Determining the Proton's Gluon Cloud Geometry from HERA Data

Abstract

The transverse shape of the proton's small-$x$ gluon distribution is determined from exclusive $J/\psi$ photoproduction at HERA. We derive analytic expressions for the coherent and incoherent diffractive cross sections in the hotspot model at leading twist, enabling a global fit to all 104 available H1 and ZEUS data points, with $|t|<30{\mathrm{GeV}}^2$ and $40\le W\le 251\mathrm{GeV}$, with ${\chi }^2/\mathrm{ndf}=0.72$. The gluonic hotspots are resolved into a core of size 0.088(10) fm surrounded by an exponential halo of range 0.20(2) fm, matching the penetration depth of lattice flux tubes. This shape is stable over $\xpom$ and over the assumed number of hotspots in the range $5\le N_{hs}\le 12$. We find the Ginzburg-Landau parameter of the QCD vacuum to be $\kappa =2.7(7)$, which corresponds to fluxtube geometry in a type-II dual superconductor. The calculated QCD string-tension from the extracted parameter values is in agreement with theoretical calculations on the lattice. The gluonic geometry evolves only through a slow transverse diffusion of the hotspot centers with ${\alpha }_{eff.}^{\prime }=0.060(19){\mathrm{GeV}}^{-2}$, while the incoherent cross section at small $|t|$ is dominated by shot-noise fluctuations at the order of a few gluons per hotspot.

14 pages, 6 figures