Generalized Schwinger mass formula

We generalize Schwinger's original mass formula to the case of an additiona l isosinglet mixing with the nonet mesons. We then make further generalizat ion to either (i) an arbitrary number of additional isosinglets mixing with nonet mesons, or (ii) an arbitrary number of mesons mixing with an additio nal isosinglet. In the former case, we present an explicit relation, while in the latter case, we show by numerical example that the new mass formula is only weakly affected by the inclusion of additional mesons, and hence ho lds with good accuracy for each of the 3 X 3 mass sub-matrices. (C) 1999 El sevier Science B.V. All rights reserved.