On the $ZH$ amplitudes at two loop in QCD

TL;DR

This paper presents a method to construct two-loop QCD amplitudes for $b\bar{b} \rightarrow ZH$ using vector form factors, avoiding issues with $\\gamma_5$, and discusses the necessity of a four-point operator in Higgs effective field theory calculations.

Contribution

It introduces a novel approach to compute $ZH$ amplitudes at two loops in QCD, bypassing complications with $\\gamma_5$, and highlights the need for a four-point operator in Higgs EFT.

Findings

Amplitudes can be constructed from vector form factors, simplifying calculations.

Avoids subtle issues with chiral $\\gamma_5$ in dimensional regularization.

Introduces a four-point operator to maintain physical properties in Higgs EFT.

Abstract

Through this article, we show that the amplitudes for the $b\bar{b} \rightarrow ZH$ in the presence of bottom-Higgs Yukawa coupling can be constructed, up to a few anomalous diagrams, solely from a set of vector form factors of properly grouped classes of diagrams. Thereby, we can completely bypass the subtle issues involving the chiral quantity $\gamma_5$. In the second part, we demonstrate that while computing the $q\bar{q} \rightarrow ZH$ amplitudes in Higgs effective field theory employing a non-anticommuting $\gamma_5$ in dimensional regularization, we need to introduce a four-point effective composite operator to the renormalized Lagrangian in order to retain the physical properties of the amplitude.