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

TL;DR

This paper uses Basis Light-front Quantization to compute the transverse color Lorentz force inside a proton, linking theoretical wave functions to observable spin-dependent phenomena.

Contribution

It introduces a novel calculation of the transverse force components inside a proton using light-front wave functions derived from QCD inputs.

Findings

Computed transverse force distributions in impact-parameter space.

Extracted the twist-3 matrix element d_2 consistent with other results.

Provided form factors related to the Sivers asymmetry.

Abstract

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.