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arXiv · 2610.08456

Energy-momentum tensor at small $x$ from gravitational transverse-momentum distributions

Tomoya Uji
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Abstract

We investigate the momentum-space mechanical properties of small-$x$ gluons and sea quarks using gravitational transverse-momentum distributions (gravitational TMDs). For gluons, we formulate these distributions using the light-front gauge-invariant canonical energy-momentum tensor and derive their relations to ordinary TMD correlators, identifying momentum densities, the transverse flux of inertia, and transverse stresses. In the eikonal approximation, the longitudinal and transverse canonical gluon momentum densities are determined by the unpolarized distribution, whereas the transverse flux of inertia and transverse stresses vanish. For an unpolarized target, we numerically evaluate the gluon and sea-quark momentum densities using a common initial condition based on the McLerran--Venugopalan model and fixed-coupling leading-order Balitsky--Kovchegov evolution. We also evaluate the sea-quark transverse flux of inertia through the twist-three quark TMD at the high transverse-momentum region. These results illustrate departures from the free-particle relation between canonical transverse momentum and the effective transverse velocity governing inertia flow.

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Tomoya Uji. 2026-10-06. Energy-momentum tensor at small $x$ from gravitational transverse-momentum distributions. https://arxiv.org/abs/2610.08456

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