Graviton graviton scattering, Bel-Robinson and energy (pseudo)-tensors

Motivated by recent work involving the graviton-graviton tree scattering amplitude, and its twin descriptions as the square of the Bel-Robinson tensor, Bµnualphabeta, and as the `current-current interaction' square of gravitational energy pseudo-tensors talphabeta, we find an exact tensor-square root equality , for a combination of Einstein and Landau-Lifschitz talphabeta, in Riemann normal coordinates. In the process, we relate, on-shell, the usual superpotential basis for classifying pseudo-tensors with one spanned by polynomials in the curvature.