  Final state quark-antiquark interactions give origin to non zero values of
the off-diagonal element rho_{1,-1} of the helicity density matrix of vector
mesons produced in e+e- annihilations, as confirmed by recent OPAL data on Phi,
D^* and K^*'s. New predictions are given for rho_{1,-1} of several mesons
produced at large x_E and small p_T -- i.e. collinear with the parent jet -- in
the annihilation of polarized e+ and e-; the results depend strongly on the
elementary dynamics and allow further non trivial tests of the Standard Model.
