τ−→π−γντ as a source of background on the lepton-flavour violating decay τ−→μ−γ

We calculate the decay of τ−→π−γντ in the framework of Resonance Chiral Theory (RχT). By demanding the high energy constraints from QCD on the related form factors, we could predict the various physical observables of τ−→π−γντ without any free parameter. Our results 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 already been detected at the heavy-flavour factories. Another interesting subject we have studied based on our calculation of the decay τ−→π−γντ is the experimental background estimation of the lepton flavour violation process τ−→μ−γ. We point out that although the description of radiation that PHOTOS provides -which has been used by BaBar and Belle collaborations to estimate this source of background- is in excellent agreement with the theoretical expectations in the low energy region in τ−→π−γντ decay, this is not the case in the high energy region, precisely where it is easier that this decay mimics the process τ−→μ−γ.