Measuring Dual-Superconductor Length Scales in the QCD Vacuum at HERA

Abstract: In the dual superconductor picture, the QCD vacuum is a condensate of chromomagnetic monopoles characterised by two lengths: the penetration depth $λ$ of the chromoelectric field and the coherence length $ξ$ of the condensate. These have previously been accessible only through lattice calculations of static flux tubes. We show that they can instead be measured in exclusive diffraction, where the transverse profile of a gluonic hotspot is the vacuum's response to a localised color source. We therefore use the Clem vortex profile to describe the hotspot geometry. Fitting Clem's vortex profile to all 104 available H1 and ZEUS exclusive $J/ψ$ photoproduction points, spanning $|t|&lt;30~{\rm GeV}<sup>2$ and $40\leq W\leq 251~{\rm GeV}$, we obtain $χ^2/{\rm ndf}=0.72$ and extract $λ=0.19(2)~{\rm fm}$, $ξ_v=0.087(13)~{\rm fm}$, and a Ginzburg--Landau parameter $κ=2.7(7)$, corresponding to the type-II regime. The corresponding vector mass $1/λ=1.03(11)~{\rm GeV}$ agrees with lattice determinations of the lightest gluelump. The resulting Ginzburg--Landau string tension implied by $λ$ and $κ$ reproduces the QCD string tension well; the matching requires $α_S=0.37(9)$ compared with $α_S(1/λ<sup>2)=0.36(2)$ in the same LO scheme used for the dipole amplitude calculation.