SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks

TL;DR

This work extends supersymmetric Ward identities to relate multi-gluon amplitudes with a massive quark pair to those with massive scalars, enabling the use of all-multiplicity scalar amplitudes computed by on-shell recursion to construct heavy-quark amplitudes relevant for top-quark physics. By formulating a SUSY toy model and deriving transformation laws under a common reference spinor, the authors obtain simple SWIs that connect quark and scalar amplitudes, including key relations for amplitudes with positive helicity gluons. They develop a Berends-Giele recursion for degree-zero amplitudes and show that heavy-quark amplitudes factorize into a spinor-ratio times the scalar amplitudes, with explicit 5- and 6-point results and consistency checks against alternative formalisms. The results provide a practical pathway to leverage scalar-helicity amplitude results to obtain heavy-quark amplitudes, with implications for precision predictions in top-quark production plus jets. The approach also offers internal consistency checks and can be cross-validated against independent scalar-amplitude calculations, strengthening confidence in the heavy-quark predictions.

Abstract

We use supersymmetric Ward identities to relate multi-gluon helicity amplitudes involving a pair of massive quarks to amplitudes with massive scalars. This allows to use the recent results for scalar amplitudes with an arbitrary number of gluons obtained by on-shell recursion relations to obtain scattering amplitudes involving top quarks.