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

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( Q 2 Λ 2 ). We have solved the system of equations at LO, NLO and NNLO respectively by the Lagranges method. The resulting analytical expressions are compared with the available global PDF fits as well as with the results of the BDM model. We have further performed a χ 2 test to check the compatibility 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.