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.