Two-Loop Master Integrals for $q \bar{q} \to V V$: the Planar Topologies

TL;DR

This paper computes two-loop master integrals for vector boson pair production in QCD, using differential equations and harmonic polylogarithms, advancing the precision of theoretical predictions for collider processes.

Contribution

It introduces a method to reduce and compute two-loop four-point integrals with off-shell legs relevant to planar Feynman diagrams, employing differential equations and algebraic structures of polylogarithms.

Findings

Analytic expressions for master integrals in terms of generalized harmonic polylogarithms.

Reduction of complex two-loop integrals to a manageable set of master integrals.

Enhanced computational techniques for planar two-loop Feynman amplitudes.

Abstract

The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master integrals by solving linear relations among them. We then use differential equations in the external invariants to compute all master integrals that are relevant to planar Feynman amplitudes. Our results are expressed analytically in terms of generalised harmonic polylogarithms. The calculation relies heavily on techniques that exploit the algebraic structure of these functions, which we describe in detail.