Two-loop corrections to Higgs boson production

TL;DR

This work provides the complete two-loop vertex corrections for scalar and pseudoscalar Higgs production in the heavy-top-quark limit using an effective Lagrangian, including general SU(N) color factors and both conserved and non-conserved operators. It delivers explicit Higgs form factors and soft-plus-virtual coefficient functions, with the first explicit pseudoscalar result and a key result that the single-pole term is determined by 1/2 γ_{ii}^{(1)} + f_{i,2}^{(1)}. The analysis connects the pole structure to anomalous dimensions and extends electromagnetic form-factor insights to Higgs processes, enabling more precise predictions for hadron-collider Higgs cross sections. The results also provide a framework for predicting higher-order vertex corrections using known three-loop anomalous dimensions.

Abstract

In this paper we present the complete two-loop vertex corrections to scalar and pseudo-scalar Higgs boson production for general colour factors for the gauge group ${\rm SU(N)}$ in the limit where the top quark mass gets infinite. We derive a general formula for the vertex correction which holds for conserved and non conserved operators. For the conserved operator we take the electromagnetic vertex correction as an example whereas for the non conserved operators we take the two vertex corrections above. Our observations for the structure of the pole terms $1/ε^4$, $1/ε^3$ and $1/ε^2$ in two loop order are the same as made earlier in the literature for electromagnetism. However we also elucidate the origin of the second order single pole term which is equal to the second order singular part of the anomalous dimension plus a universal function which is the same for the quark and the gluon. [3mm]

Figures (4)

• Figure 1: General structure of the one-loop vertex correction g-g-B ($B=H,A$).
• Figure 2: General structure of the two-loop vertex correction g-g-B ($B=H,A$).
• Figure 3: Interference term between diagrams with operators $O_1$ and $O_2$.
• Figure :