Fractal Inspired Models of Quark and Gluon Distributions and Longitudinal Structure Function FL(x, Q2) at small x

TL;DR

This paper explores fractal-inspired models of quark and gluon distributions at small x to predict the longitudinal structure function FL(x, Q2), finding compatibility with QCD expectations for a specific model.

Contribution

It introduces and tests fractal-inspired models for small-x parton distributions, focusing on the longitudinal structure function within a QCD framework.

Findings

Model II predictions align with QCD expectations.

Model I is unsuitable due to singularities.

Qualitative agreement with theoretical predictions.

Abstract

In recent years, Fractal Inspired Models of quark and gluon densities at small x have been proposed. In this paper, we investigate longitudinal structure function F-L (x, Q2) within this approach. We make predictions using the QCD based approximate relation between the longitudinal structure function and the gluon density. As the Altarelli-Martinelli equation for the longitudinal structure function cannot be applied to Model I due to the presence of a singularity in the Bjorken x-space we consider Model II only. The qualitative feature of the prediction of Model II is found to be compatible with the QCD expectation.