Towards gauge theories in four dimensions

TL;DR

This paper introduces a novel loop-tree duality method for gauge theories that simplifies infrared divergence cancellation at the integrand level, enabling four-dimensional higher-order calculations without traditional subtraction techniques.

Contribution

The paper presents a new LTD-based approach to handle infrared divergences directly at the integrand level, simplifying NLO calculations in gauge theories.

Findings

Successfully applied to example cases demonstrating divergence cancellation

Reinterprets ultraviolet divergences physically within the framework

Enables purely four-dimensional NLO calculations without subtractions

Abstract

The abundance of infrared singularities in gauge theories due to unresolved emission of massless particles (soft and collinear) represents the main difficulty in perturbative calculations. They are typically regularized in dimensional regularization, and their subtraction is usually achieved independently for virtual and real corrections. In this paper, we introduce a new method based on the loop-tree duality (LTD) theorem to accomplish the summation over degenerate infrared states directly at the integrand level such that the cancellation of the infrared divergences is achieved simultaneously, and apply it to reference examples as a proof of concept. Ultraviolet divergences, which are the consequence of the point-like nature of the theory, are also reinterpreted physically in this framework. The proposed method opens the intriguing possibility of carrying out purely four-dimensional implementations of higher-order perturbative calculations at next-to-leading order (NLO) and beyond free of soft and final-state collinear subtractions.