Recursion Relations for Gauge Theory Amplitudes with Massive Vector Bosons and Fermions

TL;DR

This paper extends on-shell recursion relations to compute gauge theory amplitudes involving massive vector bosons and fermions, providing compact formulas and generalizations for processes with multiple particles and spins.

Contribution

It introduces methods to construct multi-vector boson currents with massive particles using recursion relations, including internal lines with spin, advancing computational techniques in gauge theories.

Findings

Derived compact expressions for vector boson currents with multiple partons.

Extended recursion relations to include massive particles with spin on internal lines.

Demonstrated the approach with $gg \to t\bar t$ process.

Abstract

We apply the on-shell tree-level recursion relations of Britto, Cachazo, Feng and Witten to a variety of processes involving internal and external massive particles with spin. We show how to construct multi-vector boson currents where one or more off-shell vector bosons couples to a quark pair and number of gluons. We give compact results for single vector boson currents with up to six partons and double vector boson currents with up to four partons for all helicity combinations. We also provide expressions for single vector boson currents with a quark pair and an arbitrary number of gluons for some specific helicity configurations. Finally, we show how to generalise the recursion relations to handle massive particles with spin on internal lines using $gg \to t\bar t$ as an example.