The NNLO QCD analysis of gluon distribution function at small-x

TL;DR

This paper presents an NNLO QCD analytical calculation of the gluon distribution function at small-x, demonstrating the importance of NNLO corrections and validating results against global PDF sets and models.

Contribution

The paper introduces an analytical NNLO approach to determine the gluon distribution function at small-x using DGLAP equations and compares it with existing models and data.

Findings

NNLO corrections significantly impact the gluon distribution at small-x.

The analytical solutions agree well with global PDF sets.

NNLO results are consistent with perturbative QCD predictions.

Abstract

A next-to-next-to-leading order (NNLO) QCD calculation of gluon distribution function at small-x is presented. The gluon distribution function is explored analytically in the DGLAP approach by a Taylor expansion at small x as two first order partial differential equations in two variables : Bjorken x and t (t = ln(Q2/{\Lambda}2) ). We have solved the system of equations at LO, NLO and NNLO respectively by the La- granges method. The resulting analytical expressions are compared with the available global PDF sets as well as with the results of the BDM model. We have further performed a \c{hi}2 test to check the com- patibility of our predictions and observed that our results can be consistently described in the context of perturbative QCD. A comparative analysis of the obtained results at LO, NLO and NNLO reveals that the NNLO approximation has a significant contribution to the gluon distribution function particularly in the small-x region.