We formulate and prove a QCD factorization theorem for hard exclusive electroproduction of mesons in QCD. The proof is valid for the leading power in Q and all logarithms. This generalizes previous work on vector meson production in the diffractive region of small x. The amplitude is expressed in terms of off-diagonal generalizations of the usual parton densities. The full theorem applies to all kinds of meson and not just to vector mesons. The parton densities used include not only the ordinary parton density, but also the helicity density (g_1 or $\Delta q$) and the transversity density ($h_1$ or $\delta q$), and these can be probed by measuring the polarization of the produced mesons with unpolarized protons.Comment: 50 pages, revtex, figures included, uses epsf.sty. Correction of citations, and of predictions for meson productio

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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 lightcone qq wave function of the vector meson and the gluon distribution of the target. In particular, we calculate the Q2 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. PACS numberk): 13.60. Le, 12.38.Bx,

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Hard diffractive electroproduction of longitudinally polarized vector mesons is calculated within the leading $\alpha_s\ln{Q^2\over\Lambda_{QCD}^2}$ approximation of QCD using the leading order parton densities within the nucleon. Novel QCD features of the production of excited states and of the restoration of flavor symmetry are analyzed. At the onset of the asymptotic regime, our analysis finds an important role of quark Fermi motion within the diffractively produced vector mesons, and we suggest to use this effect to measure the high momentum tail of the wave function of the vector mesons. We deduce a kinematical boundary for the region of applicability of the decomposition of the hard amplitudes over powers of $Q^2$ and/or a limit on the increase of the cross sections of hard processes at small $x$, and briefly analyze its consequences. We also estimate the nuclear attenuation of the diffractive electroproduction of vector mesons and compare with estimates of the shadowing of the longitudinal structure function.Comment: 64 pages, REVTeX, 16 figures optionally included using epsfig.sty, Revisions in regards to Charmonium photo- and electroproduction, final version to appear in Phys. Rev.