In this work we consider the most general analysis
of $\tau\rightarrow (K\pi)^{-} \nu_{\tau}$ decays within an effective field theory description of heavy new physics (NP) including SM operators up to dimension six with massless neutrinos. All hadron form factors are built exploiting chiral symmetry, dispersion relations and (lattice) data. Within this framework we:
i) confirm that it is impossible to understand the BaBar anomaly in the CP asymmetry measurement (we find an upper bound for the NP contribution slightly larger than in Phys. Rev. Lett. 120 (2018) no.14, 141803, but still irrelevant compared to the experimental uncertainty by four orders of magnitude approximately);
ii) first show that the anomalous bump measured in the Belle experiment for the $K_S\pi^-$ invariant mass distribution at low energies is also impossible to understand in the presence of heavy NP;
iii) first bind the heavy NP effective couplings using $\tau^-\to(K\pi)^-\nu_\tau$ decays and show that they are competitive with those found in hyperon semileptonic decays (but clearly not with those obtained for non-standard scalar interactions in Kaon (semi)leptonic decays).
Finally to have a good control of potential new physics effects, we study carefully the SM contribution, namely, we compare the SM predictions with possible deviations caused by NP in three different observables: a couple of Dalitz plot distributions, in the forward-backward asymmetry and in the di-meson invariant mass distribution.