On-shell constituent approach to the light-front partonic energy-momentum tensor

Abstract

The forward matrix elements of the energy-momentum tensor in momentum space, parameterized by gravitational transverse-momentum distributions (TMDs), provide a microscopic window into hadronic mechanical structure. While the longitudinal and transverse columns match to canonical vector TMDs up to twist-4, the light-front minus column involves the unintegrated parton energy $k^-$, leaving this sector undetermined in general quantum chromodynamics. Working within relativistic light-front constituent frameworks where active quarks are modeled as effective on-shell quasiparticles, we show that this energy factorizes algebraically. This establishes a closed matching relating all 32 gravitational TMDs to canonical vector TMDs up to twist-4, including target polarization and T-odd final-state interactions. This completion provides access to the light-front energy density and its transverse Sivers dipole distortion, demonstrates the local equivalence between convective energy and momentum transport velocities, and determines the longitudinal normal stress. Comparing longitudinal and transverse stresses yields a boost-invariant anisotropy ratio that charts the mechanical crossover from collinear confinement dominance to transverse isotropic balance. While formulated within the constituent approximation, these results offer baseline insights into the three-dimensional continuum mechanics of the nucleon.