Article

# Improved dispersion relations for γγ→ππ

Departamento de Física, Universidad de Murcia, E-30071 Murcia, Spain

Physics Letters B (Impact Factor: 6.13). 01/2008; 659(1-2):201-208. DOI: 10.1016/j.physletb.2007.11.030 Source: arXiv

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**ABSTRACT:**Glueballs, hybrids and multiquark states are predicted as bound states in models guided by quantum chromodynamics, by QCD sum rules or QCD on a lattice. Estimates for the (scalar) glueball ground state are in the mass range from 1000 to 1800MeV, followed by a tensor and a pseudoscalar glueball at higher mass. Experiments have reported evidence for an abundance of meson resonances with 0 −+, 0 ++ and 2 ++ quantum numbers. In particular the sector of scalar mesons is full of surprises starting from the elusive σ and κ mesons. The a0(980) and f0(980), discussed extensively in the literature, are reviewed with emphasis on their Januslike appearance as K ¯ K molecules, tetraquark states or q¯q mesons. Most exciting is the possibility that the three mesons f0(1370), f0(1500), and f0(1710) might reflect the appearance of a scalar glueball in the world of quarkonia. However, the existence of f0(1370) is not beyond doubt and there is evidence that both f0(1500) and f0(1710) are flavour octet states, possibly in a tetraquark composition. We suggest a scheme in which the scalar glueball is dissolved into the wide background into which all scalar flavour singlet mesons collapse. There is an abundance of meson resonances with the quantum numbers of the η. Three states are reported below 1.5GeV/c 2 whereas quark models expect only one, perhaps two. One of these states, ι(1440), was the prime glueball candidate for a long time. We show that ι(1440) is the first radial excitation of the η meson. Hybrids may have exotic quantum numbers which are not accessible by q¯q mesons. There are several claimsPhysics Reports 08/2007; · 20.03 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We shortly report on the two-photon decay width of the light $\sigma$-meson interpreted as a quarkonium state. Results are given in dependence on the $\sigma$-mass and the constituent mass of the light quark. The triangle quark-loop diagram, responsible for the two-photon transition, is carefully evaluated: a term in the transition amplitude, often omitted in literature, results in destructive interference with the leading term. As a result we show that the two-photon decay width of the $\sigma $ in the quarkonium picture is less than 1 keV for the physical range of parameters.Physical review D: Particles and fields 11/2007; 77(3). DOI:10.1103/PHYSREVD.77.034007 · 4.86 Impact Factor -
##### Article: Scalar radius of the pion and two photons into two pions. Strong S-wave final state interactions

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**ABSTRACT:**The quadratic pion scalar radius, <r^2>^\pi_s, plays an important role for present precise determinations of \pi\pi scattering. The solution of the Muskhelishvili-Omn\`es equations for the non-strange null isospin (I) pion scalar form factor determines that <r^2>^\pi_s=(0.61\pm 0.04) fm^2. However, by using an Omn\`es representation of this form factor, Yndur\'ain recently obtains <r^2>^\pi_s=(0.75\pm 0.07) fm^2. A large discrepancy between both values, given the precision, then results. We show that Yndur\'ain's method is indeed compatible with the determinations from the Muskhelishvili-Omn\`es equations once a zero in the scalar form factor for some S-wave I=0 T-matrices is considered. Once this is accounted for, the resulting value is <r^2>^\pi=(0.63\pm 0.05) fm^2. On the other hand, we perform a theoretical study of the reaction \gamma\gamma\to \pi^0\pi^0 based on dispersion relations. The large source of uncertainty for \sqrt{s}\gtrsim 0.5 GeV, due to variations in the phase used in the Omn\`es function above the K\bar{K} threshold, is removed by taking one more subtraction in the dispersion relation. This allows us to make sharper predictions for the cross section so that one could use this reaction to distinguish between different low energy \pi\pi parameterizations, once independent experiments are available. We also study the role played by the \sigma or f_0(600) meson in this reaction and determine its width to two photons.