Effective field theory approach to lepton number violating tau decays

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