We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to four massless quarkanti- 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 super Yang-Mills theory (N = 4 SYM) onto the relevant components yielding all gluongluino tree amplitudes in N = 4 SYM. We show how these results carry over to the corresponding QCD amplitudes, including massless quarks of di erent avors 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 gluongluino trees. These in turn yield all QCD trees with up to four external arbitrary- avored massless quark-anti-quark pairs.
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