Poincar\'e constraints on the gravitational form factors for massive states with arbitrary spin

Abstract

In this work we analyse the constraints imposed by Poincar\'e symmetry on the gravitational form factors appearing in the Lorentz decomposition of the energy-momentum tensor matrix elements for massive states with arbitrary spin. By adopting a distributional approach, we prove for the first time non-perturbatively that the zero momentum transfer limit of the leading two form factors in the decomposition are completely independent of the spin of the states. It turns out that these constraints arise due to the general Poincar\'e transformation and on-shell properties of the states, as opposed to the specific characteristics of the individual Poincar\'e generators themselves. By expressing these leading form factors in terms of generalised parton distributions, we subsequently derive the linear and angular momentum sum rules for states with arbitrary spin.