First Numerical Implementation of the Loop-Tree Duality Method

TL;DR

This paper presents the first numerical implementation of the Loop-Tree Duality method, enabling the calculation of one-loop scattering amplitudes through a novel Monte Carlo approach in quantum field theory.

Contribution

It introduces the first practical numerical implementation of the Loop-Tree Duality method for one-loop amplitudes, expanding its applicability beyond simple scalar integrals.

Findings

Successful numerical calculation of scalar integrals.

Implementation of contour deformation techniques.

Validation of the method with tensor integrals.

Abstract

The Loop-Tree Duality (LTD) is a novel perturbative method in QFT that establishes a relation between loop-level and tree-level amplitudes, which gives rise to the idea of treating them simultaneously in a common Monte Carlo. Initially introduced for one-loop scalar integrals, the applicability of the LTD has been expanded to higher order loops and Feynman graphs beyond simple poles. For the first time, a numerical implementation relying on the LTD was realized in the form of a computer program that calculates one-loop scattering amplitudes. We present details on the employed contour deformation as well as results for scalar and tensor integrals.