Mending $\rho\pi\pi$ vertex through the $\pi a_1$ diagonalization

Abstract

The problem of the strong momentum dependence of the $\rho\pi\pi$-vertex in the extended Nambu -- Jona-Lasinio model is solved by an appropriate choice of fields for spin-1 particles. A corresponding phenomenological Lagrangian is derived. As straightforward applications, the decay widths of $\rho\to\pi\pi$, and $a_1\to\rho\pi$ transitions are calculated and compared with known empirical data and previous theoretical estimates.