Interplay of colour kinematics duality and analytic calculation of multi-loop scattering amplitudes: one and two loops

TL;DR

This paper reviews recent advances in calculating multi-loop scattering amplitudes, highlighting the role of colour-kinematics duality and the development of automated analytical and numerical methods for one- and two-loop computations.

Contribution

It introduces new integral relations derived from colour-kinematics duality and demonstrates preliminary automation of the adaptive integrand decomposition algorithm for multi-loop amplitudes.

Findings

New integral relations at one-loop level via Loop-Tree duality

Preliminary automation of the adaptive integrand decomposition algorithm

Analytic reduction results for $$-elastic scattering at one- and two-loop levels

Abstract

In this talk, we review recent developments towards the calculation of multi-loop scattering amplitudes. In particular, we discuss how the colour-kinematics duality can provide new integral relations at one-loop level via the Loop-Tree duality formalism. On the other hand, in order to compute scattering amplitudes at one- and two-loop level, numerically and analytically, we describe the preliminary automation of the adaptive integrand decomposition algorithm. We show preliminary results on the analytic reduction of the $\mu e$-elastic scattering at one- and two-loop level.