Scattering equations, generating functions and all massless five point tree amplitudes

A bstractWe argue that one does not need to know the explicit solutions of the scattering equations in order to evaluate a given amplitude. We consider the most general quantity consistent with SL(2, ℂ) invariance that can appear in an amplitude that admits a scattering equation description. This quantity depends on all cross ratios that can be formed from n points and we evaluate it for the first non-trivial case of n = 5. The combinatorial nature of the problem is captured through the construction of an appropriate generating function that depends on five variables.