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

Abstract

We calculate the decay of ${\tau }^{-}\to {\pi }^{-}\gamma {\nu }_{\tau }$ in the framework of Resonance Chiral Theory ($R\chi T$). By demanding the high energy constraints from QCD on the related form factors, we could predict the various physical observables of ${\tau }^{-}\to {\pi }^{-}\gamma {\nu }_{\tau }$ 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 ${\tau }^{-}\to {\pi }^{-}\gamma {\nu }_{\tau }$ is the experimental background estimation of the lepton flavour violation process ${\tau }^{-}\to {\mu }^{-}\gamma$. 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 ${\tau }^{-}\to {\pi }^{-}\gamma {\nu }_{\tau }$ decay, this is not the case in the high energy region, precisely where it is easier that this decay mimics the process ${\tau }^{-}\to {\mu }^{-}\gamma$.

Comments: 6 pages, 7 figures. Contribution to the Proceedings of the TAU10 Conference held in Manchester, 13-17 September 2010. To be published in Nucl. Phys. Proc. Suppl