Two-loop helicity amplitudes for $gg \to ZZ$ with full top-quark mass effects

TL;DR

This paper computes two-loop QCD corrections for gluon fusion into Z bosons, incorporating full top-quark mass effects, using a novel method for constructing finite integrals with advanced algebraic techniques.

Contribution

It introduces a new systematic approach to construct finite Feynman integrals with full mass dependence, improving precision in high-energy particle collision calculations.

Findings

Results agree with previous asymptotic expansions

Provides ab initio calculations for intermediate energies

Extends calculations to non-central scattering at high energies

Abstract

We calculate the two-loop QCD corrections to $gg \to ZZ$ involving a closed top-quark loop. We present a new method to systematically construct linear combinations of Feynman integrals with a convergent parametric representation, where we also allow for irreducible numerators, higher powers of propagators, dimensionally shifted integrals, and subsector integrals. The amplitude is expressed in terms of such finite integrals by employing syzygies derived with linear algebra and finite field techniques. Evaluating the amplitude using numerical integration, we find agreement with previous expansions in asymptotic limits and provide ab initio results also for intermediate partonic energies and non-central scattering at higher energies.