Accessing the stringy structure of proton in the framework of Color Glass Condensate

Abstract To investigate the possible geometric structure of the proton, an improved stringy proton model is constructed beyond the smallest distance approximation and treats the constituent (up and down) quark-initiated gluon tubes separately, where the constituent quarks are connected by gluon tubes which merge at the Fermat point of the quark triangle. The exclusive diffractive vector meson production process in electron-proton deep inelastic scattering is used to test the stringy structure of the proton. We calculate the coherent and incoherent differential cross sections of the exclusive diffractive J /Ψ photoproduction in the framework of Color Glass Condensate. The results show that our calculations are in good agreement with HERA data. Especially, our results give a better description of the HERA data at small t as compared to the ones from the hot spot model where the constituent quarks are independently distributed in the proton. Meanwhile, the radius of the proton resulting from the improved stringy proton model is coincident with the one from fitting to the data from GlueX Collaboration at Jefferson Lab, which indicates that the predictive power of the stringy proton model is significantly improved once it goes beyond the smallest distance approximation and treats the constituent quarks separately, instead of using the same profile for the up and down quarks initiated gluon tubes. Moreover, we assume that the transverse shape of the gluon tube satisfies Gaussian distribution, and explore the distribution width of the individual gluon tubes. We find an interesting result that the up quark-initiated gluon tube seems to have a larger distribution width than the down quark-initiated gluon tube, which is favored by the HERA data.