Abstract
The small-$x$ evolution of protons is determined from numerical solutions of the JIMWLK equations, starting from an initial condition at moderate $x$ for a finite size proton. The resulting dipole amplitude is used to calculate the total reduced cross section $\sigma_r$ and charm reduced cross section $\sigma_{rc}$, as well as diffractive vector meson production. We compare results to experimental data from HERA and discuss fundamental problems arising from the regime sensitive to non-perturbative physics. We emphasize that information on the gluonic content of the proton, gluon spatial distributions and correlations over wide ranges in $x$, which can in principle be constrained by our study, are essential ingredients for describing the initial state in proton-proton and proton-ion collisions. Future electron nucleus collisions at an electron-ion collider will provide important additional insight for heavier nuclei. We further demonstrate that it is not possible to probe gluon saturation in electron-proton collision at HERA energies and that electron-heavy ion collisions will be essential to access the saturation regime.
Highlights
Deep inelastic scattering (DIS) is a clean and powerful process to explore the structure of hadrons as a function of longitudinal momentum fraction x and distance scale Q2
We study proton structure functions and diffractive processes, which are sensitive to the dipole amplitude, which measures the correlation between two Wilson lines
Note that as our setup is slightly different than in our previous work [16], we do not get exactly the same parameters even though we are comparing with the same data set when using a similar initial condition with v 1⁄4 0.0
Summary
Deep inelastic scattering (DIS) is a clean and powerful process to explore the structure of hadrons as a function of longitudinal momentum fraction x and distance scale Q2. In this work we perform for the first time calculations of proton structure functions and diffractive vector meson production using this most fundamental description of the target proton by its JIMWLK evolved Wilson lines.2 This has various advantages over simple parametrization models or those invoking BK evolution. Apart from the fundamental interest in the proton and nuclear structure at small x, it is crucial to understand the Wilson line configurations in protons and nuclei at high energy from electron scattering events in order to constrain the initial states in complex nuclear collisions Avoiding approximations like those done in the IPsat or bCGC models and performing explicit small x evolution of a finite size system comes with a variety of problems.
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