How fast do small x structure function rise ? A comparative analysis

TL;DR

This paper analyzes the small x behavior of the proton structure function F_2 by parametrizing it with powers and logarithms of 1/x across various Q^2 values, revealing a slowdown in its rise at high Q^2.

Contribution

It introduces a comparative parametrization method for F_2 at small x and Q^2, providing insights into its evolution and aiding model discrimination.

Findings

F_2's increase slows at high Q^2

Parametrizations fit data with minimal chi-squared

Derivative analysis quantifies the slowdown

Abstract

We parametrize the small x, singlet component of the proton structure function F_2 by powers and logarithms of 1/x for discrete values of Q^2 between 0.2 and 2000 GeV^2, and compare these parametrizations by applying the criterion of minimal $\chi^2$. The obtained values of the fitted parameters may be used to study the evolution of F_2 in Q^2 and/or in discriminating between dynamical models. A slowing-down in the increase of F_2 towards highest available values of Q^2 is revealed. The effect is quantified in terms of the derivative ${\frac{d\ell n F_2(x,Q^2)}{{d\ell n (1/x)}}}$.