Massless scattering at special kinematics as Jacobi polynomials
Abstract
We study the scattering equations recently proposed by Cachazo, He and Yuan in the special kinematics where their solutions can be identified with the zeros of the Jacobi polynomials. This allows for a non-trivial two parameter family of kinematics. We present explicit and compact formulae for the n-gluon and n-graviton partial scattering amplitudes for our special kinematics in terms of Jacobi polynomials. We also provide alternative expressions in terms of gamma functions. We give an interpretation of the common reduced determinant appearing in the amplitudes as the product of the squares of the eigenfrequencies of small oscillations of a system whose equilibrium is the solutions of the scattering equations.
Cite
@article{arxiv.1312.7743,
title = {Massless scattering at special kinematics as Jacobi polynomials},
author = {Chrysostomos Kalousios},
journal= {arXiv preprint arXiv:1312.7743},
year = {2015}
}
Comments
9 pages; v2: clarifications and references added, published version; v3: a factor of (n-3)! in equation 11 and in the final expression of the gluon amplitude was corrected