Diffractive Leptoproduction of Vector Mesons in QCD

TL;DR

The authors develop a perturbative QCD description of forward diffractive leptoproduction of vector mesons, expressing the amplitude in terms of the vector meson’s light-cone wavefunction and the target’s gluon distribution. They show that the dominant longitudinal channel yields a leading twist result with a characteristic $d\sigma/dt|_{t=0} \propto [xG(x,Q^2)]^2 / Q^6$, and that the nuclear dependence follows from color transparency and gluon shadowing, offering a direct probe of nuclear gluon densities. The analysis connects the production amplitude to the vector meson distribution amplitude via the inverse moment $\eta_V$, enabling tests of non-perturbative structure through measurable quantities like $f_V$ and $\Gamma_V$. The work predicts a universal, slowly varying $t$-dependence governed by a two-gluon form factor and highlights distinct behavior for longitudinal vs. transverse polarizations, providing clear experimental signatures for HERA-class kinematics and nuclear targets.

Abstract

We demonstrate that the distinctive features of the forward differential cross section of diffractive leptoproduction of a vector meson can be legitimately calculated in perturbative QCD in terms of the light-cone $q \bar q$ wave function of the vector meson and the gluon distribution of the target. In particular, we calculate the $Q^2$ and nuclear dependence of the diffractive leptoproduction of vector mesons and estimate the cross section. The production of longitudinally polarized vector mesons by longitudinally polarized virtual photons is predicted to be the dominant component, yielding a cross section behaving as $Q^{-6}$. The nuclear dependence of the diffractive cross sections, which follows from a factorization theorem in perturbative QCD, provides important tests of color transparency as well as constraints on the shadowing of the gluon structure functions and the longitudinal structure functions of nuclei.