Nonlinear GLR-MQ evolution equation and $$Q^2$$ Q 2 -evolution of gluon distribution function

Abstract

In this paper we have solved the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu (GLR-MQ) evolution equation for 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 incorporate a Regge like behaviour of gluon distribution function to obtain the solution of GLR-MQ evolution equation. We have also investigated the Q 2dependence of gluon distribution function from the solution of 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. Results also confirm that the steep behavior of gluon distribution function is observed at R = 5 GeV −1 , whereas it is lowered at R = 2 GeV −1 with decreasing x as Q 2 increases. In this work we have also checked the sensitivity of λ 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.

NNLO solution of nonlinear GLR–MQ evolution equation to determine gluon distribution function using Regge like ansatz

“…Here ρ = xg(x,Q 2 ) πR 2 , where R is the correlation radius between two interacting gluons, πR 2 is the target area. The factor γ is evaluated by Muller and Quie that is found to be γ = 81 16 for N c = 3 [7]. Now in terms of gluon distribution function G (x, Q 2 )= xg (x, Q 2 ) the GLR-MQ equation can be written in standard form [23] ∂G (x, Q 2 )…”

Small-x analysis on the effect of gluon recombinations inside hadrons in light of the GLR-MQ-ZRS equation

“…This shadowing term, which is quadractic in gluon density is coming from gluon recombinations inside the hadrons. In our previous work, we have studied extensively the gluon distribution functions by obtaining the solutions of GLR-MQ equation at leading order(LO) [14,15], next-to-leading order(NLO) [16] and next-to-next-to-leading order(NNLO) [17,18]. We observed the taming of gluon distribution function towards small- [19].…”

Parton distribution functions of heavy mesons on the light front

“…Here, we consider the range x ≥ 10 −3 . We expect that at low initial scale the DGLAP evolution with a leading twist is not sufficient at low x [93,94] and one needs to consider the higher twist corrections in the DGLAP equation [95][96][97][98][99][100][101]. It should be mentioned here that there is also uncertainty from the longitudinal basis resolution within the initial scale PDFs.…”