Gluon Saturation Model with Geometric Scaling for Net-Baryon Distributions in Relativistic Heavy Ion Collisions

The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scattering. The net-baryon distributions, nuclear stopping power and gluon saturation features in the SPS and RHIC energy regions are investigated by taking advantage of the gluon saturation model with geometric scaling. Predications are made for the net-baryon rapidity distributions, mean rapidity loss and gluon saturation features in central Pb ＋ Pb collisions at LHC.

Gluon saturation and net-proton spectra in relativistic nucleus-nucleus collisions

By means of the AKK08 fragmentation function, the net-proton transverse momentum （pT） spectra in A＋A collisions are studied with two phenomenological models based on the Color Glass Condensate formalism. After a χ2 analysis of the experimental data from BRAHMS, the normalization constant C is extracted at RHIC energies of √sNN =62.4 and 200 GeV, and the theoretical results of the net-proton pT spectra at selected rapidities are also given. It is shown that the theoretical results are in good agreement with the experimental data. Finally, assuming the constant C should have an exponent dependence of √sNN, we also predict the theoretical results of net-proton pT spectra at LHC energies of √sNN = 2.76, 3.94, and 5.52 TeV.

Gluon saturation and baryon stopping in the SPS, RHIC, and LHC energy regions

A new geometrical scaling method with a gluon saturation rapidity limit is proposed to study the gluon saturation feature of the central rapidity region of relativistic nuclear collisions. The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scattering. We take advantage of the gluon saturation model with geometric scaling of the rapidity limit to investigate net baryon distributions, nuclear stopping power and gluon saturation features in the SPS and RHIC energy regions. Predictions for net-baryon rapidity distributions, mean rapidity loss and gluon saturation feature in central Pb＋Pb collisions at the LHC are made in this paper.

Gluon saturation and pseudo-rapidity distributions of charged hadrons at RHIC energy regions

We modified the gluon saturation model by rescaling the momentum fraction according to satu- ration momentum and introduced Cooper-Frye hydrodynamic evolution to systematically study the pseudo- rapidity distributions of final charged hadrons at different energies and different centralities for Au-Au collisions in relativistic heavy-ion collisions at the BNL Relativistic Heavy Ion Collider （RHIC）. The features of both gluon saturation and hydrodynamic evolution at different energies and different centralities for Au-Au collisions are investigated in this paper.

Single inclusive hadron production at the LHC with an improved impact parameter dependent saturation model

To obtain a reasonable description of the hadron production at the LHC energies,the impact parameter dependent saturation model is modified by inclusion of an anomalous dimensionγ,which controls the slope of the scattering amplitude in the transition from the dilute region to the saturation region.We calculate the transverse momentum distribution and nuclear modification factor of theπ^(0)and charged hadrons with the improved model,and the results are consistent with measurements performed at the LHC.Moreover,we use the original impact parameter dependent model to study the aforementioned measurements performed at the LHC by adjusting its parameters.We find that the improved model is more consistent with the experimental data than the original one,as the anomalous dimension plays a significant role in the suppression of the evolution of the scattering amplitude.

Probing valence quark width of the proton in deeply virtual Compton scattering at high energies

We use the refined hot spot model to study the valence quark shape of the proton with the deeply virtual Compton scattering at high energies in the color glass condensate framework.To investigate the individual valence quark shape,a novel treatment of the valence quark width is employed.We calculate the cross-sections for coherent and incoherent deeply virtual Compton scattering using,for the first time,different widths(Bu and Bd)for the profile density distributions of the up and down quarks instead of using the same width as in the literature.We find that the cross-sections calculated with Bu≥Bd at each collision energy are consistent with each other,which is in agreement with theoretical expectations,whereas those computed with Bu<Bd show some discrepancies.This outcome implies that the up quark might emit more gluons than the down quark,leading to Bu≥Bd at high energy.The impact of energy on the outcome is estimated.Our results show that as the collision energy increases,the aforementioned discrepancies are not only significantly broadened,but also shift to a relatively smaller momentum transfer range at the future Electron-Ion Collider(EIC)and Large Hadron Electron Collider(LHeC)energies,which indicates that the EIC and LHeC can provide an unprecedented chance to access the shape of the valence quark of the proton.

Hadron production with collinearly-improved unintegrated gluon distributions in high energy proton-proton collisions

The collinearly-improved Balitsky-Kovchegov(ciBK)equation evolved unintegrated gluon distribution(UGD)is used for the first time to study hadron production in high energy proton-proton collisions in order to improve the predictive power of the Color Glass Condensate effective theory.We show that the ciBK equation evolved UGD provides a relatively better description of LHC data on the transverse momentum and integrated multiplicity distributions of charged hadron and neutral pion production for several collision energies compared with the running coupling Balitsky-Kovchegov(rcBK)equation evolved UGD.This is because the ciBK evolved UGD has a sharper transverse momentum distribution than the rcBK UGD.The impact of running coupling prescriptions on hadron production is studied,and it is found that the parent dipole and smallest dipole running coupling prescriptions provide similar depictions of the data.Moreover,the scale dependence of the fragmentation function is investigated by taking three typical values of scale.We find that the differences resulting from the scale dependence of the fragmentation function can be fully absorbed into the normalization factor,which lumps higher order corrections.

Solution to the Sudakov suppressed Balitsky-Kovchegov equation and its application to HERA data

We analytically solve the Sudakov suppressed Balitsky-Kovchegov evolution equation with fixed and running coupling constants in the saturation region. The analytic solution of the S-matrix shows that the exp(-O(η^2))rapidity dependence of the solution with the fixed coupling constant is replaced by the exp(-O(η^3/2))dependence in the smallest dipole running coupling case, as opposed to obeying the law found in our previous publication, where all the solutions of the next-to-leading order evolution equations comply with exp(-O(η))rapidity dependence once the QCD coupling is switched from the fixed coupling to the smallest dipole running coupling prescription. This finding indicates that the corrections of the sub-leading double logarithms in the Sudakov suppressed evolution equation are significant, which compensate for a part of the evolution decrease of the dipole amplitude introduced by the running coupling effect. To test the analytic findings, we calculate the numerical solutions of the Sudakov suppressed evolution equation, and the numerical results confirm the analytic outcomes. Moreover, we use the numerical solutions of the evolution equationto fit the HERA data. This demonstrates that the Sudakov suppressed evolution equation can achieve a good quality fit to the data.

Exclusive and dissociative J/ψproduction with collinear-improved Balitsky-Kovchegov equation

We extend the hotspot model to include the virtuality dependence and use it to study the exclusive and dissociative J/Ψ production combined with the dipole amplitude in the target rapidity representation.We determined that virtuality takes effect on a number of hotspots,thus providing a better description of the J/Ψ production data at HERA.The collinear improved Balitsky-Kovchegove equation in the target rapidity representation is numerically solved and used to fit the J/Ψ experimental data with a series of hotspot sizes.We infer that virtuality significantly influences the number and size of hotspots.The expression χ^(2)/d.o.f=1.0183 resulting from the fit with the collinear improved dipole amplitude in the target rapidity representation is more reasonable than the correspondingχ^(2)/d.o.f=1.3995 originating from the leading order fit,which indicates that the collinear improved evolution equation in the target rapidity representation can provide a relatively good depiction of the exclusive and dissociative HERA data.

Energy dependent growth of nucleon and inclusive charged hadron distributions

In the Color Glass Condensate formalism, charged hadron p T spectra in p＋p and p＋Pb collisions are studied by considering an energy-dependent broadening of nucleon density distribution. Then, in the glasma flux tube picture, the n-particle multiplicity distributions at different pseudo-rapidity ranges are investigated. Both the theoretical results show good agreement with the recent experimental data from ALICE and CMS at LHC energies.The predictive results for p T or multiplicity distributions in p＋p and p＋Pb collisions at the Large Hadron Collider are also given in this paper.

A modified explanation of cold nuclear matter effects on J/ψ production in p+A collisions

A modified explanation of the cold nuclear matter （CNM） effects on J/ψ production in p＋A collisions is presented in this paper. The advantage of the modified explanation is that all the CNM effects implemented in this model have clear physical origins and are mostly centered on the idea of multiple parton scattering. With the CNM effects presented in this paper, we calculated the nuclear modification factor RpA in J/ψ production under different collision energies. The results are compared with the corresponding experiment data and the factors calculated with classic nuclear effects. The factors calculated with CNM effects presented in this paper can accurately reproduce almost all existing J/ψ measurements in p-A collisions, which is much better than results obtained with the factors calculated with classic nuclear effects. The new model is therefore a more suitable approach to explain CNM effects in the hardproduction of quarkonium.

Running coupling effect in next-to-leading order Balitsky-Kovchegov evolution equations

Balitsky-Kovchegov equations in projectile and target rapidity representations are analytically solved for fixed and running coupling cases in the saturation domain. Interestingly, we find that the respective analytic S-matrices in the two rapidity representations have almost the same rapidity dependence in the exponent in the running coupling case, which provides a method to explain why the equally good fits to HERA data were obtained when using three different Balitsky-Kovchegov equations formulated in the two representations. To test the analytic outcomes, we solve the Balitsky-Kovchegov equations and numerically compute the ratios between these dipole amplitudes in the saturation region. The ratios are close to one, which confirms the analytic results. Moreover, the running coupling, collinearly-improved, and extended full collinearly-improved Balitsky-Kovchegov equations are used to fit the HERA data. We find that all of them provide high quality descriptions of the data, and the χ^(2)/d.o.f obtained from the fits are similar. Both the analytic and numerical calculations imply that the Balitsky-Kovchegov equation at the running coupling level is robust and has a sufficiently strong predictive power at HERA energies;however, higher order corrections could be significant for future experiments, such as those at the EIC or LHeC.