$\tau^- \to \omega \pi^- \nu_\tau$ decay in R$\chi$T with tensor sources

We present a study of the $\tau^- \to \omega\pi^-\nu_\tau$ decay in the framework of low-energy effective field theory. By analyzing the $J^{PG}$ quantum numbers of the quark currents and the $\omega\pi$ final state, we find that only the Standard Model (SM) vector interaction and the non-standard tensor interaction can contribute to this decay. We construct the resonance chiral theory Lagrangian with external tensor sources and calculate both the vector and tensor form factors, with resonance couplings determined through QCD short-distance constraints, spectral function fitting, and chiral perturbation theory matching. The new physics (NP) effect is investigated in the spectral function and forward-backward asymmetry distributions. Our results show that the spectral function is dominated by the SM, while the forward-backward asymmetry, which can only arise from a non-zero tensor interaction, provides a sensitive probe of this NP effect. Future measurements at Belle II, Tera-Z, and STCF facilities are therefore strongly motivated.