Pure Spinor Superspace Identities for Massless Four-point Kinematic   Factors
  Using the pure spinor formalism we prove identities which relate the tree-level, one-loop and two-loop kinematic factors for massless four-point amplitudes. From these identities it follows that the complete supersymmetric one- and two-loop amplitudes are immediately known once the tree-level kinematic factor is evaluated. In particular, the two-loop equivalence with the RNS formalism (up to an overall coefficient) is obtained as a corollary. 
Carlos R. Mafra (Sao Paulo, IFT and UCLA)