All tree-level amplitudes in massless QCD

TL;DR

This paper provides compact analytical formulas for all tree-level massless QCD amplitudes involving gluons and quarks, derived from super-amplitudes of N=4 SYM, with explicit expressions for specific helicity configurations.

Contribution

It introduces a general combinatorial formula for tree-level QCD amplitudes and connects them to N=4 SYM super-amplitudes, including a public Mathematica package for calculations.

Findings

Explicit formulas for NMHV and NNMHV amplitudes.

A method to derive QCD amplitudes from N=4 SYM super-amplitudes.

A Mathematica package GGT for computing these amplitudes.

Abstract

We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to three massless quark-anti-quark pairs. A general formula is presented based on the combinatorics of paths along a rooted tree and associated determinants. Explicit expressions are displayed for the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (NNMHV) gauge theory amplitudes. Our results are obtained by projecting the previously-found expressions for the super-amplitudes of the maximally supersymmetric Yang-Mills theory (N=4 SYM) onto the relevant components yielding all gluon-gluino tree amplitudes in N=4 SYM. We show how these results carry over to the corresponding QCD amplitudes, including massless quarks of different flavors as well as a single electroweak vector boson. The public Mathematica package GGT is described, which encodes the results of this work and yields analytical formulae for all N=4 SYM gluon-gluino trees. These in turn yield all QCD trees with up to four external arbitrary-flavored massless quark-anti-quark-pairs.