${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ decay induced by QED one-loop effects

Abstract

The ${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ decay is forbidden in the Standard Model in the limit of exact $G$-parity, it becomes a rare decay due to isospin symmetry breaking and it is very sensitive to the effects of effective scalar interactions. Since the parameters driving isospin breaking, $(m_d-m_u)/(m_s-\bar{m})$ and $\alpha$, are of the same order, one may expect their $G$-parity breaking effects in this decay can be of similar magnitudes. In this work, we evaluate the effects of isospin-breaking amplitudes originated from a virtual photon at one-loop in a resonance dominance model to describe photon-hadron interactions. We find that these effects can shift the leading SM predictions based on the $u-d$ quark mass difference by roughly $12\%$, and should be taken into consideration in a precision comparison of theory and experiment in order to draw meaningful conclusions on New Physics. The effects in the rate of the analogous ${\tau }^{-}\to {\pi }^{-}{\eta }^{\prime }{\nu }_{\tau }$ decay can be larger ($\sim$ $78\%$), under the approximations assumed in this model.

Comments: 22 pages, 1 figure, 4 tables