 0.97 GeV, 1.27 GeV, 1.95 GeV,2.45 GeV and 3.15 GeV. The results of the first three W points are after the unfolding. VII. SYSTEMATIC ERRORS
We summarize the evaluation of the systematic errors for σ ( | cos θ ∗ | < .
8) ( σ ( | cos θ ∗ | < .
6) with
W < .
72 GeV) for each W point. They come from the following major errorsources: Trigger efficiency : The systematic error of the Clst4 trigger is assigned as 2 / W < . W re-gion. The systematic errors from the two triggers are added in quadrature. This systematicerror is large in the low W region, 20%-30% for W < . The reconstruction efficiency : 6% for two pions.
The p t -balance cut : 3%-5%. One half of the correction size discussed in Sect. V.12 s ( gg p p ) ( nb ) |cos q *| < 0.8
40 BelleCrystal Ball
W (GeV)
FIG. 9: The cross section results integrated over the angular regions | cos θ ∗ | < . Background subtraction : 20% of the size of the subtracted component is assigned as theerror from this source. In the W region where the background subtraction is not applied( W > . < W < . W > . p t -balance distributions. Luminosity function
W < ( > )3 . W region, 1.05 GeV < W < . W , 15% at W = 0 .
85 GeV, 30% at W = 0 .
70 GeV and 55%at W = 0 .
61 GeV. The error is dominated by the background subtraction for low W . Forhigher W , the systematic error is rather stable, 10%-11% for 2.7 GeV < W < . VIII. DISCUSSION
We compare our results with the previous measurements by Crystal Ball at DORISII [10] (Fig. 9). The agreement is fairly good. The error bars from the two experiments arestatistical only, and the systematic errors ( 7% (11%) for
W > ( < ) 0 . f (980) and f (1270), respectively and are observed also in the γγ → π + π − process [1]. Itis for the first time that the f (980) is observed as a clear peak in γγ → π π . We find clearevidence for rather broad peaks at 1.65 GeV and 1.95 GeV. For these, any quick assignmentto well known states is not easy. In addition, we find a hint of a possible inflection pointnear 1.4 GeV and a structure in the mass region of two charmonium states χ c and χ c . Thestructures above found in the 1.2 - 2.1 GeV region are somewhat similar to the distributionobserved in the π π spectrum from the π − p → π π n experiment, GAMS [15].We fit the yield distribution in the range 2.8 GeV < W < . | cos θ ∗ | < . χ c and χ c charmonia with a binned maximum-likelihood13 R a t i o s(p+p-) Ratio s(p0p0)/s(p+p-)s(p0p0)
FIG. 10: The cross sections of the γγ → π π and γγ → π + π − reactions for | cos θ ∗ | < .
6. Theblue closed circle and the violet triangles are the cross sections of the two reactions in units of nb.The red closed circle is the ratio. The error bars are statistical only. method. The fit is shown in Fig. 2(b). We take into account the finite invariant-mass reso-lution effect introduced in the last section in the fit. We have fixed the nominal masses andthe width of χ c to the world averages [16] (we neglect the width of χ c ). The backgroundcomponent is assumed to have the shape of ∼ W − n .From the fit, we find the yields 35 . ± . . ± . χ c and χ c , respectively. These yields provide the products of the two-photon decay widths andthe branching fractions, Γ γγ ( χ cJ ) B ( χ cJ → π π ) = 8 . ± . stat. ) ± . syst. ) eV and0 . ± . ± .
03 eV, for χ c and χ c , respectively. The former and latter provide ev-idence for the γγ → χ c → π π signal at the 4 . σ level and an upper limit at the90% C.L., Γ γγ ( χ c ) B ( χ c → π π ) < .
75 eV which is obtained from the yield wherethe two times the log-likelihood of the fit is smaller by (1 . than that of the best fit,respectively. The above central values show good agreement with the world averages ofΓ γγ ( χ cJ ) B measured in the χ cJ → π + π − process [16], considering isospin invariance (apply π π : ππ = 1 : 3 to the branching fractions), which includes the Belle measurements of theprocess γγ → χ cJ → π + π − [2].The general trend of the angular dependence of the differential cross section is as follows:The differential cross section has a maximum at | cos θ ∗ | = 0 for the W < . W > . W region, the point in c.m. angle at which the rise in the differentialcross section begins moves toward the forward direction, and the rise gets steeper, as W increases.We show the cross section ratio between γγ → π π and γγ → π + π − [2] for | cos θ ∗ | < . < W < . γγ → π + π − measurements above the charmo-nium masses have larger systematic errors, ∼ W > . W and angular dependences in comparisonwith the predictions of the QCD models to test the expected asymptotic nature. IX. CONCLUSION
We have measured the cross section of the process γγ → π π in the γγ c.m. energyand angular regions of 0.60 GeV < W < . | cos θ ∗ | < .
8. In the cross section,several resonant structures are seen, including a statistically significant peak from the f (980). We find that the angular dependence (forward- and/or large-angle enhancements)changes drastically at around W = 2 . γγ → π π and γγ → π + π − in the 3 GeV region is also obtained.We thank the KEKB group for the excellent operation of the accelerator, the KEKcryogenics group for the efficient operation of the solenoid, and the KEK computer groupand the National Institute of Informatics for valuable computing and Super-SINET networksupport. We acknowledge support from the Ministry of Education, Culture, Sports,Science, and Technology of Japan and the Japan Society for the Promotion of Science; theAustralian Research Council and the Australian Department of Education, Science andTraining; the National Natural Science Foundation of China under contract No. 10575109and 10775142; the Department of Science and Technology of India; the BK21 program ofthe Ministry of Education of Korea, the CHEP SRC program and Basic Research program(grant No. R01-2005-000-10089-0) of the Korea Science and Engineering Foundation, andthe Pure Basic Research Group program of the Korea Research Foundation; the PolishState Committee for Scientific Research; the Ministry of Education and Science of theRussian Federation and the Russian Federal Agency for Atomic Energy; the SlovenianResearch Agency; the Swiss National Science Foundation; the National Science Council andthe Ministry of Education of Taiwan; and the U.S. Department of Energy. [1] Belle Collaboration, T. Mori et al. , Jour. Phys. Soc. Jpn. , 074102 (2007); Belle Collabora-tion, T. Mori et al. , Phys. Rev. D , 051101(R) (2007).[2] Belle Collaboration, H. Nakazawa et al. , Phys. Lett. B , 39 (2005).[3] Belle Collaboration, W.T. Chen et al. , Phys. Lett. B , 15 (2007).[4] Belle Collaboration, C.C. Kuo et al. , Phys. Lett. B , 41 (2005).[5] Belle Collaboration, S. Uehara et al. , Phys. Rev. Lett. , 082003 (2006).[6] S.J. Brodsky and G.P. Lepage, Phys. Rev. D , 1808 (1981).[7] M. Benayoun and V.L. Chernyak, Nucl. Phys. B , 209 (1990); V.L. Chernyak, Phys. Lett.B , 246 (2006).[8] M. Diehl, P. Kroll and C. Vogt, Phys. Lett. B , 99 (2002).[9] JADE Collaboration, T. Oest et al. , Zeit. Phys. C , 343 (1990);[10] Crystal Ball Collaboration, H. Marsiske et al. , Phys. Rev. D , 3324 (1990).[11] S. Kurokawa and E. Kikutani, Nucl. Instr. and. Meth. A , 1 (2003), and other papersincluded in this volume.[12] Belle Collaboration, A. Abashian et al. , Nucl. Instr. and Meth. A , 117 (2002).[13] A. H¨ocker and V. Kartvelishvili, Nucl. Instr. Meth. A , 469 (1996).
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