Fixing the vector coupling constant $g_{\rho }=5.0$ in the NJL model and final-state interactions in processes $\rho \to e^{+}{e}^{-}[{\mu }^{+}{\mu }^{-}]$, $\rho \to {\pi }^{+}{\pi }^{-}$, $\tau \to {\pi }^{-}{\pi }^0{\nu }_{\tau }$, and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$

Abstract

The possibility to use the width of the decay $\rho \to e^{+}{e}^{-}$ to fix the input parameter $g_{\rho }=5.0$ of the $SU(2)\times SU(2)$ chiral-symmetric Nambu--Jona-Lasinio model is discussed. It is shown that for a consistent simultaneous description of the processes $\rho \to e^{+}{e}^{-}$, $\rho \to {\pi }^{+}{\pi }^{-}$, ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$, and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ can be constructed. Taking into account the interaction of pions in the final state appears to be important. The obtained theoretical results for the considered processes are in a satisfactory agreement with experimental data.

4 pages, 6 figures, misprints are corrected