Energy dependence of the proton geometry in exclusive vector meson production

TL;DR

This paper explores how the proton's size changes with energy in exclusive vector meson production, introducing models that account for gluon distribution growth at small x, and compares them with experimental data.

Contribution

The study introduces novel models for the x dependence of the gluon distribution in the proton, incorporating size increase at small x, and compares these with HERA data.

Findings

Models with increasing proton size at small x fit the data better.

Differences observed in t-spectra slopes between models.

Cross section ratios vary with the proton size models.

Abstract

The gluon radius of the proton is expected to increase at small gluon momentum fractions $x$, an effect which has hitherto not been considered in the dipole model framework. We investigate the energy dependence of exclusive $J/\psi$, $\phi$, and $\rho$ production by introducing three models for $x$ dependence of the gluon thickness function. We allow the transverse width of the proton to increase as $x$ decreases, using novel parametrisations in the spherical proton and the hotspot model. We compare these with a model where the number of hotspots increases as $x$ decreases and confront the models with HERA data. The models exhibit clear differences in the slope of the $t$-spectra and in the cross section ratios between coherent and incoherent events. Comparisons to $t$-slopes and $W_{\gamma p}$ measurements show a preference for models where the proton's size increases as $x$ decreases.