The Color Dipole Picture and extracting the ratio of structure functions at small $x$

TL;DR

This paper develops formulas to extract the ratio of structure functions at small x using NNLO perturbative theory, compares results with experimental data, and discusses implications for future collider experiments.

Contribution

It introduces a new method to determine the ratio of structure functions from parameterized data at NNLO, applicable to low x physics and future collider analyses.

Findings

Ratios agree well with HERA data across fixed invariant mass

Ratios are influenced by nonlinear corrections at low Q^2

Method is suitable for LHeC and FCC-eh analyses

Abstract

We present a set of formulas to extract the ratio $F_{L}(x,Q^{2})/F_{2}(x,Q^{2})$ and $R(x,Q^{2})$ from the proton structure function parameterized in the next-to-next-to-leading order of the perturbative theory at low $x$ values. The behavior of these ratios are considered with respect to the power-law behavior of the proton structure function. The results are compared with experimental data and the color dipole model bounds. These ratios are in good agreement with the HERA data throughout the fixed value of the invariant mass. The behavior of these ratios controlled by the nonlinear corrections at low values of $Q^{2}$. These results and comparison with HERA data demonstrate that the suggested method for the ratio of structure functions can be applied in analyses of the LHeC and FCC-eh projects.