Decays $\tau \to \pi \pi \eta\nu_\tau$ and $\tau \to \pi\eta\eta\nu_\tau$ in the extended Nambu-Jona-Lasinio model

In the framework of the extended Nambu-Jona-Lasinio model, the processes $\tau \to \pi \pi \eta(\eta')\nu_\tau$ and $\tau \to \pi\eta\eta(\eta')\nu_\tau$ are considered taking into account mesons in the ground and first radially excited intermediate states. It is shown that in the processes $\tau \to \pi \pi \eta(\eta')\nu_\tau$ the vector channel is dominant, and in the processes $\tau \to \pi\eta\eta(\eta')\nu_\tau$ the main contribution is given by the axial vector channel. The scalar meson $a_0$ plays a dominant role in processes with two $\eta$-mesons in the final state. The significance of the relative phase between the ground and first radially excited states for these processes is shown. The obtained results for the $\tau \to \pi \pi \eta\nu_\tau$ process are in satisfactory agreement with the recent experimental data from BaBar and CMD-3, which differ from the averaged values given in the PDG tables.

M.K. Volkov, A.A. Pivovarov, K. Nurlan · 2025