Efficient integrand reduction for particles with spin

TL;DR

This paper introduces an efficient method for reducing scattering amplitudes involving spinning particles into scalar integrals, revealing new consistency relations and providing explicit multi-loop results in Yang-Mills theory.

Contribution

It presents a novel integrand reduction technique that simplifies spinning particle amplitudes and uncovers previously unknown relations among master integrals.

Findings

Decomposition of spinning particle amplitudes into simple building blocks

Explicit two- and three-loop planar scattering amplitude results in Yang-Mills theory

Discovery of new consistency relations among master integrals

Abstract

Scattering amplitudes with spinning particles are shown to decompose into multiple copies of simple building blocks to all loop orders, which can be used to efficiently reduce these amplitudes to sums over scalar integrals. Absence of unphysical kinematic singularities cleanly exposed by the method uncover novel consistency relations among master integrals and their coefficients. Analytic results are obtained for the five gluon, two loop, and four gluon, three loop planar scattering amplitudes in pure Yang-Mills theory as well as for leading singularities to even higher orders.