Current algebra with a four-flavor effective Lagrangian

A current-algebra treatment of the low-lying spin-zero meson mass spectrum (with four flavors) is given on the basis of a Lagrangian which includes not only the "quark mass" symmetry-breaking terms but also the simplest effective term which breaks the U(4) × U(4) down to SU(4) × SU(4) × "quark number." A term of this sort has been used previously in the linear $\sigma$ model and has been claimed by 't Hooft to arise from the effects of the pseudoparticle on the color-gauge-theory vacuum. In this way good agreement with what is currently known about the mass spectrum can be achieved. We also show that this term provides a source for violation of the Okubo-Zweig-Iizuka rule even without considering unitarity corrections. Predictions are made for the mass of the $F$ meson, the decay constants of the $D$ and $F$ mesons, the $\eta -{\eta }^{\prime }-{\eta }^{\prime \prime }$ mixing angles, etc. All the parameters involved in the model-the "quark masses," the vacuum parameters, and the strength of the new effective term—are estimated. Generalizations of the model to include isospin breaking and more flavors are also discussed. Finally, throughout the discussion we have taken note of the points at which the conventional current-algebra treatment (which we use) are open to question and we have referred to different approaches.