Advances towards the systematization of calculations with Implicit Regularization

B. Z. Felippe; A. P. Baêta Scarpelli; A. R. Vieira; J. C. C. Felipe

doi:10.1140/epjc/s10052-022-10535-2

2022 Impact factor 4.4

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 583
https://doi.org/10.1140/epjc/s10052-022-10535-2

Regular Article - Theoretical Physics

Advances towards the systematization of calculations with Implicit Regularization

B. Z. Felippe¹^,2^a, A. P. Baêta Scarpelli¹, A. R. Vieira³ and J. C. C. Felipe⁴

¹ Centro Federal de Educação Tecnológica-MG, Avenida Amazonas, 7675, Nova Gameleira, 30510-000, Belo Horizonte, MG, Brazil
² Universidade Federal de Itajubá-Campus Itabira, Rua Irmã Ivone Drumond, 200-Distrito Industrial II, Itabira, MG, Brazil
³ Universidade Federal do Triângulo Mineiro, Campus Iturama, Iturama, MG, Brazil
⁴ Instituto de Engenharia, Ciência e Tecnologia, Universidade Federal dos Vales do Jequitinhonha e Mucuri, Avenida Um, 4050, Cidade Universitária, 39447-790, Janaúba, MG, Brazil

^a brunofelippe@unifei.edu.br

Received: 8 December 2021
Accepted: 18 June 2022
Published online: 4 July 2022

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.

© The Author(s) 2022

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