Consistent treatment of spin-1 mesons in the light-front quark model

Abstract

We analyze the matrix element of the electroweak current between $q \qb$ vector meson states in the framework of a covariant extension of the light-front formalism. The light-front matrix element of a one-body current is naturally associated with zero modes, which affect some of the form factors that are necessary to represent the Lorentz structure of the light-front integral. The angular condition contains some information on zero modes, i.e., only if the effect of zero modes is accounted for correctly, is it satisfied. With plausible assumptions we derive from the angular condition several consistency conditions which can be used quite generally to determine the zero mode contribution of form factors. The correctness of this method is tested by the phenomenological success of the derived form factors. We compare the predictions of our formalism with those of the standard light-front approach and with available data. As examples we discuss the magnetic moment of the $\rho$, the coupling constant $g_{D^\ast D \pi}$, and the coupling constants of the pseudoscalar density, $g_\pi$ and $g_K$, which provide a phenomenological link between constituent and current quark masses.