A first computation of three-loop master integrals for the production of two off-shell vector bosons with different masses

TL;DR

This paper computes three-loop master integrals for the production of two off-shell vector bosons with different masses, providing analytic expressions and semi-numeric solutions crucial for precision calculations in particle physics.

Contribution

It presents the first analytic computation of three-loop master integrals for this process, expressed in multiple polylogarithms and supplemented with semi-numeric solutions.

Findings

Analytic results for four integral families up to order six in dimensional regulator.

Expressions in terms of real-valued multiple polylogarithms.

Semi-numeric solutions using generalized power series expansions.

Abstract

We present analytic results on physical kinematics for four integral families that are relevant to the production of two off-shell vector bosons with different masses. Our study consists of a ladder-box, a tennis-court, and two reducible ladder-box-like families. The results for the master integrals of these families are expressed up to order six in the dimensional regulator in terms of real-valued multiple polylogarithms. Furthermore, a semi-numeric solution is provided, employing generalized power series expansions using the package DiffExp.