Regularization Schemes and Higher Order Corrections

TL;DR

This paper evaluates various regularization schemes in multi-loop calculations, revealing that while some are consistent at higher orders, others like the four dimensional helicity scheme produce incorrect or singular results, questioning their unitarity.

Contribution

The study compares common regularization schemes at higher orders, highlighting the limitations of the four dimensional helicity scheme in multi-loop calculations.

Findings

Dimensional regularization and dimensional reduction are consistent at higher orders.

The four dimensional helicity scheme yields incorrect results at NNLO.

The four dimensional helicity scheme produces singular results at N3LO.

Abstract

I apply commonly used regularization schemes to a multi-loop calculation to examine the properties of the schemes at higher orders. I find complete consistency between the conventional dimensional regularization scheme and dimensional reduction, but I find that the four dimensional helicity scheme produces incorrect results at next-to-next-to-leading order and singular results at next-to-next-to-next-to-leading order. It is not, therefore, a unitary regularization scheme.