Numerical calculation of 3-pion Coulomb scattering using scalar QED

Abstract

The Coulomb scattering between three charged pions is shown to be perturbatively calculable using scalar QED for the relative momenta accessible to high-energy experiments of particle collisions. For the triplet relative momenta, $Q_3\gtrsim 50$ MeV/$c$, the calculated three-pion correlation function at $O({\alpha }^2)$ is very similar to the commonly-used triple-product of pair factors -- Riverside approximation. At lower $Q_3$, but above the lowest existing experimental measurement of $\sim 15$ MeV/$c$, terms of $O({\alpha }^3)$ or higher are needed to obtain a convincing description of three-pion Coulomb interactions. This is in contrast to two-pion correlations, for which the known exact solution is shown to be saturated by the lower orders at comparable pair relative momenta.

Comments: 6 pages, 7 figures