Effective field theory approach to lepton number violating τ decays *

We continue our endeavor to investigate lepton number violating (LNV) processes at low energy in the framework of effective field theory (EFT). In this work we study LNV tau decays $\tau^+\rightarrow \ell^-P_i^{+}P_j^{+}$, where $\ell=e,~\mu$ and $P^+_{i,j}$ are lowest-lying charged pseudoscalars $\pi^+,~K^+$. analyze dominant contributions a series EFTs from high scales, namely, standard model (SMEFT), low-energy (LEFT), chiral perturbation ($\chi$PT). The decay branching ratios expressed terms Wilson coefficients dimension-five -seven operators SMEFT hadronic constants. These involve first second generations quarks all leptons thus cannot be explored such as nuclear neutrinoless double or kaon decays. Unfortunately, current experimental upper limits on too weak set useful constraints those coefficients. Or, if assume new physics scale is larger than 1 TeV, well below bounds. also estimate uncertainties incurred applying $\chi$PT $\tau$ by computing one-loop logarithms attempt improve convergence employing dispersion relations short-distance part amplitudes.