Computation of NLO Processes Involving Heavy Quarks Using Loop-Tree Duality

TL;DR

This paper introduces a novel method based on Loop-Tree Duality for calculating higher-order quantum corrections involving heavy quarks, enabling local cancellation of infrared singularities without subtraction terms.

Contribution

It presents a new approach that simplifies NLO computations by using Loop-Tree Duality and a momentum mapping to handle singularities directly at the integrand level.

Findings

Successfully applied to a scalar toy model decay rate

Achieves local infrared singularity cancellation

Provides a framework for NLO and higher-order calculations

Abstract

We present a new method to compute higher-order corrections to physical cross-sections, at Next-to-Leading Order and beyond. This method, based on the Loop Tree Duality, leads to locally integrable expressions in four dimensions. By introducing a physically motivated momentum mapping between the momenta involved in the real and the virtual contributions, infrared singularities naturally cancel at integrand level, without the need to introduce subtraction counter-terms. Ultraviolet singularities are dealt with by using dual representations of suitable counter-terms, with some subtleties regarding the self-energy contributions. As an example, we apply this method to compute the $1\to2$ decay rate in the context of a scalar toy model with massive particles.