On the dependence of the widths of the $\tau \rightarrow [\rho^{0}(770), \rho^{0}(1450)] \pi^{-} \nu_{\tau}$ decays on the parameters of the intermediate $a_1$ meson

The widths of the $\tau \rightarrow [\rho^{0}(770), \rho^{0}(1450)] \pi^{-} \nu_{\tau}$ decays have been calculated within the extended Nambu–Jona-Lasinio model including both the ground and first radially excited intermediate meson states. The axial-vector channel with intermediate $a_1$ mesons dominates. The values of the masses and total widths of the $a_1$ meson recently obtained by the COMPASS and JPAC Collaborations have been taken into account.