Two loops, four tops and two $\gamma_5$ schemes: a renormalization story

TL;DR

This paper computes two-loop renormalization constants for fermion and gluon fields considering four-top operators, comparing different $ ext{gamma}_5$ schemes, to improve understanding of renormalization group equations in quantum chromodynamics.

Contribution

It provides the first detailed calculation of four-top operator contributions to two-loop renormalization constants in different $ ext{gamma}_5$ schemes, with a strategy to translate between schemes.

Findings

Calculated two-loop renormalization constants for fermion and gluon fields.

Compared $ ext{gamma}_5$ schemes and provided translation strategies.

Presented beta functions in both schemes.

Abstract

We calculate the four-top quark operator contributions to the two-loop renormalization constants of the fermion and gluon fields, necessary to obtain the renormalization group equations for the fermion masses and the strong coupling constant. The computation has been carried out in the na\"{\i}ve dimensional regularization scheme for the $\gamma_5$ matrix. We also discuss a strategy to translate the results into the Breitenlohner--Maison--'t~Hooft--Veltman scheme and present the corresponding beta functions in both schemes.