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

Abstract

We present a study of the contribution of antishadowing effects on the gluon distribution functions G(x, Q 2 ) in light of the Gribov-Levin-Ryskin-Mueller-Qiu, Zhu-Ruan-Shen (GLR-MQ-ZRS) nonlinear equation at small-x, where x is the momentum fraction or Bjorken variable and Q 2 is the four momentum transfer squared or photon virtuality. In this work, we have solved the GLR-MQ-ZRS nonlinear equation using Regge like behaviour of gluons in the kinematic range of 10 −2 ≤ x ≤ 10 −6 and 5 GeV 2 ≤ Q 2 ≤ 100 GeV 2 respectively. We have obtained the solution of G(x, Q 2 ) by considering two particular cases: (a) α s fixed; and (b) the leading order QCD dependency of α s on Q 2 . A comparative analysis is also performed where we compare the gluon distribution function due to inclusion of the antishadowing effect with that of the gluon distribution without including the antishadowing effect. Our obtained results of G(x, Q 2 ) are compared with NNPDF3.0, CT14 and PDF4LHC. We also compare our results with the result obtained from the IMParton C++ package. Using the solutions of G(x, Q 2 ), we have also predicted x and Q 2 evolution of the logarithmic derivative of proton's F 2 structure function i.e. dF 2 (x, Q 2 )/d ln Q 2 .We incorporated both the leading order(LO) and next-to-leading order (NLO) QCD contributions of the gluon-quark splitting kernels, in dF 2 (x, Q 2 )/d ln Q 2 . Our result of dF 2 (x, Q 2 )/d ln Q 2 agrees reasonably well with the experimental data recorded by HERA's H1 detector. * mlalung@tezu.ernet.in † pragyanp@tezu.ernet.in ‡ jks@tezu.ernet.in

On analytical solutions of the DIS structure functions in the framework of GLR-MQ-ZRS equation

“…The main difference between GLR-MQ equation and ZRS version is the presence of an additional antishadowing term in the latter. In our previous work [18], we have obtained solutions for gluon distribution function G(x, Q 2 ) and we had shown that our predicted results of proton's F 2 derivative dF 2 / ln Q 2 were in good agreement with the HERA data. In this work, however, we have obtained the solution of F 2 (x, Q 2 ) and F L (x, Q 2 ) structure functions from the GLR-MQ-ZRS equation.…”

Considering the heavy-quark distribution functions at low x

“…In these figures, the nonlinear effects are considered at the hot-spot point (R = 2 GeV −1 ). We compared our computed results of the linear and nonlinear gluon distribution with respect to the parametrization method with PDFs of groups such as NNPDF3.0 [21], CT14 [22] and GRV92 [23] (also, one can see [24][25][26][27]). Also, in figure 1, the ratio of the NNPDF3.0 and CT14 data to the linear and nonlinear gluon distribution functions is shown.…”

An analytical solution of Balitsky-Kovchegov equation using homotopy perturbation method

“…Some analytical solutions of nonlinear QCD evolution equations incorporating parton-parton recombination can be found in ref. [14][15][16][17]. The parton-parton recombination will tame down the gluon density in the high gluon density region of the scattering process.…”