Multiloop calculations with Implicit Regularization in massless theories

TL;DR

This paper presents a systematic method for calculating multiloop amplitudes in massless theories using Implicit Regularization, effectively handling infrared safety, symmetry violations, and finite integrals.

Contribution

It introduces a comprehensive approach to multiloop calculations with Implicit Regularization, including techniques for finite integrals and infrared divergence management.

Findings

Systematic calculation of multiloop amplitudes in massless models.

Identification and handling of symmetry-violating surface terms.

Development of a convenient method for finite multiloop integrals.

Abstract

We establish a systematic way to calculate multiloop amplitudes of infrared safe massless models with Implicit Regularization (IR), with a direct cancelation of the fictitious mass introduced by the procedure. The ultraviolet content of such amplitudes have a simple structure and its separation permits the identification of all the potential symmetry violating terms, the surface terms. Moreover, we develop a technique for the calculation of an important kind of finite multiloop integral which seems particularly convenient to use Feynman parametrization. Finally, we discuss the Implicit Regularization of infrared divergent amplitudes, showing with an example how it can be dealt with an analogous procedure in the coordinate space.