The Pseudothreshold Expansion of the 2-loop Sunrise Selfmass Master Amplitudes

TL;DR

This work analyzes the two-loop sunrise self-mass with three arbitrary internal masses by formulating a system of first-order differential equations in p^2 and exploiting the pseudothreshold as a regular point. By expanding around n=4 and solving the resulting algebraic equations, the authors obtain explicit pseudothreshold values for the master amplitudes and derive the p^2-expansion coefficients, including a finite H^{(0,2)} term computed via a subtracted dispersion relation. The approach yields closed-form expressions for key quantities and provides a framework for higher-order p^2 and (n-4) corrections, with results consistent with existing literature. The results enhance analytic control over the sunrise integrals and offer robust checks for numerical evaluations in multi-loop calculations.

Abstract

The values at pseudothreshold of two loop sunrise master amplitudes with arbitrary masses are obtained by solving a system of differential equations. The expansion at pseudothreshold of the amplitudes is constructed and some lowest terms are explicitly presented.