Three-loop master integrals for ladder-box diagrams with one massive leg

TL;DR

This paper computes three-loop master integrals for ladder-box diagrams with one massive leg, providing explicit series expansions crucial for high-precision theoretical predictions in particle physics.

Contribution

It introduces a method to solve complex differential equations for three-loop integrals using Magnus exponential, yielding results expressed in multiple polylogarithms up to weight six.

Findings

Explicit three-loop integrals expressed in polylogarithms

Results applicable to NN3LO virtual corrections in collider processes

Provides series expansions for integrals relevant to Higgs and jet production

Abstract

The three-loop master integrals for ladder-box diagrams with one massive leg are computed from an eighty-five by eighty-five system of differential equations, solved by means of Magnus exponential. The results of the considered box-type integrals, as well as of the tower of vertex- and bubble-type master integrals associated to subtopologies, are given as a Taylor series expansion in the dimensional regulator parameter epsilon = (4-d)/2. The coefficients of the series are expressed in terms of uniform weight combinations of multiple polylogarithms and transcendental constants up to weight six. The considered integrals enter the next-to-next-to-next-to-leading order virtual corrections to scattering processes like the three-jet production mediated by vector boson decay, V* -> jjj, as well as the Higgs plus one-jet production in gluon fusion, pp -> Hj.