Two-loop results on the renormalization of vacuum expectation values and infrared divergences in the FDH scheme

TL;DR

This paper reviews recent advances in understanding vacuum expectation values and infrared divergences across different regularization schemes, providing new two-loop calculations and transition rules between schemes.

Contribution

It presents the computation of beta functions for vacuum expectation values and clarifies the infrared structure in FDH and DRED schemes, including transition rules from CDR.

Findings

Beta functions for vacuum expectation values computed at two loops.

Infrared structure in FDH and DRED schemes matches explicit form factor calculations.

Transition rules between CDR and FDH amplitudes established.

Abstract

Recent progress in the understanding of vacuum expectation values and of infrared divergences in different regularization schemes is reviewed. Vacuum expectation values are gauge and renormalization-scheme dependent quantities. Using a method based on Slavnov-Taylor identities, the renormalization properties could be better understood. The practical outcome is the computation of the beta functions for vacuum expectation values in general gauge theories. The infrared structure of gauge theory amplitudes depends on the regularization scheme. The well-known prediction of the infrared structure in CDR can be generalized to the FDH and DRED schemes and is in agreement with explicit computations of the quark and gluon form factors. We discuss particularly the correct renormalization procedure and the distinction between MSbar and DRbar renormalization. An important practical outcome are transition rules between CDR and FDH amplitudes.