Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion

TL;DR

This paper calculates the impact of third generation quarks on two-loop helicity amplitudes for W boson pair production in gluon fusion, providing detailed phase space analysis and reference values using numerical methods.

Contribution

It introduces a novel calculation of third generation quark contributions to two-loop amplitudes in gluon fusion processes, with efficient numerical evaluation techniques.

Findings

Amplitude plots across phase space

Reference values for specific kinematic points

Efficient numerical evaluation of master integrals

Abstract

We compute the contribution of third generation quarks ($t,\ b$) to the two-loop amplitude for on-shell $W$ boson pair production in gluon fusion $gg \to WW$. We present plots for the amplitude across partonic phase space as well as reference values for two kinematic points. The master integrals are efficiently evaluated by numerically solving a system of ordinary differential equations.