The general problem of including these states in ChPT has been addressed in [@Ecker89; @Pich89]. Notice, that there is a different interpretation of $a_1(1260)$ and $f_1(1285)$. Assuming that these resonances not belong to the large-$N_c$ ground state of QCD (i.e. the $qq\bar q\bar q$ states), one can generate them in ChPT by implementing unitarity in coupled-channels (see, for instance, [@Lutz04; @Roca05; @Zhou14; @Xie15] and references therein). This approach can provide an alternative platform for studying of the $\tau\to f_1\pi^-\nu_\tau$ decay.

Over last years, not much has been done with respect to the theoretical study of this particular mode of the $\tau$-decay. One can indicate just a few attempts. This is an approach based on a meson dominance model considered in [@Calderon13], which leads to a strong disagreement with the data of BABAR Collaboration, namely the calculated branching ratio Br$(\tau \to f_1\, \pi^{-} \nu_{\tau})=1.3\times 10^{-4}$ is three times less of the experimental value Br$(\tau \to f_1\, \pi^{-} \nu_{\tau})=(3.9\pm 0.5)\times 10^{-4}$ reported by the Particle Data Group [@Patrignani16]. More encouraging but relatively old result, Br$(\tau \to f_1\, \pi^{-} \nu_{\tau})=2.91\times 10^{-4}$, gives the model [@Li97] based on the hypothesis of $a_1(1260)$-meson dominance.

Both ideas are naturally realized under the framework of the Nambu 