Theoretical investigation of the process γγ → ππ at low energies

Abstract

Dispersion relations and unitarity are used, and allow firm predictions for the low-energy cross sections in terms of the s-wave ππ phase shifts. The Born term (one-pion exchange) completely dominates over other exchanges. Unitarity implies (for a definite isospin ππ state) that the phases of the partial waves for γγ → ππ are just the elastic ππ phase shifts; this gives a well defined correction to the Born term for γγ → π + π −, and also implies a definite cross section for γγ → π o π o (where there is no Born term). Experimental data on these processes would allow one to deduce the s-wave ππ phase shifts, at low energies.