All-Multiplicity Amplitudes with Massive Scalars

TL;DR

This paper uses BGKS on-shell recursion to derive all-multiplicity analytic tree-level amplitudes for a pair of massive scalars with an arbitrary number of gluons, focusing on configurations with all gluons of identical helicity and with a single opposite-helicity gluon. The authors present explicit, mass-dependent formulas for these amplitudes, prove them via induction using specific complex-momentum shifts, and validate them against independent recursions up to twelve external legs. The results provide compact building blocks for unitarity-based one-loop QCD calculations in nonsupersymmetric theories and offer a framework for extending similar techniques to other massive particles. Collectively, the work demonstrates the power of on-shell methods in handling massive states and sets the stage for broader applications in precision QCD computations.

Abstract

We compute two infinite series of tree-level amplitudes with a massive scalar pair and an arbitrary number of gluons. We provide results for amplitudes where all gluons have identical helicity, and amplitudes with one gluon of opposite helicity. These amplitudes are useful for unitarity-based one-loop calculations in nonsupersymmetric gauge theories generally, and QCD in particular.