Wilson coefficients for Higgs boson production and decoupling relations to $\mathcal{O}\left(\alpha_s^4\right)$

TL;DR

This paper computes four-loop Wilson coefficients for Higgs-gluon couplings in QCD, providing essential ingredients for precise Higgs boson property calculations in the infinite top mass limit.

Contribution

It presents the first direct four-loop calculation of the Wilson coefficient for two Higgs bosons, $C_{HH}$, and also computes $C_H$ and decoupling relations, advancing theoretical precision.

Findings

Calculated $C_{HH}$ to four loops for the first time.

Derived all four-loop decoupling relations in QCD.

Provided detailed discussion on operator product renormalization.

Abstract

An important ingredient for the calculation of Higgs boson properties in the infinite top quark mass limit is the knowledge of the effective coupling between the Higgs bosons and gluons, i.e. the Wilson coefficients $C_H$ and $C_{HH}$ for one and two Higgs bosons, respectively. In this work we calculate for the first time $C_{HH}$ to four loops in a direct, diagrammatic way, discussing in detail all issues arising due to the renormalization of operator products. Furthermore, we also calculate the Wilson coefficient $C_H$ for the coupling of a single Higgs boson to gluons as well as all four loop decoupling relations in QCD with general SU$(N_c)$ colour factors. The latter are related to $C_H$ and $C_{HH}$ via low-energy theorems.