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

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.

Figures (2)

• Figure 1: Plots of the FFs $\Phi_1, \Phi_2$ and $\Phi_3$ as a function of $-t$ for quarks inside a proton. The blue dash-dotted line stands for $d$ quark at the initial scale and purple solid line stands at 5 GeV$^2$. The red dashed line represents results for $u$ quark at the initial scale and the green solid line at 5 GeV$^2$.
• Figure 2: Plots of the force components $\mathcal{F}_1, \mathcal{F}_2$ and $\mathcal{F}_3$ distributions in coordinate space for quarks together with quark density distributions. Left panel for down quark and right panel for up quark. From top to down they are $\mathcal{F}_1, \mathcal{F}_2$ and $\mathcal{F}_3$, respectively. The gray sphere in the lower-left corner denotes the proton, the black arrow represents the proton polarization direction, where L stands for longitudinal polarization and T for transverse polarization, and the red dot stands for unpolarized quark.