Studies of τ^{-}→ηK^{-}ν_{τ} and τ^{-}→ηπ^{-}ν_{τ} at BABAR and a search for a second-class current

We report on analyses of tau lepton decays τ-→ηK-ντ and τ-→ηπ-ντ, with η→π+π-π0, using 470 fb-1 of data from the BABAR experiment at PEP-II, collected at center-of-mass energies at and near the Υ(4S) resonance. We measure the branching fraction for the τ-→ηK-ντ decay mode, B(τ-→ηK-ντ)=(1.42±0.11(stat)±0.07(syst))×10-4, and report a 95% confidence level upper limit for the second-class current process τ-→ηπ-ντ, B(τ-→ηπ-ντ)<9.9×10-5.