$τ^{-} \to π^{-} π^{0} ν_τ$ decay in the extended NJL model

The width of the decay $τ^{-} \to π^{-} π^{0} ν_τ$ was calculated in the extended NJL model. Contact interaction of $W$ boson with pion pair as well as the contribution of the $ρ$ mesons in ground and first radial-exited states are taken into account. The sum of the contact diagram and diagram with intermediate $ρ$ meson in the ground state leads to the result which coincides with the result of the vector-dominance model. Our results are in satisfactory agreement with experimental data.

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