Hidden Local Symmetry and Effective Chiral Theory for Vector and Axial-vector Mesons

Abstract

We present the effective chiral Lagrangian of mesons (peusodoscalars, vectors and axial-vectors) obtained in the chiral limit by using two approaches. The first approach is based on symmetries: the explicit global chiral symmetry and hidden local chiral symmetry. In this approach, it is noticed that there are in general fourteen interacting terms up to the dimension-four of covariant derivative for meson fields rather than the usual eleven interacting terms given in literature from hidden local symmetry approach. Of particular, the additional terms are found to be very important for understanding the vector meson dominance and providing consistent predictions on the decay rates of a1 → γπ and a1 → ρπ as well as for resulting a consistent effective chiral Lagrangian with chiral perturbation theory. The second approach is motivated from the chiral symmetry of chiral quarks and the bound state solutions of nonperturbative QCD at low energy and large Nc. The second approach is more fundamental in the sense that it is based on the QCD Lagrangian of quarks and only relies on two basic parameters in addition to the ones in the standard model. As a consequence, it allows us to extract, in terms of only two basic parameters, all the fourteen parameters in the more general effective Lagrangian constructed from symmetries in the first approach. It is surprising to note that except the necessity of three additional new interacting terms introduced in this paper, the resulting values of the coupling constants for other three interacting terms at the dimension-four are also quite different from the ones given in the literature. It is likely that the structures of the effective chiral Lagrangian for the dimension-four given in the literatures by using hidden local symmetry are incomplete and consequently the resulting coulpings are not reliable. It is shown that the more general effective chiral Lagrangian given in the present paper shall provide a more consistent prediction for all the low energy phenomenology of ρ - a1 system and result in a more consistent description on the low energy behavior of light flavor mesons. Its fourteen parameters up to the dimension-four of covariant derivative may be uniquely determined from the effective chiral theory based on the second approach, which is consistent with the chiral perturbation theory.