Radially excited scalar, pseudoscalar, and vector meson nonets in a chiral quark model

Abstract

A chiral Lagrangian containing, besides the usual meson fields, their first radial excitations is constructed. The Lagrangian is derived by bosonization of a Nambu--Jona-Lasinio (NJL) type quark model with separable nonlocal interactions. The nonlocality is described by form factors corresponding to 3-dimensional excited state wave functions. The spontaneous breaking of chiral symmetry is governed by the standard NJL gap equations. A simple SU(2)xSU(2) version of the model is used to demonstrate all low-energy theorems to hold valid in the chiral limit. A more realistic U(3)xU(3) model with 't Hooft interaction is constructed to describe the mass spectrum of excited scalar, pseudoscalar, and vector mesons. On the basis of global chiral symmetry, we use the same form factors for the scalar and pseudoscalar mesons. Having fixed the form factor parameters by masses of pseudoscalar mesons, we predict the mass spectrum of scalar mesons. This allows us to interpret experimentally observed scalar, pseudoscalar, and vector meson states as members of quark-antiquark nonets. It is shown that the a_0(1450), K^*_0(1430), f_0(1370), f_J(1710) scalar meson states are the first radial excitations of the ground states: a_0(980), K^*_0(960), f_0(400-1200), f_0(980). The weak decay constants F_π, F_{π'}, F_K, F_{K'} and the main strong decay widths of the scalar, pseudoscalar, and vector meson nonets are calculated.