TVID 2: Evaluation of planar-type three-loop self-energy integrals with arbitrary masses

TL;DR

TVID 2 is a C program that numerically evaluates complex three-loop self-energy integrals with arbitrary masses, improving computational methods for diagrams with two fermion loops.

Contribution

It introduces an enhanced numerical evaluation method for three-loop self-energy integrals, combining dispersion relations and modified Ghinculov techniques.

Findings

Efficient numerical evaluation of three-loop integrals with arbitrary masses.

Separation of UV divergent and finite parts for accurate computation.

Applicability to diagrams with two closed fermion loops.

Abstract

We present TVID 2, a program to numerically evaluate an important class of planar three-loop self-energy master integrals with arbitrary masses. As with the predecessor version (TVID 1) the integrals are separated into a known piece, containing the UV divergencies, and a finite piece that is integrated numerically, implemented in C. The set of master integrals under consideration was found with self-energy diagrams containing two closed fermion loops in mind. Two techniques are employed in deriving the expressions for the finite pieces that are then numerically integrated: (a) Sub-loop dispersion relations in the case of topologies containing sub-bubbles, and (b) a modification of the procedure suggested by Ghinculov for integrals with only sub-loop triangles.