ar X iv : h ep - p h / 97 10 55 7 v 1 3 1 O ct 1 99 7 Theoretical Study of the γγ → Meson - Meson Reaction

We present a unified theoretical picture which studies simultaneously the γγ → π + π − , π 0 π 0 , K + K − , K 0 ¯ K 0 , π 0 η reactions up to about √ s = 1.4 GeV reproducing the experimental cross sections. The present work implements in an accurate way the final state interaction of the meson-meson system, which is shown to be essential in order to reproduce the data, particularly the L = 0 channel. This latter channel is treated here following a recent theoretical work in which the meson-meson amplitudes are well reproduced and the f 0 , a 0 , σ resonances show up clearly as poles of the t matrix. The present work, as done in earlier ones, also incorporates elements of chiral symmetry and exchange of vector and axial resonances in the crossed channels, as well as a direct coupling to the f 2 (1270) and a 2 (1370) resonances. We also evaluate the decay width of the f 0 (980) and a 0 (980) resonances into the γγ channel. The γγ → meson-meson reaction provides interesting information concerning the structure of hadrons, their spectroscopy and the meson-meson interaction , given the sensitivity of the reaction to the hadronic final state interaction (FSI) [2]. The chiral perturbation approach [5,6] is valid only for low energies. However , chiral symmetry is one of the important ingredients when dealing with the meson-meson interaction. In addition to the f 0 (980), a 0 (980) and σ resonances , which come up naturally in the approach of ref. [3], which we use here, we introduce phenomenologically the f 2 (1270) and a 2 (1320) resonances .Another relevant aspect of this reaction, which has been reported previously, is the role of the vector and axial resonance exchange in the t, u channels.