Analytical models of the Proton Structure Function and the gluon distribution at small x beyond leading order

TL;DR

This paper develops analytical models for the proton structure function and gluon distribution at small x, incorporating higher-order QCD corrections (NLO and NNLO) and comparing with exact results.

Contribution

It introduces analytical solutions for structure functions at NLO and NNLO, extending previous models beyond leading order at small x.

Findings

Analytical solutions at NLO and NNLO are successfully derived.

Models show good agreement with exact results.

Higher-order corrections improve the accuracy of structure function predictions.

Abstract

We incorporate the next-to-leading order (NLO) and the next-to-next-to-leading order (NNLO) effects in the models of the Singlet Structure function F_2^S(x,t) and the gluon distribution G(x,t) using DGLAP equations approximated at small x. Analytical solutions both at the next-to leading order (NLO) as well as the next-to-next-to leading order (NNLO) are obtained. We then make comparisons with exact results.