Final NOMAD results on $\nu_{\mu} \to \nu_{\tau}$} and $\nu_e \to \nu_{\tau}$ oscillations including a new search for $\nu_{\tau}$ appearance using hadronic $\tau$ decays

Results from the $\nu_{\tau}$ appearance search in a neutrino beam using the full NOMAD data sample are reported. A new analysis unifies all the hadronic $\tau$ decays, significantly improving the overall sensitivity of the experiment to oscillations. The ``blind analysis" of all topologies yields no evidence for an oscillation signal. In the two-family oscillation scenario, this sets a 90\% C.L. allowed region in the $\sin^22\theta_{\mu\tau} - \Delta m^2$ plane which includes $\sin^22\theta_{\mu\tau}\ \ 3.3\times10^{-4}$ at large $\Delta m^2$ and $\Delta m^2 0.7$ eV$^2$/$c^4$ at $\sin^22\theta_{\mu \tau}=1$. The corresponding contour in the $\nuenutau$ oscillation hypothesis results in $\sin^22\theta_{e\tau}\ \ 1.5\times10^{-2}$ at large $\Delta m^2$ and $\Delta m^2 5.9$ eV$^2$/$c^4$ at $\sin^22\theta_{e \tau}=1$. We also derive limits on effective couplings of the $\tau$ lepton to \numu or \nue. \end{abstract} \begin{keyword} appearance, neutrino mass, neutrino oscillations \end{keyword} \end{frontmatter}