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

## TL;DR

This paper investigates how Poincaré symmetry constrains gravitational form factors in the energy-momentum tensor for massive states of any spin, revealing spin-independent properties and deriving sum rules.

## Contribution

It provides a non-perturbative proof that certain form factors are spin-independent at zero momentum transfer and connects these to generalized parton distributions.

## Key findings

- Zero momentum transfer limit of leading form factors is spin-independent.
- Derived linear and angular momentum sum rules for arbitrary spin states.
- Established Poincaré symmetry constraints are general and not generator-specific.

## 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.