Abstract
This paper investigates how tree-level amplitudes with massless quarks, gluons and/or massless scalars transforming under a single copy of the gauge group can be expressed in the context of the scattering equations as a sum over the inequivalent solutions of the scattering equations. In the case where the amplitudes satisfy cyclic invariance, KK- and BCJ-relations the only modification is the generalisation of the permutation invariant function E(z, p, ε). We present a method to compute the modified Ê(z, p, ε). The most important examples are tree amplitudes in \( \mathcal{N}=4 \) SYM and QCD amplitudes with one quark-antiquark pair and an arbitrary number of gluons. QCD amplitudes with two or more quark-antiquark pairs do not satisfy the BCJ-relations and require in addition a generalisation of the Parke-Taylor factors C σ(z). The simplest case of the QCD tree-level four-point amplitude with two quark-antiquark pairs is discussed explicitly.
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Weinzierl, S. Fermions and the scattering equations. J. High Energ. Phys. 2015, 141 (2015). https://doi.org/10.1007/JHEP03(2015)141
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DOI: https://doi.org/10.1007/JHEP03(2015)141