Longitudinal structure function from the parton parameterization

TL;DR

This paper derives formulas to extract the longitudinal structure function from the proton structure function at low x using NNLO perturbative QCD, and compares the results with experimental data, showing good agreement.

Contribution

It introduces a new set of formulas for calculating the longitudinal structure function from the proton structure function at NNLO, applicable at very low x.

Findings

Good agreement with experimental data at low x

Behavior of R(x;Q2) and FL(x;Q2) matches color dipole model predictions

Applicable to ultra-high energy processes in LHeC region

Abstract

We present a set of formulas to extract the longitudinal structure function from the proton structure function and its derivatives with respect to lnQ2 in the next-to-next-to-leading order of the perturbative theory at low x based on a hard poemron exchange. The behavior of the DIS cross section ratio R(x;Q2) and the ratio FL(x;Q2)=F2(x;Q2) studied and compared with the experimental data, also these behaviors controlled by the color dipole model bound. These results show a good agreement with the DIS experimental data throughout the low values of x. These results within the next-to-next-to-leading order approximation at very low x can be applied in the LHeC region for analyses of ultra-high energy processes.