Study of resonance formation in the mass region 1400-1500 MeV through the reaction gamma gamma -> K0sK+-Pi-+

JHEP03(2007)018 Published by Institute of Physics Publishing for SISSA Received: December 12, 2006 Accepted: February 1, 2007 Published: March 6, 2007 Study of resonance formation in the mass region 1400 −1500 MeV through the reaction γγ→K0 SK±π∓ L3 Collaboration Abstract: The K0 SK±π∓final state in two-photon collisions is studied with the L3 detector at LEP at e+e−centre-of-mass energies from 183 to 209 GeV with an integrated luminosity of 664.6 pb−1. The η(1475) and f1(1420) mesons are observed and their contribution is separated by measuring the formation rates as a function of the photon virtuality Q2. The η(1475) is found to be dominant for Q2≤0.01 GeV2and its two-photon width is measured to be 0.23 ±0.05 (stat.) ±0.05 (sys.) keV. At higher Q2, the f1(1420) is formed and decays to K∗(892)K. The γγ coupling and form factor parameters of this state are measured to be Γγγ = 3.2±0.6 (stat.) ±0.7 (sys.) keV and Λ1= 926 ±72 (stat.) ±32 (sys.) MeV, respectively. Keywords: e+-eExperiments. c °SISSA 2007 http://jhep.sissa.it/archive/papers/jhep032007018 /jhep032007018.pdf JHEP03(2007)018 Contents 1. Introduction 1 2. Monte Carlo generators 3 3. Event selection 4 4. Results 4 4.1 Q2dependence 4 4.2 Global fit 7 4.3 Systematic uncertainties 8 4.4 The η(1475) resonance 9 4.5 The f1(1420) resonance 10 4.6 The f1(1420)→K∗(892)K decay 11 5. Conclusion 11 1. Introduction The study of resonance formation by two virtual photons is well suited to classify q¯q states into SU(3) nonets. Only C= +1 resonances can be formed and their two-photon width can be calculated in the framework of quark models. As direct gluon-photon coupling is forbidden, gluonium states are suppressed and the absence of a well-established resonance in the two-photon mass spectrum may be a signature of a gluon-rich partonic structure. This Letter presents a study of resonance formation by two virtual photons in the reaction e+e−→e+e−γγ →e+e−K0 SK±π∓. Untagged two-photon collisions are considered, corresponding to cases where the outgoing electron and positron carry almost the full beam energy and are not detected. The data used for this analysis were collected with the L3 detector [1] at LEP at e+e−centre-of-mass energies, √s, between 183 GeV and 209 GeV, comprising a total integrated luminosity of 664.6 pb−1. In the mass region 1400 −1500 MeV, two pseudoscalar mesons (JP C = 0−+), η(1405) and η(1475), and an axial vector meson (JP C = 1++), f1(1420), are observed in the K0 SK±π∓final state [2]. The η(1405), observed in J/ψ(1S) radiative decay and p¯p collisions at rest, also decays into ηππ while the η(1475) decays predominantly to K ¯ Kπ. In a previous Letter [3] we reported the observation of the pseudoscalar η(1475) and of the axial vector f1(1420) in the K0 SK±π∓final state, but no evidence was found for the η(1405) either in the K0 SK±π∓or in the ηπ+π−final state. The η(1475) can be identified as the first radial excitation of the η0[4, 5], while the η(1405) could be a gluonium candidate. The – 1 – JHEP03(2007)018 axial vector f1(1420) was previously observed in two-photon collisions in the K¯ Kπfinal state by several experiments [6 – 9]. A recent search for η(1475) →K0 SK±π∓by the CLEO Collaboration in untagged two-photon events gave a negative result [10]. The same study observed the production of the axial vectors f1(1285) and f1(1420) in tagged two-photon collisions [10]. This Letter presents an analysis of the K0 SK±π∓final state with the entire L3 statistics obtained during the high-energy LEP runs. This statistics is 50% higher than that used previously [3]. In order to separate the f1(1420) from the η(1475), the formation of the resonances is studied as a function of the transverse momentum squared of the K0 SK±π∓ system, P2 T. To a good approximation, P2 T=Q2, where Q2is the largest virtuality of the two interacting photons. Production of spin-one resonances is forbidden for real photons, according to the Landau-Yang theorem [11]. Therefore, at low Q2, states with spin J6= 1 dominate. The cross section for a resonance Rof mass M, spin J, parity P, charge conjugation Cand width Γ is: σγγ→R= 8π(2J+ 1) ΓγγΓ (W2−M2)2+ Γ2M2F2 JP C (Q2),(1.1) where Wis the two-photon mass, Γγγ, the two-photon width, and F2 JP C (Q2) the square of the form factor. For a spin-one resonance, f1, the γγ-coupling parameter is defined [2] as Γγγ(f1) = lim Q2→0 M2 Q2ΓTS γγ∗, with ΓTS γγ∗the partial width for the transverse-scalar two-photon interaction. In the following, the model of Reference [12] is used. It is based on a hard-scattering approach [13] and describes the Q2dependence of the form factors as: F2 0−+(Q2) = 1 (1 + Q2/Λ2 0)2(1.2) and F2 1++ (Q2) = Q2 M2µ1 + Q2 2M2¶2 (1 + Q2/Λ2 1)4,(1.3) where Λ0and Λ1are pseudoscalar and axial-vector meson form-factor parameters, respectively. The values of Λ0and Λ1are expected to be equal to the rho mass, mρ, for light mesons and to be closer to the resonance mass for heavier states [12]. The different behaviour of the two form factors as a function of Q2is presented in figure 1. The same model was used for the analysis of the f1(1285) →η π+π−final state and found to reproduce well the Q2-dependence of resonance formation [14]. In contrast, the model proposed in Reference [15] and used in previous analyses [6, 7] with a form factor F2 1++ (Q2) = Q2 M2µ1 + Q2 2M2¶2 (1 + Q2/m2 ρ)2(1.4) was excluded by the data [14]. – 2 – JHEP03(2007)018 η(1475) f1(1420) Q2 (GeV2) F2(Q2) 10 -1 1 0246810 Figure 1: Dependence on Q2of the square of the form factors of the η(1475) (solid line) and f1(1420) (dashed line) mesons. The form factor parameters of formulae (1.2) and (1.3) are chosen as Λ0= 1470 MeV and Λ1= 1420 MeV, respectively. 2. Monte Carlo generators Two Monte Carlo generators are used in this study to describe two-photon resonance formation: EGPC [16] and GaGaRes [17]. The EGPC Monte Carlo describes the two-photon process as the product of the luminosity function for transverse photons [18] and the resonance production cross section. It is used to tune event selection criteria and calculate selection efficiencies. The decay distributions of the resonance are generated according to Lorentz invariant phasespace. About 105Monte Carlo events are generated for each of three resonance masses: 1.41 GeV,1.44 GeV and 1.48 GeV. Only one value of the e+e−center-of-mass energy is generated, √s= 189 GeV, since detector efficiencies and Q2distributions are found to have a very weak dependence on √sfor the energy range investigated. The events are passed through the L3 detector simulation based on the GEANT [19] and GEISHA [20] programs. Time-dependent detector efficiencies, as monitored during the data-taking period, are also simulated. The GaGaRes generator, which calculates a matrix element for the process e+e−→ e+e−R, describes the Q2dependence of resonance formation according to the form factors given in formulae (1.2) and (1.3). It is used to compare the experimental cross sections – 3 – JHEP03(2007)018 with the expectations and to extract the resonance parameters Γγγ(η), Γγγ(f1), Λ0and Λ1. 3. Event selection The events are collected by two charged-track triggers. The first trigger [21] requires at least two wide-angle tracks, back-to-back within ±41◦in the plane transverse to the beam. The second trigger [22] is based on an artificial neural network which was trained to select low-multiplicity events while rejecting beam-gas and beam-wall background. The procedure to select e+e−→e+e−K0 SK±π∓events is similar to that used in the previous analysis [3]. Events are selected by requiring four charged particles in the central tracker associated to two vertices: two tracks associated to the e+e−interaction point, and a pair of tracks coming from a secondary vertex, corresponding to K0 Sdecay into π+π−. The tracks must have more than 9 hits and the number of hits must be greater than 60% of that expected from the track length. The secondary vertex must be at least 2 mm away from the e+e−interaction point in the plane transverse to the beam. The mass of the π+π−system, shown in figure 2a, must be in the range 470 −520 MeV. The K±and π∓tracks are identified by the dE/dxmeasurements shown in figure 2b. For each pair of particles, a joint χ2is calculated for the hypotheses π+π−, K+K−or K±π∓. The identification requires a confidence level (CL) greater than 5% for the hypothesis K±π∓ while the charge-conjugate hypothesis, K∓π±, must have a CL<3%, in order resolve the K−πambiguity. The hypotheses π+π−and K+K−must have a CL<10%. Since the 4πbackground is higher at low Q2, the confidence level for dE/dxidentification for the hypothesis π+π−is lowered to 0.1% for Q2<0.12 GeV2. For Q2>0.4 GeV2, the dE/dx performance degrades, but the background is lower, therefore events are accepted if they satisfy one of the following requirements: the same dE/dxcriteria as for the 0.12 < Q2< 0.4 GeV2range; all tracks have at least 20 hits; the secondary vertex is at least 4 mm away in the transverse plane from the e+e−interaction point. Events with candidate photons are rejected. An electromagnetic cluster, with energy greater than 100 MeV, is considered as a candidate photon if it is separated from all tracks by more than 0.2 radians. Events with a second K0 Scandidate are also rejected. This selection results in 820 events with a K0 SK±π∓effective mass below 2.7 GeV and Q2in the range 0 −7 GeV2. 4. Results 4.1 Q2dependence For the following analysis, the data is subdivided into five Q2ranges listed in the first column of table 1. The corresponding K0 SK±π∓effective mass spectra for the five Q2 ranges are presented in figure 3. A clear peak between 1.35 GeV and 1.55 GeV is present in each sub-sample. At high Q2-values, another peak, which we associate with the f1(1285) meson, is also seen. Each mass spectrum of figure 3 is fitted with a Gaussian function over a background function of the form (W−1.16)2exp(p1+p2W2), where Wis the K0 SK±π∓mass and – 4 – JHEP03(2007)018 0 500 1000 1500 0.45 0.5 0.55 M(π+π−) (GeV) Events / 4 MeV a) L3 Momentum (GeV) dE / dx (arbitrary units) L3 b) K candidates π candidates 0 1 2 3 4 0 0.25 0.5 0.75 1 1.25 Figure 2: a) Spectrum of the π+π−mass before any other selection cut. The arrows indicate the K0 Scandidate window. b) The dE/dxdistribution for charged particles at the e+e−interaction vertex. Q2range ²T R (%) ²[f1(1420)] (%) ²[η(1475)] (%) Events M(MeV) σ(MeV) 0−0.01 92 ±2 0.51 ±0.03 0.53 ±0.03 43 ±9 1464 ±12 54 ±10 0.01 −0.12 94 ±2 0.49 ±0.05 0.45 ±0.05 40 ±9 1462 ±16 63 ±20 0.12 −0.4 91 ±2 0.82 ±0.10 0.79 ±0.09 32 ±7 1426 ±9 32 ±8 0.4−0.9 83 ±2 1.19 ±0.15 1.25 ±0.15 45 ±9 1453 ±9 42 ±9 0.9−7 67 ±5 1.92 ±0.24 1.78 ±0.22 33 ±10 1431 ±19 32 ±10 Table 1: Results of a Gaussian fit to the peaks of the mass spectra of figure 3. For each Q2range the trigger efficiency, ²T R, the overall efficiency of the resonances, ², the number of events, the mass, M, and the width, σ, of the Gaussian peak are presented. All uncertainties are statistical only. – 5 – JHEP03(2007)018 0 10 20 1 1.5 2 2.5 0 10 20 1 1.5 2 2.5 0 10 20 1 1.5 2 2.5 0 10 20 1 1.5 2 2.5 M(K0 S K±π ) (GeV) Events / 40 MeV ± L3 Data Fit Bkgd b) d) a) c) e) 0 10 20 1 1.5 2 2.5 Figure 3: The K0 SK±π∓effective mass spectra for five Q2bins: a) 0 −0.01 GeV2; b) 0.01 − 0.12 GeV2; c) 0.12 −0.4 GeV2; d) 0.4−0.9 GeV2; e) 0.9−7 GeV2. Fits of a Gaussian function over a Q2-dependent background are superimposed on the data. For spectra with Q2>0.12 GeV2, an additional Gaussian function, representing the f1(1285), is added with fixed mass and width: M= 1282 MeV and σ= 20 MeV. 1.16 GeV is the edge of the mass spectrum. For the spectra above Q2>0.12 GeV2, an additional Gaussian function, representing the f1(1285), is added with a fixed mass, M= 1282 MeV [2], and a fixed width corresponding to the experimental mass resolution, σ= 20 MeV. The peak yield for each Q2-range is presented in table 1 together with the mass and width obtained by the fit. Table 1 also presents the trigger efficiencies. These are evaluated by using the data themselves comparing the rates of two independent triggers. The selection efficiencies are also listed in the table. They are determined as the ratio of selected to generated Monte Carlo events in the mass range around the resonance peak. The efficiencies are estimated for each Q2interval. The trigger efficiency decreases at higher Q2due to the back-to-back requirement imposed on the tracks. In contrast, the geometrical acceptance – 6 – JHEP03(2007)018 Q2 (GeV2) Events L3 a) Data η(1475) f1(1420) 0 25 50 75 100 10 -3 10 -2 10 -1 1 Q2 (GeV2) Events / ∆Q2 (1/GeV2) L3 b) Data Global fit η(1475) f1(1420) 1 10 10 2 10 3 10 4 10 -3 10 -2 10 -1 1 Figure 4: a) Number of events obtained by the Gaussian fit presented in table 1 and figure 3 compared to Monte Carlo predictions in presence of a single resonance, either the η(1475) (dotteddashed line) or the f1(1420) (dashed line). b) Number of events per ∆Q2range observed in data, together with the results a global fit (solid line) including two contributions: f1(1420) (dashed line) and η(1475) (dotted-dashed line). In both figures the uncertainties are statistical only. of the detector increases with increasing Q2. The numbers of events in the peak are compared in figure 4a to the expectations of the GaGaRes Monte Carlo for the formation of a single pseudoscalar meson, η(1475), or a single axial-vector meson, f1(1420). A χ2comparison of the five bins of this histogram gives a confidence level of 3×10−4for the f1(1420) hypothesis and 6×10−9for the η(1475) hypothesis. Therefore the data cannot be described by a single pseudoscalar or axial-vector meson: both states must be included in a fit to the mass spectra. In addition, there is no evidence that also the formation of η(1405) or f1(1510) must be included, consistent with a gluon-rich partonic structure for these states. 4.2 Global fit The five K0 SK±π∓mass spectra are fitted simultaneously with a binned maximumlikelihood method, using a mass bin of 5 MeV,1in the hypothesis of the presence of both pseudoscalar and axial-vector resonances. The relative yield of the resonances as a function of Q2is fixed according to the GaGaRes program. Each resonance is described by the convolution of a Breit-Wigner function with a Gaussian resolution function estimated by Monte Carlo. The resolution is of the order of σ= 20 MeV. The free parameters of the fit are: the mass of each resonance; the η(1475) width; the Λ1parameter of the f1(1420) form factor and the overall normalisation of each resonance. The f1(1420) width is fixed to the world average value, Γ = 55 MeV [2]. If this parameter is left free the fit becomes unstable. The Λ0parameter of the η(1475) form factor cannot 1The bin width was varied between 2 MeV and 6 MeV and no significant difference in the results was observed. – 7 – JHEP03(2007)018 State Events M(MeV) Γ (MeV) ΓγγBR(K¯ Kπ) (keV) Λ (MeV) f1(1420) 133 ±23 1434 ±5±5 fixed to 55 3.2±0.6±0.7 926 ±72 ±31 η(1475) 74 ±16 1469 ±14 ±13 67 ±18 ±7 0.23 ±0.05 ±0.05 fixed to 1470 Table 2: Results of a global fit to the mass spectra of figure 5. The number of events, the mass, M, and the width, Γ, of the f1(1420) and η(1475) Breit-Wigner functions are given. The two-photon width or the two-photon coupling parameter, Γγγ, times the branching ratio for the decay to K ¯ Kπ, BR(K¯ Kπ), are extracted from the cross sections, estimated with the GaGaRes program from the fitted number of events and the efficiencies of the resonances. The form factor parameter, Λ, is also listed. The first uncertainty is statistical, the second systematic. M(η(1475)) Γ(η(1475)) Γγγ (η(1475)) M(f1(1420)) Γγγ (f1(1420)) Λ(f1(1420)) BR(K ¯ Kπ) BR(K ¯ Kπ) M(η(1475)) 1 Γ(η(1475)) −0.20 1 Γγγ (η(1475))BR(K ¯ Kπ) 0.09 −0.42 1 M(f1(1420)) −0.06 −0.11 −0.02 1 Γγγ (f1(1420))BR(K ¯ Kπ) 0.38 −0.21 0.11 0.08 1 Λ(f1(1420)) −0.28 0.20 −0.20 −0.04 −0.69 1 Table 3: Correlation coefficients for the free parameters of the global fit shown in figure 5. be determined as most of the η(1475) data is in a single bin. It is fixed to the theoretical value 1470 MeV [12]. As in the previous fit a Q2-dependent background is used. The parameters p1and p2 of the background are determined separately in each Q2interval and the f1(1285) is added to the background function in the high Q2intervals. The results of the fit are given in table 2 and presented in figures 4b and 5. The production cross section is calculated from the number of events, the efficiency and the luminosity. The two-photon width is then extracted by comparing this cross section to that estimated by the GaGaRes program. The correlation coefficients of the parameters of interest are given in table 3. A χ2comparison of this fit to the five bins presented in figure 4b gives a confidence level of 22%. The total number of events in the f1(1285) peak is found to be 19.8±4.4. The limited statistics and the uncertainties of the efficiency corrections at threshold prevent further investigation of the formation of this resonance. 4.3 Systematic uncertainties Different sources of systematic uncertainties on the η(1475) and f1(1420) parameters are considered, as listed in table 4. They are estimated by varying the selection cuts, the fixed parameters of the fit and taking into account the uncertainties on the total efficiencies: •The K0 Smass window, shown by the arrows in figure 2a, is extended to 465−525 MeV and narrowed to 475 −515 MeV. •The cut on the distance, in the transverse plane, of the K0 Sdecay vertex from the interaction point is varied to 3 mm for Q2<0.4 GeV2and to 4 mm for higher Q2. – 8 – JHEP03(2007)018 17 INFN Sezione di Firenze and University of Florence, I-50125 Florence, Italy 18 European Laboratory for Particle Physics, CERN, CH-1211 Geneva 23, Switzerland 19 World Laboratory, FBLJA Project, CH-1211 Geneva 23, Switzerland 20 University of Geneva, CH-1211 Geneva 4, Switzerland 21 University of Hamburg, D-22761 Hamburg, Germany 22 Chinese University of Science and Technology, USTC, Hefei, Anhui 230 029, China4 23 University of Lausanne, CH-1015 Lausanne, Switzerland 24 Institut de Physique Nucl´eaire de Lyon, IN2P3-CNRS,Universit´e Claude Bernard, F-69622 Villeurbanne, France 25 Centro de Investigaciones Energ´eticas, Medioambientales y Tecnol´ogicas, CIEMAT, E-28040 Madrid, Spain[ 26 Florida Institute of Technology, Melbourne, FL 32901, USA 27 INFN-Sezione di Milano, I-20133 Milan, Italy 28 Institute of Theoretical and Experimental Physics, ITEP, Moscow, Russia 29 INFN-Sezione di Napoli and University of Naples, I-80125 Naples, Italy 30 Department of Physics, University of Cyprus, Nicosia, Cyprus 31 Radboud University and NIKHEF, NL-6525 ED Nijmegen, The Netherlands 32 California Institute of Technology, Pasadena, CA 91125, USA 33 INFN-Sezione di Perugia and Universit`a Degli Studi di Perugia, I-06100 Perugia, Italy 34 Nuclear Physics Institute, St. Petersburg, Russia 35 Carnegie Mellon University, Pittsburgh, PA 15213, USA 36 INFN-Sezione di Napoli and University of Potenza, I-85100 Potenza, Italy 37 Princeton University, Princeton, NJ 08544, USA 38 University of Californa, Riverside, CA 92521, USA 39 INFN-Sezione di Roma and University of Rome, “La Sapienza”, I-00185 Rome, Italy 40 University and INFN, Salerno, I-84100 Salerno, Italy 41 University of California, San Diego, CA 92093, USA 42 Bulgarian Academy of Sciences, Central Lab. of Mechatronics and Instrumentation, BU-1113 Sofia, Bulgaria 43 The Center for High Energy Physics, Kyungpook National University, 702-701 Taegu, Republic of Korea 44 National Central University, Chung-Li, Taiwan, China 45 Department of Physics, National Tsing Hua University, Taiwan, China 46 Purdue University, West Lafayette, IN 47907, USA 47 Paul Scherrer Institut, PSI, CH-5232 Villigen, Switzerland 48 DESY, D-15738 Zeuthen, Germany 49 Eidgen¨ossische Technische Hochschule, ETH Z¨urich, CH-8093 Z¨urich, Switzerland §Supported by the German Bundesministerium f¨ur Bildung, Wissenschaft, Forschung und Technologie. ‡Supported by the Hungarian OTKA fund under contract numbers T019181, F023259 and T037350. ¶Also supported by the Hungarian OTKA fund under contract number T026178. [Supported also by the Comisi´on Interministerial de Ciencia y Tecnolog´ıa. ]Also supported by CONICET and Universidad Nacional de La Plata, CC 67, 1900 La Plata, Argentina. 4Supported by the National Natural Science Foundation of China. †Deceased. – 15 – JHEP03(2007)018 References [1] L3 collaboration, B. Adeva et al., The construction of the L3 experiment,Nucl. Instrum. Meth. A 289 (1990) 35; M. Acciarri et al., The L3 silicon microvertex detector,Nucl. Instrum. Meth. A 351 (1994) 300; M. Chemarin et al., Test beam results for an upgraded forward tagger of the L3 experiment at LEP II,Nucl. Instrum. Meth. A 349 (1994) 345; A. Adam et al., The forward muon detector of L3,Nucl. Instrum. Meth. A 383 (1996) 342; I.C. Brock et al., Luminosity measurement in the L3 detector at LEP,Nucl. Instrum. Meth. A 381 (1996) 236. [2] W.-M. Yao et al., Review of Particle Physics,J. Phys. G 33 (2006) 1. [3] L3 collaboration, M. Acciarri et al., Light resonances in K0 sK±π∓and ηπ+π−final states in γγ collisions at LEP,Phys. Lett. B 501 (2001) 1 [hep-ex/0011035]. [4] A.V. Anisovich, V.V. Anisovich, V.A. Nikonov and L. Montanet, Partial widths for the decays η1295 →γγ and η1440 →γγ,Eur. Phys. J. A6 (1999) 247 [hep-ph/9910321]. [5] T. Barnes, N. Black and P.R. Page, Strong decays of strange quarkonia,Phys. Rev. D 68 (2003) 054014 [nucl-th/0208072]. [6] G. Gidal et al., Observation of a spin 1 resonance in the reaction γγ∗→K0K±πmp,Phys. Rev. Lett. 59 (1987) 2016. [7] TPC/Two Gamma collaboration, H. Aihara et al., Formation of spin one mesons by photon-photon fusion,Phys. Rev. D 38 (1988) 1. [8] JADE collaboration, P. Hill et al., Observation of spin 1 resonance formation in the final state KKπ produced in tagged two photon collisions,Z. Physik C 42 (1989) 355. [9] CELLO collaboration, H.J. Behrend et al., K0 sKπ production in tagged and untagged γγ interactions,Z. Physik C 42 (1989) 367. [10] CLEO collaboration, R. Ahohe et al., The search for η1440 →K0 sK±π∓in two-photon fusion at CLEO,Phys. Rev. D 71 (2005) 072001 [hep-ex/0501026]. [11] L.D. Landau, The moment of a 2-photon system,Dokl. Akad. Nauk. USSR 60 (1948) 207; C.N. Yang, Selection rules for the dematerialization of a particle into two photons,Phys. Rev. 77 (1950) 242. [12] G.A. Schuler, F.A. Berends and R. van Gulik, Meson photon transition form factors and resonance cross-sections in e+e−collisions,Nucl. Phys. B 523 (1998) 423 [hep-ph/9710462]. [13] G.P. Lepage and S.J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22 (1980) 2157; S.J. Brodsky and G.P. Lepage, Large angle two photon exclusive channels in quantum chromodynamics,Phys. Rev. D 24 (1981) 1808. [14] L3 collaboration, P. Achard et al., f1(1285) formation in two-photon collisions at LEP,Phys. Lett. B 526 (2002) 269. [15] R.N. Cahn, Production of spin 1 resonances in gamma gamma collisions,Phys. Rev. D 35 (1987) 3342; Cross-sections for single tagged two photon production of resonances,Phys. Rev. D 37 (1988) 833. – 16 – JHEP03(2007)018 [16] F.L. Linde, Charm production in two-photon collisions, Ph. D. Thesis, Rijksuniversiteit Leiden (1988). [17] R. van Gulik, GaGaRes: A Monte Carlo generator for resonance production in two-photon physics,Nucl. Phys. 82 (Proc. Suppl.) (2000) 311; F.A. Berends and R. van Gulik, GaGaRes: a Monte Carlo generator for resonance production in two-photon physics,Comput. Phys. Commun. 144 (2002) 82 [hep-ph/0109195]. [18] V.M. Budnev et al., The two photon particle production mechanism. Physical problems. Applications. Equivalent photon approximation,Phys. Rept. 15 (1975) 181. [19] R. Brun et al., GEANT 3.15 preprint CERN DD/EE/84-1 (1984), revised 1987. [20] H. Fesefeldt, RWTH Aachen report PITHA 85/2 (1985). [21] P. B´en´e et al., First-level charged particle trigger for the L3 detector,Nucl. Instrum. Meth. A 306 (1991) 150. [22] D. Haas et al., The new inner-TEC trigger of the L3 experiment using a hadwired neural network processor,Nucl. Instrum. Meth. A 420 (1999) 101. [23] F.E. Close and A. Kirk, Implications of the Glueball-q¯qfilter on the 1++ nonet,Z. Physik C 76 (1997) 469 [hep-ph/9706543]. – 17 –