Excited pions, rho- and omega-mesons and their decays in a chiral SU(2) x SU(2) Lagrangian

A chiral SU(2) x SU(2) Lagrangian containing, besides the usual meson fields, their first radial excitations is considered. The Lagrangian is derived by bosonization of the Nambu-Jona-Lasinio quark model with separable non-local interactions, with form factors corresponding to 3-dimensional ground and excited state wave functions. The spontaneous breaking of chiral symmetry is governed by the NJL gap equation. The first radial excitations of the pions, rho-and omega-mesons are described with the help of two form factors. The weak decay constant F_pi' is calculated. The values for the decay widths of the processes rho -> 2 pi, pi' -> rho pi, rho' -> 2 pi, rho' -> omega pi and omega' -> rho pi are obtained in agreement with the experimental data.