Processes ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$ and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ in the chiral NJL model with final state interactions taken into account

Abstract

The processes ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$ and $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ are considered within the chiral Nambu--Jona-Lasinio model with taking into account the pion final state interactions beyond the leading $1/N_c$ approximation. The contribution of the loop correction caused by a $\rho$ meson exchange between the pions, which gives the main contribution in the P-wave channel, is caclulated. The results for both processes are in a satisfactory agreement with experimental data.

Comments: 8 pages, 8 figures, formula (10) is corrected, numerical results are slightly changed