A Phenomenological Solution Small $x$ to the Longitudinal Structure Function Dynamical Behavior

TL;DR

This paper presents a phenomenological approach to modeling the small-$x$ behavior of the longitudinal proton structure function, incorporating next-to-next-to-leading order evolution and comparing with various theoretical models and experimental data.

Contribution

It introduces a phenomenological solution for the small-$x$ evolution of the longitudinal structure function at NNLO using a hard Pomeron behavior, including separate gluonic and heavy contributions.

Findings

Total longitudinal structure functions agree with experimental data.

The model's results are consistent with DL, CD, and $k_T$ factorization models.

Provides insights into small-$x$ dynamics of proton structure.

Abstract

In this paper, the evolutions of longitudinal proton structure function have been obtained at small-$x$ up to next-to-next-to-leading order using a hard Pomeron behavior. In our paper, evolutions of gluonic as well as heavy longitudinal structure functions have been obtained separately and the total contributions have been calculated. The total longitudinal structure functions have been compared with results of Donnachie-Landshoff (DL) model, Color Dipole (CD) model, $k_{T}$ factorization and H1 data.