Abstract
In this paper we define, independent of theories, two discriminant matrices involving a solution to the scattering equations in four dimensions, the ranks of which are used to divide the solution set into a disjoint union of subsets. We further demonstrate, entirely within the Cachazo-He-Yuan formalism, that each subset of solutions gives nonzero contribution to tree-level NkMHV gauge/gravity amplitudes only for a specific value of k. Thus the solutions can be characterized by the rank of their discriminant matrices, which in turn determines the value of k of the NkMHV amplitudes a solution can support. As another application of the technique developed, we show analytically that in Einstein-Yang-Mills theory, if all gluons have the same helicity, the tree-level single-trace amplitudes must vanish.
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Du, YJ., Teng, F. & Wu, YS. Characterizing the solutions to scattering equations that support tree-level NkMHV gauge/gravity amplitudes. J. High Energ. Phys. 2016, 88 (2016). https://doi.org/10.1007/JHEP11(2016)088
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DOI: https://doi.org/10.1007/JHEP11(2016)088