A complete set of asymptotic three particle light cone distribution
amplitudes of twist 3 and 4 for a transversely polarized massive vector meson
built out of massless current quarks is constructed. The method used is based
on a modified conformal projectors technique which allows to handle kinematical
corrections due to a finite hadron mass. Consequences of our finding for the
\rho -meson hard diffractive electroproduction and \gamma \rho \pi form factor
are discussed. Our results may imply a breakdown of OPE for some exclusive
processes beyond the leading twist level.Comment: Latex, 12 pages, no figure
