$tauto u_taurho^0pi^-$ decay in the Nambu - Jona-Lasinio model

Within the context of an extended Nambu - Jona-Lasinio model, we analyze the role of the axial-vector $a_1(1260)$ and $a_1(1640)$ mesons in the decay $tauto u_tau rho^0pi^-$. The contributions of pseudoscalar $pi$ and $pi (1300)$ states are also considered. The form factors for the decay amplitude are determined in terms of the masses and widths of these states. To describe the radial excited states $pi (1300)$ and $a_1(1640)$ we introduce two additional parameters which can be estimated theoretically, or fixed from experiment. The decay rate and $rhopi$ mass spectrum are calculated.