NLO Scattering in ϕ 4 Theory Finite System Size Corrections Self-Consistency

Abstract

Previously a 2 → 2 NLO scattering amplitude for massive ϕ 4 theory with periodic boundary conditions was derived to investigate finite system size effects. This utilized new techniques and results, and as such benefited from self-consistency checks. Here we revisit the self-consistency of the derived amplitude, in order to more rigorously establish the self-consistency. Special attention is given to potentially pathological sums, which sets up for numerical evaluation investigating the finite system effects on quantities of interest, such as the effective coupling.