Gravitational transverse momentum dependent distributions for the gluons

Abstract

We investigate the momentum-space structure of the gauge-invariant gluon energy-momentum tensor (EMT) for spin-$0$ and spin-$\tfrac{1}{2}$ hadrons in the light-front formalism. We parameterize the nonlocal gluon EMT in terms of so-called gluon gravitational transverse-momentum-dependent distributions (gravitational TMDs) and derive their connections to twist-2 and twist-3 gluon TMDs. Moreover, we demonstrate that particular components of the gluon EMT encode information about the average kinetic four-momentum of gluons and the internal mechanical properties of hadrons-such as pressure and shear distributions.