Gluon Recombination Research Articles

Exploring the impact of anti-shadowing effect on unintegrated gluon distributions in the MD-BFKL equation* *Supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030301), the Major Project of Basic and Applied Basic Research of Guangdong Province, China (2020B0301030008), the Education Department of Guizhou Province, China (QJJ[2022]016), and the Basic Research Program (Natural Science) of Guizhou Province, China

This paper presents a comprehensive analysis of the MD-BFKL equation, considering both shadowing and anti-shadowing effects in gluon recombination processes. By deriving analytical expressions for unintegrated gluon distributions through the solution of the MD-BFKL equation, with and without the incorporation of the anti-shadowing effect, we offer new insights into the influence of these effects on the behavior of unintegrated gluon distributions. Our results, when compared to those from the CT18NLO gluon distribution function, demonstrate that the anti-shadowing effect has a notably stronger impact on the characteristics of unintegrated gluon distributions, particularly in regions of high rapidity and momentum. This work significantly contributes to the understanding of gluon recombination mechanisms and their implications in high energy physics.

Proton PDFs with nonlinear corrections from gluon recombination

We present numerical studies of the leading nonlinear corrections to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations of parton distribution functions (PDFs) resulting from gluon recombination. The effect of these corrections is to reduce the pace of evolution at small momentum fractions x while slightly increasing it at intermediate x. By implementing the nonlinear evolution in the framework, we have carried out fits of proton PDFs using data on lepton-proton deep inelastic scattering from HERA, BCDMS, and NMC. While we find no evidence for the presence of nonlinearities, they cannot be entirely excluded either, and we are able to set limits for their strength. In terms of the recombination scale Qr, which plays a similar role as the saturation scale in the dipole picture of the proton, we find that Qr≲2.5 GeV. We also quantify the impact of the nonlinear terms for the longitudinal structure function at the Electron-Ion Collider and the Large Hadron Electron Collider and find that these measurements could provide stronger constraints on the projected effects. Published by the American Physical Society 2024

Shadowing corrections to the evolution of singlet structure function

In this paper, a semi-analytical approach is introduced to address the solution of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu (GLR-MQ) evolution equation for sea quark distribution. Here the effect of gluon shadowing on the behaviour of singlet structure function, , has been investigated, particularly in the regime of small-x and moderate-Q 2. The predicted values of singlet structure functions with shadowing corrections align well with different experimental data and existing parametrizations. It is very fascinating to observe signatures of gluon recombination within these predictions. Notably, as x decreases, the rapid growth of singlet structure function is eventually tamed by the shadowing or nonlinear term appeared in the QCD evolution due to gluon recombination. This taming behaviour of shadowing singlet structure function towards small-x become significant at the hot spots, at R = 2 GeV−1. Further the computed ratios of with shadowing, in comparison to those without shadowing, clearly indicate that towards smaller values of x and Q 2 the nonlinear effects gradually become prominent.

Numerical evaluation of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu evolution equations for nuclear parton distribution functions

We numerically study for the first time the nonlinear GLR-MQ evolution equations for nuclear parton distribution function (nPDFs) to next-to-leading order accuracy and quantify the impact of gluon recombination at small $x$. Using the nCTEQ15 nPDFs as input, we confirm the importance of the nonlinear corrections for small $x \lesssim 10^{-3}$, whose magnitude increases with a decrease of $x$ and an increase of the atomic number $A$. We find that at $x=10^{-5}$ and for heavy nuclei, after the upward evolution from $Q_0=2$ GeV to $Q=10$ GeV, the quark singlet $\Omega(x,Q^2)$ and the gluon $G(x,Q^2)$ distributions become reduced by $9-15$%, respectively. The relative effect is much stronger for the downward evolution from $Q_0=10$ GeV to $Q=2$ GeV, where we find that $\Omega(x,Q^2)$ is suppressed by 40%, while $G(x, Q^2)$ is enhanced by 140%. These trends propagate into the $F_2^A(x,Q^2)$ nuclear structure function and the $F_L^A(x,Q^2)$ longitudinal structure function, which after the downward evolution become reduced by 45% and enhanced by 80%, respectively. Our analysis indicates that the nonlinear effects are most pronounced in $F_L^A(x,Q^2)$ and are already quite sizable at $x \sim 10^{-3}$ for heavy nuclei. We have checked that our conclusions very weakly depend on the choice of input nPDFs. In particular, using the EPPS21 nPDFs as input, we obtain quantitatively similar results.

Total hadronic and photonic cross sections and the nuclear configurational entropy concept

In the framework of eikonalized mini-jet model, contributions from gluon recombination effects are studied for the free proton in pp and \(\bar{p} p\) reactions. The nuclear configurational entropy is then used to calculate the main parameters to estimate the total proton cross sections for the recent data LHC, also corroborating to previous developments. Photoproduction cross sections with vector meson dominance and saturation effects for both total hadronic and photonic cross sections at a high-energy regime are investigated. Extreme points of the configurational entropy can shed new light on some features of specific models of nuclear reactions, which are described by the corresponding reaction cross section, providing the latter by the necessary model parameters within an optimal root-mean-square deviation.

Q2 evolution of gluon distribution function inside the hadrons with both shadowing and antishadowing effects

We deliberately attempt to solve the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu,Zhu-Ruan-Shen (GLR-MQ-ZRS) equation in the leading order of QCD to study the Q2 evolution of gluon distribution function G(x,Q2), Q2 is the resolution scale or the four momentum transfered squared and x is the Bjorken variable. Both the shadowing and antishadowing corrections due to gluon recombination processes are incorporated in GLR-MQ-ZRS equation and while solving this equation we have used Regge like behavior in gluon distribution function. We present a phenomenological study on the collective contribution due to both the shadowing and antishadowing effects on the gluon distribution functions at small-x. Our solution of GLR-MQ-ZRS equation is valid in the vicinity of saturation at small-x, where gluon recombination effects cannot be ignored. We have shown comparison of our computed results for different values of strong coupling constant αs with the PDFs of NNPDF3.0, PDF4LHC and CT14 groups.

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

We present a phenomenological study of the small-x behavior of gluon distribution function G(x,Q2) 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 (∼1/Q) fixed. We consider the NLO and NNLO corrections, of the gluon–gluon splitting function Pgg(z) and strong coupling constant αs(Q2). We have suggested semi-analytical solutions based on Regge like ansatz of gluon density G(x,Q2), which are supposed to be valid in the moderate range of photon virtuality (Q2) 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.

Statistical physics in QCD evolution towards high energies

The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical approximation relevant at high energies and at a fixed impact parameter is a peculiar branching-diffusion process, and parton branching supplemented by saturation effects (such as gluon recombination) is a reaction-diffusion process. In this review article, we first introduce the basic concepts in the context of simple toy models, we study the properties of the latter, and show how the results obtained for the simple models may be taken over to quantum chromodynamics.

Analytical approach for the solution of the nonlinear GLR-MQ equation

The present paper reports the effect of nonlinear corrections to the behaviour of gluon distribution in the Gribov-Levin-Ryskin-Mueller-Qiu (GLR-MQ) approach. Here the nonlinear GLR-MQ evolution equation is solved analytically in order to determine the x and Q 2 dependence of gluon distribution function. We observe that, the gluon distribution increases with increasing Q 2 and decreasing x, which is in agreement with the perturbative QCD fits at small- x, however this particular behaviour of the gluon distribution function is tamed by the shadowing effects of gluon recombination. The obtained results of the nonlinear gluon distribution at the hot spot are compared with different global parton analysis as well as with those obtained from the solution of the modified-DGLAP (MD-DGLAP) equation and are found to be quite compatible.

Analysis of the small-x behavior of gluon distribution and a search for gluon recombination

The behavior of gluon distributions in the small-x region are semi-numerically predicted by using the nonlinear Gribov–Levin–Ryskin and Mueller–Qiu (GLR–MQ) evolution equation with the nonlinear shadowing term incorporated. It is interesting to observe that gluon recombination at the twist-4 level lowers the rapid growth of gluon densities with decreasing x compared to the linear DGLAP evolution. The nonlinear gluon density functions are calculated and compared with different parameterizations as well as models. Results show that our predictions for the gluon density function are comparable with different parameterizations. We make a deliberate attempt to explore the effect of nonlinear or shadowing corrections and we observe that nonlinear effects play a vital role in the kinematic region of small-x (x≤10−3) and Q2 (2≤Q2≤20 GeV2).

Nonlinear effects and the behavior of total hadronic and photonic cross sections

In this work we use an eikonalized minijet model where the effects of the first nonlinear corrections to the DGLAP equations are taken into account. The contributions coming from gluon recombination effects are included in the DGLAP+GLRMQ approach for the free proton in the context of saturation models. The parameters of the model are fixed to fit total $pp$ and $\bar p p$ cross sections, including the very recent data from LHC, HiRes and P. Auger Collaborations. Glauber and multiple scattering approximations are then used to describe the inclusive inelastic proton-Air cross section. Photoproduction cross sections, without change of parameters fixed before, are also obtained from the model using Vector Meson Dominance and the Additive Quark Model. We show and discuss our main results as well as the implications of saturation effects in the behavior of total hadronic and photonic cross sections at very high energies.

Baryon enhancement in high-density QCD and relativistic heavy ion collisions

We argue that the collinear factorization of the fragmentation functions in high-energy nuclear collisions breaks down at transverse momenta pT ≲ Qs/g due to high parton densities in the colliding hadrons and/or nuclei. We find that gluon recombination dominates in that pT region. We calculate the inclusive cross section for π meson and nucleon production using the low-energy theorems for the scale anomaly in QCD, and compare our quantitative baryon-to-meson ratio to the RHIC data.

Predictions for high energy neutrino cross-sections from the ZEUS global PDF fits

We have updated predictions for high energy neutrino and antineutrino charged current cross-sections within the conventional DGLAP formalism of NLO QCD using a modern PDF fit to HERA data, which also accounts in a systematic way for PDF uncertainties deriving from both model uncertainties and from the experimental uncertainties of the input data sets. Furthermore the PDFs are determined using an improved treatment of heavy quark thresholds. A measurement of the neutrino cross-section much below these predictions would signal the need for extension of the conventional formalism as in BFKL resummation, or even gluon recombination effects as in the colour glass condensate model.

Gluon recombination in high parton density QCD: Inclusive pion production

We argue that the collinear factorization of the fragmentation functions in high energy hadron and nuclei collisions breaks down at transverse momenta ${k}_{T}\ensuremath{\lesssim}{Q}_{s}/g$ due to high parton densities in the colliding hadrons and/or nuclei. We calculate, at next-to-leading order in projectile parton density and to all orders in target parton density, the double-inclusive cross-section for production of a pair of gluons in the scalar ${J}^{PC}={0}^{++}$ channel. Using the low energy theorems of QCD we find the inclusive cross-section for $\ensuremath{\pi}$-meson production.

Antishadowing effects in the unitarized BFKL equation

A unitarized BFKL equation incorporating shadowing and antishadowing corrections of the gluon recombination is proposed. This equation reduces to the Balitsky–Kovchegov evolution equation near the saturation limit. We find that the antishadowing effects have a sizable influence on the gluon distribution function in the preasymptotic regime.

Effective Hamiltonian for QCD evolution at high energy

We construct the effective Hamiltonian which governs the renormalization group flow of the gluon distribution with increasing energy and in the leading logarithmic approximation. This Hamiltonian defines a two-dimensional field theory which involves two types of Wilson lines: longitudinal Wilson lines which describe gluon recombination (or merging) and temporal Wilson lines which account for gluon bremsstrahlung (or splitting). The Hamiltonian is self-dual, i.e., it is invariant under the exchange of the two types of Wilson lines. In the high density regime where one can neglect gluon number fluctuations, the general Hamiltonian reduces to that for the JIMWLK evolution. In the dilute regime where gluon recombination becomes unimportant, it reduces to the dual partner of the JIMWLK Hamiltonian, which describes bremsstrahlung.

Analytical evolution of nucleon structure functions with power corrections at twist-4 and predictions for ultrahigh energy neutrino-nucleon cross section

In this paper we present an analytic result for the evolution in $Q^2$ of the structure functions for the neutrino-nucleon interaction, valid at twist-2 in the region of small values of the Bjorken $x$ variable and for soft non-perturbative input. In the special case of flat initial conditions, we include in the calculation also the contribution of the twist-4 gluon recombination corrections, whose effect in the evolution is explicitly determined. Finally, we estimate the resulting charged-current neutrino-nucleon total cross section and discuss its behavior at ultra-high energies.

Contributions of gluon recombination to saturation phenomena

Parton distributions in the small x region are numerically predicted by using a modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation with Gl\"uck-Reya-Vogt (GRV)-like input distributions. We find that gluon recombination at the twist-4 level obviously suppresses the rapid growth of parton densities with x decreasing. We show that before the saturation scale ${Q}_{s}^{2}$ is reached, saturation and partial saturation appear in the small x behavior of parton distributions in the nucleus and free proton, respectively. The antishadowing contributions to the saturation phenomena are also discussed.

Analysis of the QCD evolution in the pomeron and a search for gluon recombination

The pomeron structure function is extracted from the H1 data and is subject to a leading-order QCD analysis. We compare the results obtained from the DGLAP equations with and without corrected for gluon recombination. Both cases give good fits to data but different results for the gluon distribution.

Signals of gluon recombination in deep inelastic scattering

The pomeron structure function is extracted from the latest H1 data and are subject to a QCD analysis. The result shows evidence for gluon recombination.