First Observation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi><mml:mo>→</mml:mo><mml:mn>3</mml:mn><mml:mi>π</mml:mi><mml:mi>η</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>τ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi><mml:mo>→</mml:mo><mml:mspace/><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">f</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mi>π</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>τ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Decays

We have observed new channels for $\ensuremath{\tau}$ decays with an $\ensuremath{\eta}$ in the final state. We study 3-prong tau decays, using the $\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}3{\ensuremath{\pi}}^{0}$ decay modes and 1-prong decays with two ${\ensuremath{\pi}}^{0}$'s using the $\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ channel. The measured branching fractions are $B({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}\ensuremath{\eta}{\ensuremath{\nu}}_{\ensuremath{\tau}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({3.4}_{\ensuremath{-}0.5}^{+0.6}\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and $B({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}2{\ensuremath{\pi}}^{0}\ensuremath{\eta}{\ensuremath{\nu}}_{\ensuremath{\tau}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(1.4\ifmmode\pm\else\textpm\fi{}0.6\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. We observe clear evidence for ${f}_{1}\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\pi}\ensuremath{\pi}$ substructure and measure $B({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{f}_{1}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({5.8}_{\ensuremath{-}1.3}^{+1.4}\ifmmode\pm\else\textpm\fi{}1.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. We have also searched for ${\ensuremath{\eta}}^{\ensuremath{'}}(958)$ production and obtain 90% C.L. upper limits $B({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\eta}}^{\ensuremath{'}}{\ensuremath{\nu}}_{\ensuremath{\tau}})&lt;7.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $B({\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\eta}}^{\ensuremath{'}}{\ensuremath{\nu}}_{\ensuremath{\tau}})&lt;8.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$.