Generalized chiral perturbation theory and the reaction γγ → π0π0

Abstract

The cross section for γγ → π 0 π 0 and the pion polarizabilities are computed, within generalized chiral perturbation theory, in the full one loop approximation, i.e. up to and including order O( p 5). The result depends on the parameter α ππ defining the tree level π-π scattering amplitude and on an additional low energy constant. The latter is shown to be related by an exact sum-rule to the e + e − data. The parameter α ππ is related to the quark mass ratio r = m s/m̂ via the expansion of pseudoscalar meson masses. The generalized one loop γγ → π 0 π 0 amplitude agrees with the experimental data in the threshold region provided r = m s/m̂ ≲ 10. Higher order corrections are estimated comparing our calculation with the dispersive approach.