Vector meson dominance and polarization

Abstract

The vector dominance model relates amplitudes for reactions induced by photons (e.g., ifπ-production from nucleons) to amplitudes for reactions induced by vector mesons. In the applications of such relations one conventionally assumes that the vector mesons have to be polarized transversely with respect to the c.m. system. Because of the spin rotation of a massive particle under Lorentz transformations, this choice is not well justified a priori. Our main assumptions are, that the vector meson couples to a conserved current, and that for large s, the invariant amplitudes A ( i) ( s, t)( i=1,…,6) for π production from nucleons are approximately independent of the mass λ of the vector mesons. We find that for large s the optimum approximation of the photoproduction amplitudes is obtained if the vector mesons are in the transverse helicity states (with respect to the c.m. system). Indeed, exactly these transverse amplitudes are independent of λ for s ⪢ λ 2, if the contribution of A (6)( s, t) is assumed to be small, in addition to the assumptions mentioned above.