On phenomenological study of the solution of nonlinear GLR-MQ evolution equation beyond leading order

Abstract

We present a phenomenological study of the small-x behaviour of gluon distribution function $G(x,Q^2)$ at next-to-leading order (NLO) and next-to-next-to-leading order(NNLO) in light of the nonlinear Gribov-Ryskin-Levin-Mueller-Qiu (GLR-MQ)evolution equation by keeping the transverse size of the gluons ($\sim 1/Q$) fixed. We consider the NLO and NNLO corrections, of the gluon-gluon spitting function $P_{gg}(z)$ and strong coupling constant ${\alpha }_s(Q^2)$. We have suggested semi-analytical solutions based on Regge like ansatz of gluon density $G(x,Q^2)$, which are supposed to be valid in the moderate range of photon virtuality$(Q^2)$ and at small Bjorken variable$(x)$. The study of the effects of nonlinearities that arise due to gluon recombination effects at small-x is very interesting, which eventually tames down the unusual growth of gluon densities towards small-x as predicted by the linear DGLAP evolution equation.

20 pages, 10 figures, new references added

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Cited by in corpus (5)

• Numerical evaluation of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu evolution equations for nuclear parton distribution functions
• The Color Dipole Picture and extracting the ratio of structure functions at small $x$
• Small-x analysis on the effect of gluon recombinations inside hadrons in light of the GLR-MQ-ZRS equation
• Nonlinear corrections for the nuclear gluon distribution in $eA$ processes
• Nonlinear Corrections to the Momentum Sum Rule