Abstract
Closed formulas for tree amplitudes of -particle scatterings of gluon, graviton, and massless scalar particles have been proposed by Cachazo, He, and Yuan. They depend on quantities which satisfy a set of coupled scattering equations, with momentum dot products as input coefficients. These equations are known to have solutions; hence, each is believed to satisfy a single polynomial equation of degree . In this article, we derive the transformation properties of under momentum permutation and verify them with known solutions at low , and with exact solutions at any for special momentum configurations. For momentum configurations not invariant under a certain momentum permutation, new solutions can be obtained for the permuted configuration from these symmetry relations. These symmetry relations for lead to symmetry relations for the coefficients of the single-variable polynomials, whose correctness are checked with the known cases at low . The extent to which the coefficient symmetry relations can determine the coefficients is discussed.
- Received 29 October 2014
DOI:https://doi.org/10.1103/PhysRevD.91.045019
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