Backward Compton scattering sum rule and the π⁰→2γ,η⁰→2γ decay rates

Abstract

We use the superconvergence of certain Compton scattering (s-channel) helicity amplitudes for fixed s and large t, to derive a sum rule for t- and u-channel processes. The u-channel (γN→γN) contribution contains the well-known nucleon pole terms and the continuum, which we replace by just the π-N intermediate states; we then feed in photoproduction data. The t-channel (γγ→NN̅) contribution consists of the π, η poles and the continuum. We choose a suitable combination of superconvergent amplitudes such that the effects of 0⁺, 2⁺, and 1⁺ resonances in the t channel are eliminated. Assuming that this takes care of most of the t-channel continuum, we get a sum rule for the π⁰→2γ and η⁰→2γ widths, or alternatively, by using the experimental widths, we can check the consistency of the superconvergence in question. A brief comparison is made with related work by Goldberger and Abarbanel, and by Pagels.