# The energy-momentum tensor of spin-1 hadrons: formalism

## TL;DR

This paper develops a comprehensive, gauge-invariant framework for analyzing the energy-momentum tensor of spin-1 hadrons, revealing unique spin-dependent features and relations to generalized parton distributions.

## Contribution

It provides the complete decomposition of the energy-momentum tensor for spin-1 hadrons, including new relations involving gravitational form factors and generalized parton distributions.

## Key findings

- Derived sum rules for gravitational form factors.
- Established relations between angular momentum and GPD moments.
- Highlighted features unique to spin-1 hadrons.

## Abstract

We provide the complete decomposition of the local gauge-invariant energy-momentum tensor for spin-1 hadrons, including non-conserved terms for the individual parton flavors and antisymmetric contributions originating from intrinsic spin. We state sum rules for the gravitational form factors appearing in this decomposition and provide relations for the mass decomposition, work balance, total and orbital angular momentum, mass radius, and inertia tensor. Generalizing earlier work, we derive relations between the total and orbital angular momentum and the Mellin moments of twist-2 and 3 generalized parton distributions, accessible in hard exclusive processes with spin-1 targets. Throughout the work, we comment on the unique features in these relations originating from the spin-1 nature of the hadron, being absent in the lower spin cases.