Estimate of the branching fraction ${\tau }^{-}\to \eta {\pi }^{-}{\nu }_{\tau }$, the $a_0^{-}(980)$, and non-standard weak interactions

Abstract

We consider the ``second-class current'' decay ${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ from several points of view. We first focus on the decay rate as expected within standard weak interaction and QCD due to isospin violation. The decay contributions divide into $P$- and $S$-wave parts. The former can be reliably estimated using the $\rho \eta \pi$ coupling inferred from the rates and Dalitz-plot distributions of $\eta \to 3\pi$ decays. The somewhat larger $S$-wave part, which was previously computed using chiral perturbation theory, is estimated from a simple $\bar{q}q$ model. Both estimates of the $S$-wave part depend on whether the $a_0(980)$ scalar particle is a $\bar{q}q$ or some other (4-quark) state. Finally, we discuss genuinely new, non-$V-A$ scalar weak interactions. The ${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ decay provides information on this question, which nicely complements that from precision $\beta$ decay experiments. % In summary, we discuss the possible implications of putative values of the branching fraction $\mathcal{B}({\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau })$. In the case of larger values, in particular of the $S$-wave part, not only will detection of the decay be more likely and more reliable, its implications will be more far-reaching and interesting.

arXiv comment13 pages

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Cited by in corpus (14)

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• Effective-field theory analysis of the ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$ decays
• The decays ${\rho }^{-}\to \eta {\pi }^{-}$ and ${\tau }^{-}\to \eta ({\eta }^{\prime }){\pi }^{-}\nu$ in the NJL model
• Effective-field theory analysis of the ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }$ decays
• On meson dominance in the `second class' tau \to eta pi nu_tau decay
• Estimate of the Branching Fraction of tau --> pi eta' nu_tau
• On the branching ratio of the "second class" tau --> eta' pi nu_tau decay
• Long-lived light neutralinos at Belle II
• ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }\gamma$ decays as backgrounds in the search for second class currents
• G-parity breaking in ${\tau }^{-}\to {\eta }^{(\prime )}{\pi }^{-}{\nu }_{\tau }$ decays induced by the ${\eta }^{(\prime )}\gamma \gamma$ form factor
• The second-class current decays $\tau \to \pi \eta ({\eta }^{\prime }){\nu }_{\tau }$ in the NJL model including the interaction of mesons in the final state
• Towards the (Mexican) discovery of second class currents at Belle-II
• Dispersive evaluation of the second-class amplitude $\tau \to \eta \pi {\nu }_{\tau }$ in the standard model
• ${\tau }^{-}\to {\pi }^{-}\eta {\nu }_{\tau }$ decay induced by QED one-loop effects