$\tau \to {\nu }_{\tau }{\rho }^0{\pi }^{-}$ decay in the Nambu - Jona-Lasinio model

Abstract

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 $\tau \to {\nu }_{\tau }{\rho }^0{\pi }^{-}$. 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 $\rho \pi$ mass spectrum are calculated.

Comments: 7 pages, 3 figures, 2 tables