$τ^-\toπ^-γν_τ$ as a source of background on the Lepton Flavour Violating decay $τ^-\toμ^-γ$

We calculate the decay of $τ^-\toπ^-γν_τ$ 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 $τ^-\toπ^-γν_τ$ 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 $τ^-\toπ^-γν_τ$ is the experimental background estimation of the lepton flavour violation process $τ^- \to μ^- γ$. 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 $τ^-\toπ^-γν_τ$ decay, this is not the case in the high energy region, precisely where it is easier that this decay mimics the process $τ^-\toμ^-γ$.

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