Revealing proton shape fluctuations with incoherent diffraction at high energy

Abstract: The differential cross section of exclusive diffractive vector meson production in electron proton collisions carries important information on the geometric structure of the proton. More specifically, the coherent cross section as a function of the transferred transverse momentum is sensitive to the size of the proton, while the incoherent, or proton dissociative cross section is sensitive to fluctuations of the gluon distribution in coordinate space. We show that at high energies the experimentally measured coherent and incoherent cross sections for the production of $J/\Psi$ mesons are very well reproduced within the color glass condensate framework when strong geometric fluctuations of the gluon distribution in the proton are included. For $\rho$ meson production we also find reasonable agreement. We study in detail the dependence of our results on various model parameters, including the average proton shape, analyze the effect of saturation scale and color charge fluctuations and constrain the degree of geometric fluctuations.