The Master Differential Equations for the 2-loop Sunrise Selfmass Amplitudes

TL;DR

This paper derives and utilizes differential equations for two-loop sunrise Feynman integrals with arbitrary masses, enabling precise calculations at specific momentum values and asymptotic expansions.

Contribution

It introduces the master differential equations for the two-loop sunrise integrals in arbitrary dimensions and applies them to evaluate the integrals at key momentum points and limits.

Findings

Derived differential equations for sunrise integrals in n dimensions.

Computed integral values at p^2=0 and large p^2.

Developed expansions around p^2=0 and in (n-4) limit.

Abstract

The master differential equations in the external square momentum p^2 for the master integrals of the two-loop sunrise graph, in n-continuous dimensions and for arbitrary values of the internal masses, are derived. The equations are then used for working out the values at p^2 = 0 and the expansions in p^2 at p^2 =0, in (n-4) at n to 4 limit and in 1/p^2 for large values of p^2 .