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Motivated by the success of Hodges' momentum twistor variables in planarYang-Mills, in this note we introduce a set of new variables, the S variables,which are tailored for gravity (or more generally for theories without colorordering). The S variables trivialize all on-shell constraints on kinematicdata and momentum conservation while keeping permutation invariance. Weexplicitly show the relation between the S variables and the spinor-helicityvariables as well as the connection to momentum twistors. The S variables canbe nicely understood using the geometry of Grassmannians and are determined bya 2-plane and a 4-plane in C^n, with n the number of the particles. As anillustration of their utility, we use the S variables to present areference-free form of soft factors and tree level MHV amplitudes of gravitywhich is obtained by using the recent formula given by Hodges.

New Variables For Graviton Scattering Amplitudes