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

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-evolutions 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.Comment: 26 pages, 6 figure

Nonlinear GLR-MQ evolution equation and

In this paper we have solved the nonlinear Gribov–Levin–Ryskin–Mueller–Qiu (GLR-MQ) evolution equation for the gluon distribution function $$G(x,Q^2)$$ and studied the effects of the nonlinear GLR-MQ corrections to the Leading Order (LO) Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations. Here we have incorporated a Regge-like behavior of gluon distribution function to obtain the solution of the GLR-MQ evolution equation. We have also investigated the $$Q^2$$-dependence of the gluon distribution function from the solution of the GLR-MQ evolution equation. Moreover it is interesting to observe from our results that nonlinearities increase with decreasing correlation radius ($$R$$) between two interacting gluons. The results also confirm that the steep behavior of gluon distribution function is observed at $$R=5\,\mathrm{GeV}^{-1}$$, whereas it is lowered at $$R=2\,\mathrm{GeV}^{-1}$$ with decreasing $$x$$ as $$Q^2$$ increases. In this work we have also checked the sensitivity of $$\lambda _\mathrm{G}$$ in our calculations. Our computed results are compared with those obtained by the global DGLAP fits to the parton distribution functions viz. GRV, MRST, MSTW and with the EHKQS model