SU(2) Mass Splitting in the Vector Mixing Model

Abstract

The SU(2) mass .splitting and mixing of the pseudoscalar and vector mesons are investi­ gated in connection with SU (3) breaking, under the assumption that the divergent self-energies caused by the vector mixing ,p and ifJ/OJ,P(SJ yield the tadpole-like mass splitting. The calculated values of JI = 1 mass splitting and mixing are in good agreement with experiment. It is remarkable . that our model unlike the conventionaL tadpole model gives a consistent value of m%,-mi,., and that the decay rates ~~37! and w~2rr estimated by using the calcu­ lated transitiOI1 masses are consistent with experiment. The observed value of m%.,-mi, •. and the tendency m~.-m~.>O are reproduced by a large value· of the magnetic moment. § 1. Introduction · The signs and magnitudes of the JI = 1 mass splitting and illixmg have not yet been explained satisfactorily; 1l A tadpole mbdePl was proposed to explain qualitatively the JI = 1 and SU(3) mass splittings. A common mechanism of the octet dominance is represented simply in this model. The tadpole together with the low energy contribution resulting from a few low-lying intermediate states has given a qualitative explanation of the SU(2) mass splitting. Many attempts to evaluate the tadpole term compared with the low-energy term have been carried out. It has been pointed out by Harari 3l that the JI = 2 parts of the ·mass difference may allow an unsubtracted dispersion relation, while an unknown subtraction term which· may be interpreted as the tadpole is needed for the 4T==1 mass splitting. Successively, the idea of tadpole has been given a somewhat differentinterpretation by Okubo, 4l namely that Reggeized tadpole may dominate the high-energy contribution for the JI = 1 mass splitting. The recent estimation6l of the contribution :from the deep inelastic region, based upon the parton model, showed that the high energy contribution seems to be important for the JI = 1 mass difference, but not for the JI = 2 one. On the other hand, in the case of the JI=2 mass splitting like ~;.-m;, alld ms.+ms--2mso, convergent results with the correct order of magnitude are derived by using the electro­ magnetic form factors in the Born approximation or by evaluation of the Cotting­ ham' formula 6l usillg simple pole donitnance in a dispersion relation. From these observations, it is plausible that the tadpole term of the SU(2) mass splitting represents the high energy behaviour of hadrons induced by the electromagnetic interaction. In spite of the qualitative success, it is found difficult to explain quantitatively