Recursion relations for scattering amplitudes with massive particles

TL;DR

This paper introduces new recursion relations for calculating tree-level scattering amplitudes involving massive particles using a combined complex deformation approach, extending techniques from massless theories.

Contribution

It proposes a novel class of recursion relations for massive particle amplitudes based on a combined complex deformation of momenta, validated through symmetry arguments.

Findings

Recursion relations applicable to scalar QCD and massive vector bosons.

Proof of validity via Spin-Lorentz symmetry in the infinite momentum limit.

Examples demonstrating efficient computation of tree-level amplitudes.

Abstract

We use the recently developed massive spinor-helicity formalism [1] of Arkani- Hamed et al. to propose a new class of recursion relations for tree-level amplitudes in gauge theories. These relations are based on a combined complex deformation of massless as well as massive external momenta. We use these relations to study tree-level amplitudes in scalar QCD as well as amplitudes involving massive vector bosons in the Higgsed phase of Yang-Mills theory. We prove the validity of our proposal by showing that in the limit of infinite momenta of two of the external particles, the amplitude once again is controlled by an enhanced Spin-Lorentz symmetry paralleling the proof of BCFW shift for massless gauge theories. Simple examples illustrate that the proposed shift may lead to an efficient computation of tree-level amplitudes.