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.

Exclusive photoproduction of vector meson at next-to-leading order from color glass condensate

The exclusive photoproduction of vector mesons(J/ψ/andφ)is investigated by considering the next-toleading order corrections in the framework of the color glass condensate.We compare the next-to-leading order modified dipole amplitude with the HERA data,finding a good agreement.Our studies show that theχ~2/d.o.f from the leading order,running coupling,and collinearly improved next-to-leading order dipole amplitudes are 2.159,1.097,and 0.932 for the elastic cross-section,and 2.056,1.449,and 1.357 for the differential cross-section,respectively.The results indicate that the higher-order corrections contribute significantly to the vector meson productions,and the description of the experimental data is dramatically improved once the higher order corrections are included.We extend the next-to-leading order exclusive vector meson production model to LHC energies using the same parameters obtained from HERA.We find that our model provides a rather good description of the J/ψandΦdata in proton-proton collisions at 7 TeV and 13 TeV in LHCb experiments.

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.

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.

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.