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

We 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.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP