Tree Amplitudes with Charged Matter in Pure Gauge Theory

TL;DR

The paper introduces a Mathematica package for computing tree amplitudes with gauge bosons and charged massless fermions in pure gauge theory, facilitating calculations involving multiple flavors and color structures.

Contribution

It provides a new tool that simplifies the calculation of tree amplitudes with charged matter in non-supersymmetric gauge theories, including explicit color tensor computations.

Findings

Enables calculation of amplitudes with arbitrary fermion flavors and gauge bosons.

Expresses distinct-flavor amplitudes as linear combinations of single-flavor amplitudes.

Includes a complete package and demonstration notebook.

Abstract

We describe the implementation and usage of `fermionic_amplitudes.m', a Mathematica package for the computation of tree amplitudes involving arbitrary numbers of gauge bosons and arbitrarily-charged massless fermions of (possibly) distinct flavours in pure (non-supersymmetric) gauge theory. These are given in terms of a basis of partial amplitudes involving distinct-flavoured fermions dressed by specific colour tensors. Distinct-flavour partial amplitudes are expressed as linear combinations of those involving only a single flavour, which may be evaluated as component amplitudes of (maximally) supersymmetric Yang-Mills theory. All relevant colour tensors can be realized as explicit, numeric arrays given any choice of charge generators (for any gauge theory -- including $u_1$); from these, all colour contractions relevant to cross sections may be readily computed. The complete package and a notebook demonstrating its primary usage and functionality are included in this work's submission's ancillary files on the arXiv.