Loop-Tree Duality for Multiloop Numerical Integration.

Zeno Capatti,Dario Kermanschah,Ben Ruijl,Valentin Hirschi

doi:10.1103/physrevlett.123.151602

Abstract

Loop-tree duality (LTD) offers a promising avenue to numerically integrate multiloop integrals directly in momentum space. It is well established at one loop, but there have been only sparse numerical results at two loops. We provide a formal derivation for a novel multiloop LTD expression and study its threshold singularity structure. We apply our findings numerically to a diverse set of up to four-loop finite topologies with kinematics for which no contour deformation is needed. We also lay down the ground work for constructing such a deformation. Our results serve as an important stepping stone towards a generalized and efficient numerical implementation of LTD, which is applicable to the computation of virtual corrections.

Highlights

This page was generated automatically upon download from the ETH Zurich Research Collection
We provide a formal derivation for a novel multiloop Loop-tree duality (LTD) expression and study its threshold singularity structure
In this Letter, we study the possibility of rewriting an n-loop integral as a sum of terms with n additional on shell conditions by analytically integrating over loop energies using a residue theorem

Summary

Introduction

This page was generated automatically upon download from the ETH Zurich Research Collection. We apply our findings numerically to a diverse set of up to four-loop finite topologies with kinematics for which no contour deformation is needed. LTD is appealing from a numerical standpoint for at least four reasons: (1) the n-loop integral dimensionality is fixed to 3n irrespective of the topology considered, (2) integrable singularities can be shown to be confined to a bounded volume [13] and are absent when considering certain kinematical configurations, (3) momentum-space divergent integrals naturally lend themselves to be regularized with local UV and IR counterterms [14,15,16,17,18,19,20,21,22,23], or even (4) through a direct combination with the corresponding real-emission contributions in the case of physical amplitudes [24,25,26].

Results

Conclusion