Top-Yukawa contributions to $pp\to b\bar{b}H$: two-loop leading-colour amplitudes

TL;DR

This paper presents the derivation of two-loop scattering amplitudes for bottom-quark pair production with a Higgs boson at the LHC, focusing on top-Yukawa contributions using advanced computational techniques.

Contribution

It provides the first calculation of two-loop amplitudes for this process, employing finite field evaluations and expressing results in terms of pentagon functions.

Findings

Finite remainder expressed via one-mass pentagon functions

Rational coefficients reconstructed analytically from finite field evaluations

Applicable to Higgs+2-jet production in heavy-top-quark approximation

Abstract

We derive two-loop scattering amplitudes for bottom-quark pair production in association with a Higgs boson at the LHC, focusing on terms proportional to the top-quark Yukawa coupling. We treat the bottom quark as a massless parton and employ both the leading-colour and heavy-top-quark approximations. The finite remainder of the two-loop amplitude is expressed in terms of one-mass pentagon functions, and the corresponding rational coefficients are reconstructed analytically from evaluations over finite fields. The scattering processes considered in this work also constitute a subset of Higgs+2-jet production at the LHC in the heavy-top-quark approximation.