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We calculate the decay of $\tau^-\to\pi^-\gamma\nu_\tau$ in the framework ofResonance Chiral Theory ($R\chi T$). By demanding the high energy constraintsfrom QCD on the related form factors, we could predict the various physicalobservables of $\tau^-\to\pi^-\gamma\nu_\tau$ without any free parameter. Ourresults show that for a realistic cut on the photon energy (around $100$ MeV)this mode gives a branching ratio of roughly $0.1%$ that should have alreadybeen detected at the heavy-flavour factories. Another interesting subject wehave studied based on our calculation of the decay$\tau^-\to\pi^-\gamma\nu_\tau$ is the experimental background estimation of thelepton flavour violation process $\tau^- \to \mu^- \gamma$. We point out thatalthough the description of radiation that PHOTOS provides -which has been usedby BaBar and Belle collaborations to estimate this source of background- is inexcellent agreement with the theoretical expectations in the low energy regionin $\tau^-\to\pi^-\gamma\nu_\tau$ decay, this is not the case in the highenergy region, precisely where it is easier that this decay mimics the process$\tau^-\to\mu^-\gamma$.

$\tau^-\to\pi^-\gamma\nu_\tau$ as a source of background on the Lepton Flavour Violating decay $\tau^-\to\mu^-\gamma$