Exclusive production of vector mesons $\rho, \rho'$ and $\rho''$ by real and virtual photons

Abstract

We present a non-perturbative QCD calculation of high-energy diffractive photo- and leptoproduction of vector mesons $\rho$, $\rho'$ and $\rho''$ on a nucleon. The initial photon splits up in a $q\bar{q}$-dipole and transforms into a vector meson by scattering on the quark-diquark nucleon. The dipole-dipole scattering amplitude is provided by the non-perturbative model of the stochastic QCD vacuum, the wave functions result from considerations on the light-cone. We assume the physical $\rho'$- and $\rho''$-states to be mixed states of an active 2S-excitation and a rest whose coupling to the photon is suppressed. We obtain good agreement with the experimental data and get an understanding of the markedly different spectrum in the $\pi^+\pi^-$-invariant mass for photoproduction and $e^+e^-$-annihilation.