Tension between $e^{+}{e}^{-}\to \eta {\pi }^{-}{\pi }^{+}$ and ${\tau }^{-}\to \eta {\pi }^{-}{\pi }^0{\nu }_{\tau }$ data and non-standard interactions

Abstract

We show the discrepancy between the isospin-rotated $e^{+}{e}^{-}\to \eta {\pi }^{-}{\pi }^{+}$ cross-section -- measured by various collaborations -- and the Belle ${\tau }^{-}\to \eta {\pi }^{-}{\pi }^0{\nu }_{\tau }$ spectrum, which cannot be explained by heavy new physics non-standard interactions. We give for the first time the framework needed to study these beyond the standard model contributions in three-meson tau decays.

Comments: 17 pages, 5 figures, there is an ancillary Mathematica notebook file where the terms of the unpolarized squared amplitude can be consulted or modified. This is the version accepted for publication in Phys.Rev. D