A pitfall in applying non-anticommuting $\gamma_5$ in $q\overline{q} \rightarrow ZH$ amplitudes

TL;DR

This paper reveals a critical issue when using non-anticommuting $\gamma_5$ in two-loop QCD calculations for $qar{q} o ZH$, showing it necessitates an extra operator in the Lagrangian, unlike the anticommuting case.

Contribution

It identifies a specific pitfall in applying non-anticommuting $\gamma_5$ in dimensional regularisation for Higgs production amplitudes, highlighting the need for an additional operator.

Findings

Non-anticommuting $\gamma_5$ requires an extra operator in the renormalized Lagrangian.

Anticommuting $\gamma_5$ does not require this amendment.

The discrepancy impacts calculations of $qar{q} o ZH$ amplitudes.

Abstract

In computing the two-loop QCD corrections to a class of Feynman diagrams for the process $q\overline{q} \rightarrow ZH$ in Higgs effective field theory, we discover a striking phenomenon. We find the need for an additional local composite operator in the renormalised Lagrangian while employing a non-anticommuting $\gamma_5$ in dimensional regularisation. The computation using anticommuting $\gamma_5$, however, does not require any such amendment.