On possible implications of the exponential distribution of constituent quarks within proton at high energies*

Abstract The differential cross-section of diffractive vector meson production in electron-proton deep inelastic scattering is considered one of the most promising observables to probe the spatial structure of the proton and QCD dynamics in the high-energy limit. In this work, we investigate the dependence of the differential cross-section of vector meson production on the position distribution of the constituent quarks within the hot spot model. We consider two types of distribution functions, Gaussian and exponential, and include them in the dipole-proton scattering amplitude, which is a key ingredient of the vector meson production cross-section. We calculate the cross-sections for the production of mesons as a function of the center of mass energy ( W ) and momentum transfer ( ), respectively. At low ( ), the coherent cross-sections calculated with both Gaussian and exponential position distributions of the constituent quarks provide similarly good descriptions of the production data at HERA. However, we find that at relatively large ( ), the coherent cross-sections calculated with the Gaussian position distribution function cannot describe the HERA data, while the coherent cross-sections computed with the exponential position distribution function are in good agreement with the HERA data. This outcome indicates that the position of the constituent quarks in the proton may follow an exponential distribution, and the coherent process can serve as a probe to resolve the position distribution of the constituent quarks. Moreover, our calculations show that the description of the coherent cross-section of production remains robust when modeling the constituent quark positions with an exponential distribution, independent of the particular distribution function selected for the hot spot density profiles.