Test of the TMD gluon density in a proton with the longitudinal structure function $F_L(x,Q^2)$

TL;DR

This paper examines how the longitudinal structure function $F_L(x,Q^2)$ in deep inelastic scattering depends on various models of the gluon TMD in a proton, comparing theoretical predictions with HERA data to test these models.

Contribution

It provides a comparison of different gluon TMD models against experimental data, highlighting their potential to be tested and constrained by current and future deep inelastic scattering experiments.

Findings

HERA data can test different gluon TMD models.

Large uncertainties in data still allow for model discrimination.

Future experiments could further constrain gluon TMD models.

Abstract

We investigate the dependence of the deep inelastic proton structure function $F_L(x, Q^2)$ on different forms of the transverse momentum dependent (TMD, or unintegrated) gluon distribution. We present a comparison of theoretical results with the latest experimental data taken by the H1 and ZEUS Collaborations at HERA. We demonstrate that these data, despite of having quite large uncertainties, can test different kinds of the gluon TMD in a proton. Moreover, different phenomenological models at low $x$ could be tested by future experiments on deep inelastic scattering.