The NNLO QCD analysis of gluon density at small-x

Abstract

In this paper, a next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) calculation of gluon distribution function at small-[Formula: see text] is presented. The gluon distribution function is explored analytically in the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi approach by a Taylor expansion at small-[Formula: see text] as two first-order partial differential equations in two variables: Bjorken [Formula: see text] and [Formula: see text][Formula: see text]. We have solved the system of equations at LO, NLO and NNLO, respectively, by Lagrange’s method. The resulting analytical expressions are compared with the available global parton distribution function fits as well as with the results of the Block–Durand–McKay model. We have further performed an [Formula: see text] 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-[Formula: see text] region.