We present an experimental study of jetproduction in photon-photon interactions for 0.1≲Q2≲120 GeV2 and jet transverse momentum,pT, up to 5 GeV/c. At alQ2, the data show a highpT, tail, characteristic of a point-like interaction. The jet production cross-section approaches the quarkparton model (QPM) expectation as either jetpT orQ2 increases. Overall, the data are well described in both total cross-section and event topology by the sum of a vector-dominance model and a point-like interaction, represented by the QPM.
The reaction e + e − →e + e − η ′(958) has been observed by detecting the final state π + π − γ . The two-photon width of the η′ has been measured to be Γ ( η ′→ γγ ) = 5.1±0.4±0.7 keV. A search for the ι (1440) has been made in the ϱ 0 γ final state. An upper limit has been obtained for the product Γ ( ι (1440) → γ ) gg ), B ( ι → ϱ 0 γ ) < 1.5 keV (95%CL).
We have measured the reaction γγ → π + π − π 0 using the PLUTO detector at PETRA. A pronounced enhancement is seen in the π + π − π 0 mass distribution corresponding to the A 2 meson. The event configuration in this enhancement favors a 2 + spin-parity assignment. The value of Γ γγ =1.06 ±0.18±0.19 keV obtained for the two-photon decay width of the A 2 agrees with previous measurements and with quark model predictions.
We report a measurement of the differential cross section of $\pi^0$ pair production in single-tag two-photon collisions, $\gamma^* \gamma \to \pi^0 \pi^0$, in $e^+ e^-$ scattering. The cross section is measured for $Q^2$ up to 30 GeV$^2$, where $Q^2$ is the negative of the invariant mass squared of the tagged photon, in the kinematic range 0.5 GeV < W < 2.1 GeV and $|\cos \theta^*|$ < 1.0 for the total energy and pion scattering angle, respectively, in the $\gamma^* \gamma$ center-of-mass system. The results are based on a data sample of 759 fb$^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. The transition form factor of the $f_0(980)$ and that of the $f_2(1270)$ with the helicity-0, -1, and -2 components separately are measured for the first time and are compared with theoretical calculations.
Measurements of inclusive production of the Lambda, Xi- and Xi*(1530) baryons in two-photon collisions with the L3 detector at LEP are presented. The inclusive differential cross sections for Lambda and Xi- are measured as a function of the baryon transverse momentum, pt, and pseudo-rapidity, eta. The mean number of Lambda, Xi- and Xi*(1530) baryons per hadronic two-photon event is determined in the kinematic range 0.4 GeV < pt< 2.5 GeV, |eta| < 1.2. Overall agreement with the theoretical models and Monte Carlo predictions is observed. A search for inclusive production of the pentaquark theta+(1540) in two-photon collisions through the decay theta+ -> proton K0s is also presented. No evidence for production of this state is found.
Differential cross section for LAMBDA production.
Differential cross section for LAMBDA production.
Differential cross section for XI- production.
The cross section for the production of π+π− or K+K− pairs in γγ interactions is measured for mππ between 1.7 and 3.5 GeV/c2 and for two intervals of γγ center-of-mass scattering angle. Results are compared with predictions of a QCD model.
Data read off graph.
Data read off graph.
Using data from the TPC/Two-Gamma experiment at the SLAC e+e− storage ring PEP, a C=+1 resonance has been observed in the π+π−π0γ final state resulting from the fusion of one nearly real and one quite virtual photon. The actual decay channel is probably π+π−π0π0, where one final-state photon is not detected, and the mass of the fully reconstructed state would be approximately 1525 MeV. A four-pion decay mode in turn implies that the resonance has even isospin. The nonobservation of this R(1525) when both initial-state photons are nearly real suggests a spin-1 assignment. Since the large measured value of the product of the branching ratio into π+π−π0π0 and the γγ coupling makes it unlikely that this state is the mostly s¯s f1(1510), its interpretation may lie outside of conventional meson spectroscopy. There is a second, less-significant enhancement observed in the same reaction at a four-pion mass centered around 2020 MeV.
No description provided.
Coupling parameter times the effective form factor.
None
No description provided.
No description provided.
No description provided.
We report on the exclusive production of π, K and proton pairs from photon-photon interactions at momentum transfers | t |⩾1 GeV 2 . Using the PLUTO detector at the e + e − storage ring PETRA, we have observed 15 events in an integrated luminosity of 41.7 pb −1 . The data lie far below the expectations for point-like hadrons, and are in reasonable agreement with the QCD-based predictions of Brodsky and Lepage.
THIS METHOD OF ANALYSIS OF THE OBSERVED RATIO OF HADRON TO MUON PAIRS, IS TIED TO THE SPECIFIC DETECTOR ACCEPTANCE, BUT HAS THE ADVANTAGE OF BEING VIRTUALLY INDEPENDENT OF THE HADRON MASSES.
SEE COMMENT IN PREVIOUS TABLE.
THIS METHOD OF ANALYSIS OF THE CROSS SECTION AT 90 DEG IN THE CM AS A FUNCTION OF PCM IS MORE EASILY COMPARED WITH THEORETICAL PREDICTIONS BUT MORE DEPENDENT ON THE SPECIFIC HADRON MASSES.
A measurement of gamma–gamma production of the final states$K^+ K^- \pi^+ \pi ^-$,$K^+ K^- \pi^0 \pi ^0$,$
Cross sections for the partial waves from an analysis where the five (JP,LZ) states (0+,0), (2-,0), (2+,+-2), (2+,0) and (0-,0) are included.
Cross section obtained for the three partial waves obtained when the two with smallest amplitude in the previous table are set to zero.
Cross sections for the various final states from the 'five partial wave' analysis.
Additional systematic uncertainty 25% not included.
The two-photon production of the η meson has been observed, and a value has been determined for the two-photon η decay width by a measurement of the cross section σ(e+e−→e+e−η) where η→γγ. The measurement was made with the TPC/Two-Gamma facility at the SLAC e+e− collider PEP, with an accumulated data sample of 64.5 pb−1. The η→γγ events were both triggered and detected by the pole-tip calorimeter. The measured two-photon η decay width is Γη→γγ=0.64±0.14 (statistical) ±0.13 (systematic) keV, in agreement with earlier similarly determined values.
No description provided.
The reaction γγ→π0η has been investigated with the Crystal Ball detector at the DESY storage ring DORIS II. Formation of δ(980) and A2(1320) has been observed with γγ partial widths Γγγ(A2)=1.14±0.20±0.2 6 keV and Γγγ(δ)B(δ→πη)=0.19±0.07 −0.07+0.10 keV.
No description provided.
No description provided.
The structure function F2γ for a quasireal photon has been measured in the reaction ee→eeX for Q2 in the range 0.2<Q2<7 GeV2, by use of 9200 multihadron events obtained with the TPC/Two-Gamma detector at the SLAC storage ring PEP. The data have been corrected for detector effects by a regularized unfolding procedure and are presented as F2γ(x,Q2). The structure function shows scaling in the region 0.3<Q2<1.6 GeV2, x<0.3, and rises for higher Q2 and x>0.1. Below Q2=0.3 GeV2, scaling breaks down in accordance with the finite cross-section bound for real photons.
Data read from graph.
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We report measurements of the two-photon processes e+e−→e+e−π+π− and e+e−→e+e−K+K−, at an e+e− center-of-mass energy of 29 GeV. In the π+π− data a high-statistics analysis of the f(1270) results in a γγ width Γ(γγ→f)=3.2±0.4 keV. The π+π− continuum below the f mass is well described by a QED Born approximation, whereas above the f mass it is consistent with a QCD-model calculation if a large contribution from the f is assumed. For the K+K− data we find agreement of the high-mass continuum with the QCD prediction; limits on f′(1520) and θ(1720) formation are presented.
Data read from graph. Additional overall systematic error 20% not included.
Data read from graph.. Additional overall systematic error 20% not included.
Data read from graph.. Additional overall systematic error 20% not included.. The Q**2 dependence is normalized to unity for the bin centred on Q**2 = 0.
The photon structure function F 2 γ has been measured at an average Q 2 value of 6.8 GeV 2 using data collected by the AMY detector at the TRISTAN e + e − collider. The measured F 2 γ is compared with several QCD-based parton density models.
No description provided.
None
Statistical errors only.
Statistical errors only.
Statistical errors only.
Two-photon production of the hadronic final states K + K − π + π − and K + K − π + π 0 π − has been studied using the ARGUS detector at the e + e − storage ring DORIS II at DESY. The cross sections of the reactions γγ → øϱ 0 and γγ → øω have been measured for the first time. In addition, angular distrubutions have been determined for the reaction γγ → øϱ 0 → K + K − π + π − .
No description provided.
No description provided.
The shape of jets produced in (quasi-) real photon-photon collisions as well as in e^+e^- annihilation process has been studied with a cone jet finding algorithm, using the data taken with the TOPAZ detector at the TRISTAN e^+e^- collider at an average center-of-mass energy of 58 GeV. The results are presented in terms of the jet width as a function of the jet transverse energy(E^{jet}_T) as well as a scaled transverse jet energy, x_T(=2E^{jet}_T/root(s)). The jet width narrows as E^{jet}_T increases; however, at the same value of E^{jet}_T the jet width in gamma-gamma collisions at TRISTAN is significantly narrower than that in gamma p collisions at HERA. By comparing our results with the data in other reactions, it has been shown that the jet width in gamma-gamma, gamma p, p\bar{p} collisions as well as the e^+e^- annihilation process has an approximate scaling behavior as a function of x_T.
The jet width is defined as the full width at the half maximum of the distribution of the transverse energy flow.
The jet width is defined as the full width at the half maximum of the distribution of the transverse energy flow.
We have investigated the properties of jet production in almost real γγ collisions at √ s =58 GeV with the TOPAZ detector at the TRISTAN e + e − collider. The data were analyzed with a jet-clustering method based on a cone algorithm. The jet rate shows evidence for a hard scattering effect of the hadronic constituents of a photon (resolved photon processes). We have also observed a substantial energy flow in the small-angle region, which is additional evidence for resolved photon processes. We present the transverse momentum dependence of the inclusive jet and two-jet cross sections and compare them with different model predictions.
No description provided.
No description provided.
No description provided.
The photon structure function F 2 has been measured at average Q 2 values of 73,160 and 390 ( GeV c ) 2 . We compare the x dependence of the Q 2 = 73 ( GeV c ) 2 data with theoretical expectations based on QCD. In addition we present results on the Q 2 evolution of the structure function for the intermediate x range (0.3⩽ x ⩽0.8). The results are consistent with QCD.
X dependence at Q**2 = 73 GeV**2 for light quark data.
X dependence at Q**2 = 73 GeV**2 for total data.
Photon structure function F2 for total data.
This paper presents experimental results on π + π − production threshold from the collision of quasi-real photons. The data, obtained at the e + e − collider DCI, are a combination of the results from the DM1 and DM2 experiments. Using the e + e − and π + π − production for normalization and cross-checks, we observe a pion pair yield at low invariant mass ( W < 500 MeV/ c 2 ) which is approximately twice the one expected from Born terms.
Data read from graph.
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We investigate the four-photon final state produced in γγ colissions. In the π 0 π 0 channel we observe f(1270) production with predominantly helicity 2 and measure a partial width Γ γγ 2.9 +0.6 −0.4 ± keV (independent of assumptions on the helicity). We observe A 2 (1310) production in the π 0 η channel and find a partial width Γ γγ = 0.77 ± 0.18 ± 0.27 KeV (assuming helicity 2). We give an upper limit for f ≈ ηη .
Data read from graph. Systematic error on M is of order of 2% or less.
Data read from graph.
Production of proton-antiproton pairs by two-photon scattering has been observed at the electron-position storage ring PETRA. A total of eight proton-antiproton pairs have been identified using the time-of-flight technique. We have measured a total cross section of 4.5 ± 0.8 nb in the photon-photon c.m. energy range 2.0–2.6 GeV.
No description provided.
We report on a measurement of the process e + e − →e + e − + hadrons, where one of the scattered electrons is detected at large angles, with an average Q 2 of 23 GeV. The results are analysed in terms of the photon structure function F 2 and are compared with QCD predictions.
Data read off graph.
Data read off graph.
Data read off graph.
The cross section of the γγ → p p reaction was measured at two-photon center-of-mass energy ( W γγ ) between 2.2 and 3.3 GeV, using the two-photon process at an e + e − collider, TRISTAN. The W γγ dependence of the cross section integrated over a c.m. angular region of | cos θ ∗ | < 0.6 is in good agreement with the previous measurements and the theoreticalv prediction based on diquark model in the high W γγ region.
Numerical values supplied by Hirhoshi Hamasaki.
Angular distributions.
None
ABS(COS(THETA)) < 0.4 for M(P=3 4) = 1.025 GeV.
No description provided.
No description provided.
The differential cross section of $d\sigma(e~+e~-\rightarrow e~+e~-D~{*\pm}X)/dP_T$ was measured using a soft-pion analysis of $D~{*\pm}\rightarrow \pi_s~\pm D~0(\overline{D~0})$ at TRISTAN. The average $\sqrt{s}$ was 58.1 GeV and the integrated luminosity used in this analysis was 198 pb$~{-1}$, respectively.
Soft pion cross section.
D*+- cross section from the soft-pion analysis.
Previous `full reconstruction' measurement from Enomoto et al. (to be published).
Using the VENUS detector at TRISTAN we have investigated the charm-quark production by detecting D*+ - mesons in the two-photon process of e+et - collisions. The study has confirmed that the charm-quark production rate is larger than that predicted from direct cc̅ production alone. The distribution of the transverse momentum of the D*+ t- mesons and the forward energy flow associated with the D*+ - production suggest that the main part of the observed excess comes from the contribution of a resolved photon process.
D* production cross section in the given kinematic ranges under the anti-tagging condition |cos(theta(e+-))|>0.990.
We present cross section measurements for inclusive jet production in almost-real photon-photon interactions at TRISTAN using the AMY detector. The results are compared with leading-order QCD calculations for different parameterizations of the parton density in the photon.
No description provided.
No description provided.
No description provided.
The process γγ→π+π− was measured using the detector MD-1 at VEPP-4. The two-photon reactionse+e−, μ+ μ− and π+ π− pair production were separated using scintillation counters, Cherenkov counters and shower-range chambers. A radiation widthГγγ(f2(1270))=3.1±0.35±0.35 keV was obtained.
Data read from graph.
The reaction γγ→π+π-π+π-π0 has been studied using the JADE detector at PETRA. The cross sections for γγ→ωπ+- and for γγ→ωρ0- are given. We observe no peak in these cross sections in the regionWγγ=1.9–2.0 GeV.
No description provided.
The production of charged kaon pairs in two-photon interactions has been studied with the ARGUS detector and the topological cross section has been measured. The γγ-widths and interference parameters have been determined for the tensor mesonsf2 (1270),a2 (1318) andf′2 (1525). The helicity structure assumed for the continuum contribution has a significant effect on the result. Upper limits have been obtained for the γγ-widths of the glueball candidate statesf2 (1720) andX (2230).
Data read from graph.. Errors are the square roots of the number of events.
Cross section allowing for spin components JM = 22,20,00. Data read from graph.. Additional overall systematic error 8.4%.
Cross section allowing for spin components JM = 22,00. Data read from graph.. Additional overall systematic error 8.4%.
Two-photon production of the exclusive final statesp\(\bar p\)+nπ (n=0, 1, 2, and 3) has been investigated using the ARGUS detector at thee+e− storage ring DORIS II at DESY. The reactionsγγ→p\(\bar p\)π andγγ→p\(\bar p\)π+π−π0 have been observed for the first time, as have theΔ++ and\(\overline {\Delta ^{ ++ } } \) baryons in the final statep\(\bar p\)π+π−. No evidence was found forΔ++\(\overline {\Delta ^{ ++ } } \) production. Topological cross sections for two-photon production ofp\(\bar p\),p\(\bar p\)π0,p\(\bar p\)π+π− andp\(\bar p\)π+π−π0, as well as the crosssection forγγ→Δ++\(\bar p\)π+π−+c.c., have been measured. Upper limits are given for the cross section forγγ→Δ0\(\overline {\Delta ^0 } \),γγ→Δ++\(\overline {\Delta ^{ ++ } } \) andγγ→Λ\(\bar \Lambda \).
Data read from graph.. Additional overall systematic error 13% not included.
Data read from graph.. Additional overall systematic error 13% not included.
Data read from graph.. Additional overall systematic error 13% not included.
The QED processes e^+ e^- -> e^+ e^- \mu^+ \mu^- and e^+ e^- -> e^+ e^- \tau^+ \tau^- are studied with the L3 detector at LEP using an untagged data sample collected at centre-of-mass energies 161 GeV < sqrt{s} < 209 GeV. The tau-pairs are observed through the associated decay of one tau into e\nu\nu and the other into \pi\pi\nu . The cross sections are measured as a function of sqrt{s}. For muon pairs, the cross section of the \gamma\gamma -> \mu^+\mu^- process is also measured as a function of the two-photon centre-of-mass energy for 3 GeV < W_{\gamma\gamma} < 40 GeV. Good agreement is found between these measurements and the O(\alpha^4) QED expectations. In addition, limits on the anomalous magnetic and electric dipole moments of the tau lepton are extracted.
Cross sections for muon-pair production as a function of centre of mass energy.
Cross sections for tau-pair production as a function of centre of mass energy.
Cross sections for the process GAMMA GAMMA --> MU+ MU- as a function of W.
Inclusive jet production, e+e- -> e+e- \ee$ jet X, is studied using 560/pb of data collected at LEP with the L3 detector at centre-of-mass energies between 189 and 209 GeV. The inclusive differential cross section is measured using a k_t jet algorithm as a function of the jet transverse momentum, pt, in the range 3<pt<50 GeV for a pseudorapidity, eta, in the range -1<eta<1. This cross section is well represented by a power law. For high pt, the measured cross section is significantly higher than the NLO QCD predictions, as already observed for inclusive charged and neutral pion production.
No description provided.
Exclusive rho^0 rho^0 production in two-photon collisions between a quasi-real and a mid-virtuality photon is studied with data collected at LEP at centre-of-mass energies 183GeV < sqrt{s} < 209GeV with a total integrated luminosity of 684.8/pb. The cross section of the process gamma gamma* -> rho^0 rho^0 is determined as a function of the photon virtuality, q^2, and the two-photon centre-of-mass energy, Wgg, in the kinematic region: 0.2GeV^2 < q^2 < 0.85GeV^2 and 1.1GeV < Wgg < 3GeV.
Production cross section as a function of Q**2. Differential cross sectionsare corrected to the centre of each bin.
Production cross section for two-photon data as a function of Q**2.
Production cross section as a function of W.
Exclusive rho+rho- production in two-photon collisions between a quasi-real photon, gamma, and a mid-virtuality photon, gamma*, is studied with data collected at LEP at centre-of-mass energies root(s)=183-209GeV with a total integrated luminosity of 684.8pb^-1. The cross section of the gamma gamma* -> rho+ rho- process is determined as a function of the photon virtuality, Q^2, and the two-photon centre-of-mass energy, W_gg, in the kinematic region: 0.2GeV^2 < Q^2 <0.85GeV^2 and 1.1GeV < W_gg < 3GeV. These results, together with previous L3 measurements of rho0 rho0 and rho+ rho- production, allow a study of the gamma gamma* -> rho rho process over the Q^2-region 0.2GeV^2 < Q^2 < 30 GeV^2.
Production cross section as a function of Q**2. Differential cross sectionsare corrected to the centre of each bin.
Production cross section for two-photon data as a function of Q**2.
Production cross section as a function of W.
Exclusive rho rho production in two-photon collisions involving a single highly virtual photon is studied with data collected at LEP at centre-of-mass energies 89GeV < \sqrt{s} < 209GeV with a total integrated luminosity of 854.7pb^-1 The cross section of the process gamma gamma^* -> rho rho is determined as a function of the photon virtuality, Q^2 and the two-photon centre-of-mass energy, Wgg, in the kinematic region: 1.2GeV^2 < Q^2 < 30GeV^2 and 1.1GeV < Wgg < 3GeV.
Production cross sections as a function of Q**2. The differential cross sections are corrected to the centre of each bin.
Production cross section for the two photon data as a function of Q**2.
Differential cross section for non-resonance and RHO0 RHO0 data corrected to the centre of each bin.
The exclusive production of proton-antiproton pairs in the collisions of two quasi-real photons had been studied using data taken at sqrt(s)_ee=183 GeV and 189 GeV with the OPAL detector at LEP. Results are presented for Ppbar invariant masses, W, in the range 2.15 W< <3.95 GeV. The cross-section measurements are compared with previous data and with recent analytic calculations based on the quark-diquark model.
Cross section as a function of the invariant mass of the pbar-p pair.
Cross section for two photon production of the pbar-p pair.
Angular distributions in 3 W ranges.
No description provided.
Low x domain.
A measurement of the cross section for γγ→pp¯ is performed at two-photon center-of-mass energies between 2.00 and 3.25 GeV. These results are obtained using e+e−→e+e−pp¯ events selected from 1.31 fb−1 of data taken with the CLEO II detector. The measured cross section is in reasonable agreement with previous measurements and is in excellent agreement with recent calculations based on a diquark model. However, leading order QCD calculations performed using the Brodsky-Lepage formalism are well below the measured cross section.
Data read from graph.
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The reaction e + e − → e + e − γ ∗ γ ∗ → e + e − hadrons is analysed using data collected by the L3 detector during the LEP runs at s = 130−140 GeV and s = 161 GeV . The cross sections σ(e + e − → e + e − hadrons) and σ(γγ → hadrons) are measured in the interval 5 ≤ W γγ ≤ 75 GeV. The energy dependence of the σ(γγ → hadrons) cross section is consistent with the universal Regge behaviour of total hadronic cross sections.
No description provided.
No description provided.
We report the first measurement of the differential cross section for the process gamma gamma --> eta eta in the kinematic range above the eta eta threshold, 1.096 GeV < W < 3.8 GeV over nearly the entire solid angle range, |cos theta*| <= 0.9 or <= 1.0 depending on W, where W and theta* are the energy and eta scattering angle, respectively, in the gamma gamma center-of-mass system. The results are based on a 393 fb^{-1} data sample collected with the Belle detector at the KEKB e^+ e^- collider. In the W range 1.1-2.0 GeV/c^2 we perform an analysis of resonance amplitudes for various partial waves, and at higher energy we compare the energy and the angular dependences of the cross section with predictions of theoretical models and extract contributions of the chi_{cJ} charmonia.
Angular dependence of the differential cross section for the W range 1.096 to 1.120 GeV.
Angular dependence of the differential cross section for the W range 1.120 to 1.160 GeV.
Angular dependence of the differential cross section for the W range 1.160 to 1.200 GeV.
None
No description provided.
No description provided.
No description provided.
Data read off graph.
Data read off graph.
No description provided.
We report a measurement of the cross section for the process γγ → π + π − at invariant masses 500 MeV/ c 2 < m ππ <2000 MeV/ c 2 . A value for the radiative width of the f(1270) tensor meson Γ f→ γγ = 3.6 ± 0.3 ± 0.5 KeV (helicity λ = 2) has been obtained from a fit to the observed ππ mass spectrum.
We have studied open charm production in $\gamma \gamma$ collisions with the TOPAZ detector at the TRISTAN $e~{+}e~{-}$ collider. In this study, charm quarks were identified by electrons (and positrons) from semi-leptonic decays of charmed hadrons. The data corresponded to an integrated luminosity of 95.3 pb$~{-1}$ at a center-of-mass energy of 58 GeV. The results are presented as the cross sections of inclusive electron production in $\gamma \gamma$ collisions with an anti-tag condition, as well as the subprocess cross sections, which correspond to resolved-photon processes. The latter were measured by using a sub-sample with remnant jets. A comparison with various theoretical predictions based on direct and resolved-photon processes showed that our data prefer that with relatively large gluon contents in a photon at small $x (x \le 0.1)$, with the next-to-leading order correction, and with a charm-quark mass of 1.3 GeV.
The process e + e − →e + e − μ + μ − has been studied in single-tag and double-tag configurations using the TOPAZ detector at TRISTAN. The data correspond to the integrated luminosity of 45.3pb − at center-of-mass energies ranging from 52 to 61.4 GeV. The observed events in both configurations have shown a good agreement with QED predictions in order α 4 . Although the AMY group reported an excess of e + e − →e + e − μ + μ − events in double-tag mode at low muon invariant mass region less than 1.0 GeV/c 2 , we did not observed such excess in our data.
The differential cross sections for the process $\gamma \gamma \to \pi^0 \pi^0$ have been measured in the kinematic range 0.6 GeV $< W < 4.1$ GeV, $|\cos \theta^*|<0.8$ in energy and pion scattering angle, respectively, in the $\gamma\gamma$ center-of-mass system. The results are based on a 223 fb$^{-1}$ data sample collected with the Belle detector at the KEKB $e^+ e^-$ collider. The differential cross sections are fitted in the energy region 1.7 GeV $< W <$ 2.5 GeV to confirm the two-photon production of two pions in the G wave. In the higher energy region, we observe production of the $\chi_{c0}$ charmonium state and obtain the product of its two-photon decay width and branching fraction to $\pi^0\pi^0$. We also compare the observed angular dependence and ratios of cross sections for neutral-pion and charged-pion pair production to QCD models. The energy and angular dependence above 3.1 GeV are compatible with those measured in the $\pi^+\pi^-$ channel, and in addition we find that the cross section ratio, $\sigma(\pi^0\pi^0)/\sigma(\pi^+\pi^-)$, is $0.32 \pm 0.03 \pm 0.05$ on average in the 3.1-4.1 GeV region.
Forum