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.
We report a high-statistics measurement of differential cross sections for the process gamma gamma -> pi^0 pi^0 in the kinematic range 0.6 GeV <= W <= 4.0 GeV and |cos theta*| <= 0.8, where W and theta* are the energy and pion scattering angle, respectively, in the gamma gamma center-of-mass system. Differential cross sections are fitted to obtain information on S, D_0, D_2, G_0 and G_2 waves. The G waves are important above W ~= 1.6 GeV. For W <= 1.6 GeV the D_2 wave is dominated by the f_2(1270) resonance while the S wave requires at least one additional resonance besides the f_0(980), which may be the f_0(1370) or f_0(1500). The differential cross sections are fitted with a simple parameterization to determine the parameters (the mass, total width and Gamma_{gamma gamma}B(f_0 -> pi^0 pi^0)) of this scalar meson as well as the f_0(980). The helicity 0 fraction of the f_2(1270) meson, taking into account interference for the first time, is also obtained.
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.
The differential cross section for the process $\gamma \gamma \to \eta \pi^0$ has been measured in the kinematic range $0.84 \GeV < W < 4.0 \GeV$, $|\cos \theta^*|<0.8$, where $W$ and $\theta^*$ are the energy and $\pi^0$ (or $\eta$) 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. Clear peaks due to the $a_0(980)$ and $a_2(1320)$ are visible. The differential cross sections are fitted in the energy region $0.9 \GeV < W < 1.46 \GeV$ to obtain the parameters of the $a_0(980)$. Its mass, width and $\Gamma_{\gamma \gamma} \B (\eta \pi^0)$ are measured to be $982.3 ^{+0.6}_{-0.7} ^{+3.1}_{-4.7} \MeV/c^2$, $75.6 \pm 1.6 ^{+17.4}_{-10.0} \MeV$ and $128 ^{+3}_{-2} ^{+502}_{-43} \eV$, respectively. The energy and angular dependences above 3.1 GeV are compared with those measured in the $\pi^0 \pi^0$ channel. The integrated cross section over $|\cos \theta^*|<0.8$ has a $W^{-n}$ dependence with $n = 10.5 \pm 1.2 \pm 0.5$, which is slightly larger than that for $\pi^0 \pi^0$. The differential cross sections show a $\sin^{-4} \theta^*$ dependence similar to $\gamma \gamma \to \pi^0 \pi^0$. The measured cross section ratio, $\sigma(\eta \pi^0)/\sigma(\pi^0 \pi^0) = 0.48 \pm 0.05 \pm 0.04$, is consistent with a QCD-based prediction.
Double-tag events in two-photon collisions are studied using the L3 detector at LEP centre-of-mass energies from root(s)=189 GeV to 209 GeV. The cross sections of the e+e- -> e+e- hadrons and gamma*gamma* -> hadrons processes are measured as a function of the photon virtualities, Q1^2 and Q2^2, of the two-photon mass, W_gammagamma, and of the variable Y=ln(W_gammagamma^2/(Q1 Q2)), for an average photon virtuality <Q2> = 16 GeV2. The results are in agreement with next-to-leading order calculations for the process gamma*gamma* -> q qbar in the interval 2 <= Y <= 5. An excess is observed in the interval 5 < Y <= 7, corresponding to W_gammagamma greater than 40 GeV . This may be interpreted as a sign of resolved photon QCD processes or the onset of BFKL phenomena.
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.
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.
Results are presented on the exclusive production of four-prong final states in photon-photon collisions from the TPC/Two-Gamma detector at the SLAC e+e− storage ring PEP. Measurement of dE/dx and momentum in the time-projection chamber (TPC) provides identification of the final states 2π+2π−, K+K−π+π−, and 2K+2K−. For two quasireal incident photons, both the 2π+2π− and K+K−π+π− cross sections show a steep rise from threshold to a peak value, followed by a decrease at higher mass. Cross sections for the production of the final states ρ0ρ0, ρ0π+π−, and φπ+π− are presented, together with upper limits for φρ0, φφ, and K*0K¯ *0. The ρ0ρ0 contribution dominates the four-pion cross section at low masses, but falls to nearly zero above 2 GeV. Such behavior is inconsistent with expectations from vector dominance but can be accommodated by four-quark resonance models or by t-channel factorization. Angular distributions for the part of the data dominated by ρ0ρ0 final states are consistent with the production of JP=2+ or 0+ resonances but also with isotropic (nonresonant) production. When one of the virtual photons has mass (mγ2=-Q2≠0), the four-pion cross section is still dominated by ρ0ρ0 at low final-state masses Wγγ and by 2π+2π− at higher mass. Further, the dependence of the cross section on Q2 becomes increasingly flat as Wγγ increases.
The production of thef0 in two photon collisions, with the subsequent decayf0→π+π− has been observed in the CELLO detector at PETRA. Thef0 peak was found to lie on a dipion continuum and to be shifted downwards in mass by ≃50 MeV/c2. The ππ mass spectrum from 0.8 to 1.5 GeV/c2 was well fitted by the model of Mennessier using only a unitarised Born amplitude and helicity 2f0 amplitude. The previously observed mass shift and distortion of thef0 peak are explained by strong interference between the Born andf0 amplitudes. The only free parameter in the fit of the data to the model is the radiative widthΓγγ(f0). It was found that:Γγγ(f0)=2.5±0.1±0.5 keV where the first (second) quoted errors are statistical (systematic).
We report a measurement of the reaction γγ→K+K−π+π− in both tagged and untagged events at PEP. The cross section rises with invariant γγ mass to about 15 nb at 2 GeV and falls slowly at higher masses. We find clear evidence for the processes γγ→φπ+π− and γγ→K*0(892)Kπ. Upper limits (95% C.L.) of 1.5 and 5.7 nb in the mass range from 1.7 to 3.7 GeV are obtained for φρ0 and K*0K¯*0 production, respectively.
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