Transverse-momentum-dependent gluon distributions of proton within basis light-front quantization

TL;DR

This paper calculates gluon transverse-momentum dependent distributions of the proton using basis light-front quantization, providing insights into their properties and behaviors relevant for future collider experiments.

Contribution

It introduces a novel calculation of gluon TMDs within the basis light-front quantization framework, incorporating QCD inputs and confinement effects.

Findings

Gluon TMDs satisfy Mulders-Rodrigues inequalities.

Identified correlations between transverse and longitudinal degrees of freedom.

Analyzed small-x and large-x behaviors of gluon TMDs.

Abstract

Gluon transverse-momentum dependent distributions (TMDs) are very important for revealing the internal structure of the proton. They correspond to a variety of experiments and are among the major tasks of the future electron-ion colliders. In this paper, we calculate the T-even gluon TMDs at the leading twist within the Basis Light-front Quantization framework. We employ the light-front wave functions of the proton obtained from a light-front quantized Hamiltonian with Quantum Chromodynamics input determined for its valence Fock sector with three constituent quarks and an additional Fock sector, encompassing three quarks and a dynamical gluon, with a three-dimensional confinement. After obtaining the numerical results we investigate the properties of gluon TMDs by checking whether they satisfy the Mulders-Rodrigues inequalities and investigate the correlations between transverse and longitudinal degrees of freedom. With their connection to unintegrated gluon distributions in mind, we further investigate the limiting behaviours of gluon TMDs in the small-$x$ and large-$x$ regions.