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/ψ 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 GeV2 and 40≤ W≤ 251 GeV, with χ2/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≤ Nhs≤ 12. We find the Ginzburg-Landau parameter of the QCD vacuum to be κ=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 α'eff.=0.060(19) 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.
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BibTeX
@misc{toll2026determining,
title = {{Determining the Proton's Gluon Cloud Geometry from HERA Data}},
author = {Tobias Toll and Nahid Vasim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.14955},
eprint = {2607.14955},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14955},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Determining the Proton's Gluon Cloud Geometry from HERA Data
AU - Tobias Toll
AU - Nahid Vasim
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2607.14955
UR - https://arxiv.org/abs/2607.14955
AB - The transverse shape of the proton's small-x gluon distribution is determined from exclusive J/ψ 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 GeV^2 and 40≤ W≤ 251 GeV, with χ^2/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≤ N_hs≤ 12. We find the Ginzburg-Landau parameter of the QCD vacuum to be κ=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 α'_eff.=0.060(19) 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.
ER -