Covariant analysis of the light-front quark model

Abstract

A manifestly covariant formalism is used as a guide to construct a covariant extension of the light-front quark model. Our analysis demonstrates in detail that covariance necessarily requires the inclusion of zero-mode contributions. The main goal of this paper is to use this technique in order to extend the standard light-front formalism such that all form factors that are necessary to represent the Lorentz structure of a hadronic matrix element can be calculated on the same footing. The form factors that have been calculated in the standard approach are reproduced, except for those that describe transitions that involve vector mesons. The covariant approach permits also the calculation of the scalar form factor for transitions between pseudoscalar mesons, and the form factor ${a}_{\ensuremath{-}}{(q}^{2})$ for transitions between pseudoscalar and vector mesons, which is not possible in the standard light-front formalism. The practical application of the covariant extension of the light-front quark model is successful only if the formulas for form factors are evaluated with standard light-front vertex functions. The latter violate the conditions for strict Lorentz covariance of the formalism. In order to explore the predictive power of this approach, we calculate various properties of pseudoscalar and vector mesons in the u-, d-, s-quark sector. We find good agreement with all available data for electroweak transitions.