Three-Quark Light-Cone Amplitudes of The Proton And Quark-Orbital-Motion Dependent Observables

TL;DR

This paper develops a three-quark light-cone framework incorporating transverse momenta to quantify quark orbital angular momentum in the proton within a minimal valence Fock sector. It constructs a complete set of light-cone matrix elements, inverts them to obtain the three-quark light-cone wave function, and derives how orbital motion manifests in a range of observables: transverse-momentum dependent distributions (including q_T, Δq_T, δq, δq_L), twist-three distributions g_T and h_L, helicity-flip generalized parton distribution E, and the Pauli form factor F_2. The results illustrate how non-zero orbital angular momentum produces measurable effects and provide explicit overlap-based expressions linking amplitudes to these observables, while highlighting gauge choices and the limitations of the valence truncation. The framework offers a semi-realistic bridge between proton spin structure and experimental data, setting the stage for phenomenological fits and lattice validations while indicating the need to include gluons and sea quarks for a complete picture.

Abstract

We study the three-quark light-cone amplitudes of the proton including quarks' transverse momenta. We classify these amplitudes using a newly-developed method in which light-cone wave functions are constructed from a class of light-cone matrix elements. We derive the constraints on the amplitudes from parity and time-reversal symmetries. We use the amplitudes to calculate the physical observables which vanish when the quark orbital angular momentum is absent. These include transverse-momentum dependent parton distributions $Δq_T(x, k_\perp)$, $q_T(x, k_\perp)$, $δq(x, k_\perp)$, and $δq_L(x,k_\perp)$, twist-three parton distributions $g_T(x)$ and $h_L(x)$, helicity-flip generalized parton distributions $E(x, ξ=0, Q^2)$ and its associates, and the Pauli form factor $F_2(Q^2)$.