Vector meson leptoproduction and nonperturbative gluon fluctuations in QCD

TL;DR

This work develops a nonperturbative QCD treatment of diffractive vector-meson electroproduction using the stochastic vacuum model, representing the photon and vector mesons as $q\bar{q}$ dipoles and computing cross sections by coupling their light-cone wave functions to a gauge-invariant dipole-dipole amplitude derived from Wilson-loop correlators. The approach yields predictions for $d\sigma/dt$ and the ratio $R=\sigma_L/\sigma_T$ across $\rho$, $\omega$, $\phi$, and $J/ψ$, with a continuum from soft to semi-hard scales controlled by $Q^2$ and meson mass; it achieves qualitative and, in several channels, quantitative agreement with data using parameters fixed from soft hadron physics and $pp$ scattering. The results highlight the role of hadron size and nonperturbative gluon fluctuations in diffractive processes and provide a framework to study the transition from large to small dipole sizes, though energy dependence will require incorporating hard-pomeron dynamics. Overall, the work links confinement-driven nonperturbative QCD to observable diffractive electroproduction phenomena and offers testable predictions for polarization, $t$-dependence, and channel-specific behavior.

Abstract

We present a nonperturbative QCD calculation of diffractive vector meson production in virtual photon nucleon scattering at high energy. We use the nonperturbative model of the stochastic QCD vacuum which yields linear confinement and makes specific predictions for the dependence of high-energy scattering cross sections on the hadron size. Using light cone wave functions of the photon and vector mesons, we calculate electroproduction cross sections for $ρ$, $ω$, $φ$ and $J/ψ$. We emphasize the behavior of specific observables such as the ratio of longitudinal to transverse production cross section and the t-dependence of the differential cross section.

Figures (14)

• Figure 1: Kinematics of the reaction $\gamma^* +p\to V+p$.
• Figure 2: Configuration of the two interacting loops in the transverse plane. With our choice of frame, the loops 1 and 2 lie, in the $(x^0,x^3)$-plane, on the lines $x^0=x^3$ and $x^0=-x^3$ respectively.
• Figure 3: Space-time representation of the pyramids and their transverse projection. The sliding sides of the pyramids give the domains $S_1$ and $S_2$ of the surface integrations. Note that the two Wilson loops are not parallel in the transverse plane.
• Figure 4: (a) Color interaction amplitude Eq. (\ref{['dipole-dipole']}) for the non-confining case, $\kappa=0$, as a function of the impact position between the two dipoles. Dipole 1 has a transverse size $r_1=a$ and we sum over its orientation. Dipole 2 has a transverse size $r_2=12\,a$ and lies along the $x$-axis. (b) Color interaction amplitude for the confining case, $\kappa=1$.
• Figure 5: Dipole-proton total cross section as a function of the dipole size for $z=0$ and $z=0.5$. The dependence in $z$ is rather marginal as it becomes noticeable only for very large separation of the $q\bar{q}$ pair. The cross section behaves as $\sigma_{q\bar{q}}\propto r^n$ with $n=2$ for small extension and slowly decreasing at larger distances.