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.

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

References in corpus (3)

• Ambitwistor strings and the scattering equations at one loop
• N-Point Tree-Level Scattering Amplitude in the New Berkovits' String
• Fundamental BCJ Relation in N=4 SYM From The Connected Formulation

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