Field theory and the nonrelativistic quark model: A parametrization of the meson masses

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Abstract
We apply the method developed in previous papers [Phys. Rev. D 40, 2997 (1989); 40, 3111 (1989)] to write a general parametrization of the masses of the lowest meson nonets. We compare the mass formulas obtained in this way with those used currently in a nonrelativistic quark model (NRQM). As in the previous work, the aim is to separate the features specific to the NRQM from those that follow from a relativistic field theory satisfying a few rather general conditions (satisfied by QCD). For the meson masses it turns out that the formulas obtained from field theory have essentially the same structure and number of parameters as those in the NRQM. This explains the good fit that the NRQM provides in this case; the internal v/c of the qq¯ pair is irrelevant. As a by- product, the mixing angle for the I=0 mesons (e.g., η and η’) predicted from the masses turns out to be model independent to first order in flavor breaking. We discuss the question of the linear versus quadratic or, say, square-root mixing angles.