$\gamma_{5}$ in FDH

TL;DR

This paper examines the treatment of $ ext{γ}_5$ in the FDH regularization scheme, demonstrating the effectiveness of a four-dimensional formulation at one- and two-loop levels for calculating pseudo-scalar form factors.

Contribution

It introduces a four-dimensional formulation of FDH for $ ext{γ}_5$ that simplifies calculations at one- and two-loop levels, providing practical methods for operator renormalization.

Findings

FDF is a viable alternative for one-loop calculations.

The method extends successfully to two-loop pseudo-scalar form factors.

Complexity reduction in intermediate steps improves computational efficiency.

Abstract

We investigate the regularization-scheme dependent treatment of $\gamma_{5}$ in the framework of dimensional regularization, mainly focusing on the four-dimensional helicity scheme (FDH). Evaluating distinctive examples, we find that for one-loop calculations, the recently proposed four-dimensional formulation (FDF) of the FDH scheme constitutes a viable and efficient alternative compared to more traditional approaches. In addition, we extend the considerations to the two-loop level and compute the pseudo-scalar form factors of quarks and gluons in FDH. We provide the necessary operator renormalization and discuss at a practical level how the complexity of intermediate calculational steps can be reduced in an efficient way.