Advances towards the systematization of calculations with Implicit Regularization

TL;DR

This paper introduces a systematic method using Constrained Implicit Regularization to simplify and unify the calculation of one-loop and higher-loop amplitudes in quantum field theories, aiding precise theoretical predictions for collider data.

Contribution

It develops a new, unified procedure for applying Constrained Implicit Regularization that simplifies amplitude calculations and is applicable to both massive and non-massive models.

Findings

Simplifies the calculation of divergent and finite parts of amplitudes.

Establishes universal scale relations independent of specific situations.

Extends the method to higher-loop order calculations.

Abstract

There is currently a high demand for theoretical predictions for processes at next-to-next-to-leading order (NNLO) and beyond, mainly due to the large amount of data which has already been collected at LHC. This requires practical methods that meet the physical requirements of the models under study. We develop a new procedure for applying Constrained Implicit Regularization which simplifies the calculation of amplitudes, including finite parts. The algebraic identities to separate the divergent parts free from the external momenta are used after the Feynman parametrization. These algebraic identities establish a set of scale relations which are always the same and do not need to be calculated in each situation. This procedure unifies the calculations in massive and non-massive models in an unique procedure. We establish a systematization of the calculation of one-loop amplitudes and extend the procedure for higher-loop orders.