Transverse force tomography inside a proton from Basis Light-front Quantization

The twist-3 transverse spin--dependent nucleon structure function $g_2$ arises in high-energy processes involving a transversely polarized nucleon. Its connection to quark--gluon correlations allows for an interpretation in terms of the average transverse color Lorentz force acting on unpolarized quarks inside a transversely polarized nucleon. In this work, we investigate this force using light-front wave functions obtained by diagonalizing the light-front Hamiltonian with quantum chromodynamics inputs within the Basis Light-front Quantization approach. We evolve our results to a common scale of $5~\mathrm{GeV}^2$ and present the corresponding form factors in momentum space as well as the transverse force components in impact-parameter space. These distributions provide a complementary perspective on the Sivers asymmetry in transversely polarized deep-inelastic scattering. In the forward limit, we extract the twist-3 reduced matrix element $d_2$, and our results are found to be comparable with those from other theoretical calculations and experimental determinations.