The structure of quark mass corrections in the $gg \rightarrow HH$ amplitude at high-energy

TL;DR

This paper analyzes the origin of large logarithmic mass corrections in high-energy Higgs pair production amplitudes, proposing a factorized pattern to reduce theoretical uncertainties related to top-quark mass scheme choices.

Contribution

It introduces a method to understand and compute the mass corrections in $gg o HH$ amplitudes using the Method of Regions and Soft-Collinear Effective Theory, reducing scheme uncertainty.

Findings

Identifies the pattern of mass corrections in high-energy limit

Provides leading power leading logarithmic correction results

Reduces theoretical uncertainty in double Higgs production amplitudes

Abstract

The leading and next-to-leading order QCD predictions for Higgs boson pair production at hadron colliders suffer from a significant mass renormalisation scheme uncertainty related to the choice of the top-quark mass. The functional dependence of the result on the value of the intermediate quark mass can be understood in the high-energy limit using the Method of Regions and the tools of Soft-Collinear Effective Theory. In this work, we study the origin of the sizeable logarithmic mass corrections in the $gg \to HH$ amplitudes at leading and next-to-leading power in the limit $s,|t|,|u| \gg m_t^2 \gg m_H^2$. We argue that the mass corrections follow a predictable factorised pattern that can be exploited to simplify their computation. We present results for the leading power leading logarithmic corrections, our analysis leads to a significant reduction in the theoretical uncertainty of the double Higgs production amplitudes at high-energy due to the top-quark mass scheme.