Theoretical investigation of the reaction γγ → ππ and the ϵ → γγ and f → γγ decay widths

Abstract

The γγ → ππ cross section and the ϵ → γγ decays width are calculated on the basis of partial-wave dispersion relations. The left hand cut integral is approximated by vector meson exchange diagrams. On the right hand cut elastic unitarity is taken into account which establishes a close correspondence between the cross section and the ππ phase shifts. The I = 0, J = 2 phase shift is parametrized in terms of the f(1260) and for the corresponding J = 0 phase shift a “down” and an “up” solution (ϵ Breit-Wigner) is considered. The cross section is found to depend sensitively on the form of the ππ final state interaction. The obtained ϵ → γγ and f → γγ couplings are compared with other estimates.