Nearly massless pion in a modified bag model

Abstract

The properties of the pions are studied in a modified bag model. The pion wave function is approximated by the projection of the qq-bar wave function in the bag that has zero center-of-mass motion. The parameters of the model are determined by the usual stability condition and the additional requirement that the pion mass m/sub ..pi../ approach zero in a manner consistent with the hypothesis of partially conserved axial-vector current (PCAC). This fixes the bag volume energy to be m/sub ..pi..//4. Static pion properties are in good agreement with data provided that quarks in the pion are correlated by a modulating function characterized by a correlation momentum p/sub c/approx.300 MeV/c. The bag-model and Nambu-Goldstone views of the pion are reconciled as a distinction is made between constituent and current quarks. Assuming their fields to be related by a transformation analogous to that of Nambu and Jona-Lasinio we calculate the vacuum expectation value of the current quark density to be 0.04 GeV/sup 3/, corresponding to a current quark mass of 5 MeV. We test our ideas by calculating, to first order of the gluon-exchange interaction, the pion decay constant and the vector and axial-vector form factors for pion radiative decay. Inmore » our model the pion decay constant satisfies the PCAC requirement that it has a finite value in the limit of zero-mass pion.« less