A Precise Determination of the Shape of the Proton's Gluon Cloud from HERA data

We show the results from a comprehensive study of the gluonic structure of the proton at small $x$ extracted from exclusive $J/\psi$ production at the H1 and ZEUS experiments at HERA. We present an analytical calculation of the coherent and incoherent cross sections in the hotspot model of the proton at leading twist. We fit the model to all available exclusive diffractive photo-production measurements, and extract a precise shape of the proton's gluon cloud. The model shows an excellent fit to data with $\chi^2/{\rm ndf}=0.77$. We find that the hotspots have a perturbative Gaussian core of size $0.105(1)$ fm, surrounded by a non-perturbative exponential halo of 0.220(2) fm. This shape is independent of $\xpom$ or hotspot number. The fit also shows a remarkably stable energy dependence with $\alpha'_{\rm eff}=0.046(19)$.