Breaking of G-parity or new weak (second class) currents can be responsible for τ^- →η^(')π^- ν_τ decays. Forthcoming measurements of τ lepton properties at the Belle II experiment will be able to measure this decay channel for the first time. Isolating new physics contributions from the measured rates will require a careful evaluation of G-parity breaking contributions. Here we evaluate the one-loop contribution to τ^- →η^(')π^- ν_τ decays induced by the emission of two virtual photons and its

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... later conversion into an η^(') meson. As expected, this contribution is very small and may be relevant only for new physics searches contributing at the 10^-4 level to the decay rate of τ^- →η^(')π^- ν_τ .