The decay $\tau \to (\pi ,{\pi }^{\prime }){\nu }_{\tau }$ in the Nambu - Jona-Lasinio model

Abstract

In the Nambu - Jona-Lasinio model the decay widths $\tau \to (\pi ,{\pi }^{\prime }(1300)){\nu }_{\tau }$ were calculated. For the calculation of the decay width $\tau \to \pi {\nu }_{\tau }$ the standard NJL model was used with taking into account the intermediate axial-vector meson and the extended Nambu - Jona-Lasinio model with the intermediate $a_1(1260)$ and $a_1^{\prime }(1647)$ mesons. These results are in good agreement with each other. For the calculation of the decay width $\tau \to {\pi }^{\prime }{\nu }_{\tau }$ extended Nambu - Jona-Lasinio model was used. The results are in satisfactory agreement with the experimental data. Numerical estimates for the constant $F_{\pi }$ and $F_{{\pi }^{\prime }}$ are also in satisfactory agreement with both the experimental values for $F_{\pi }$ and the results obtained by calculations on the lattice.

Comments: 14 pages, 4 figures