Implicit regularization beyond one loop order: scalar field theories

TL;DR

This paper extends the application of implicit regularization to multi-loop scalar field theories, establishing a systematic renormalization scheme that handles divergences without mixing infrared and ultraviolet modes.

Contribution

It introduces a generalized IR method for higher-loop calculations in scalar theories, providing a natural renormalization scheme that isolates divergences and clarifies the renormalization group scale.

Findings

A minimal renormalization scheme emerges naturally.

Infrared divergences cancel systematically at all loop orders.

Ultraviolet and infrared modes remain decoupled, avoiding ambiguities.

Abstract

Implicit regularization (IR) has been shown as an useful momentum space tool for perturbative calculations in dimension specific theories, such as chiral gauge, topological and supersymmetric quantum field theoretical models at one loop level. In this paper, we aim at generalizing systematically IR to be applicable beyond one loop order. We use a scalar field theory as an example and pave the way for the extension to quantum field theories which are richer from the symmetry content viewpoint. Particularly, we show that a natural (minimal) renormalization scheme emerges, in which the infinities displayed in terms of integrals in one internal momentum are subtracted, whereas infrared and ultraviolet modes do not mix and therefore leave no room for ambiguities. A systematic cancelation of the infrared divergences at any loop order takes place between the ultraviolet finite and divergent parts of the amplitude for non-exceptional momenta leaving, as a byproduct, a renormalization group scale.