Evolution of singlet structure functions from DGLAP equation at next-to-next-to-leading order at small-x

Abstract

A semi-numerical solution to Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations at leading order (LO), next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) in the small-x limit is presented. Here we have used Taylor series expansion method to solve the evolution equations and, t- and x-evolutions of the singlet structure functions have been obtained with such solution. We have also calculated t- and x-evolution of deuteron structure functions $F_{2}^{d}$ , and the results are compared with the E665 data and NMC data. The results are also compared to those obtained by the fit to $F_{2}^{d}$ produced by the NNPDF collaboration based on the NMC and BCDMS data.