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^2(2theta)-Delta m^2 plane which includes sin^2(2theta)<3.3 x 10^{-4} at large Delta m^2 and Delta m^2 < 0.7 eV^2/c^4 at sin^2(2theta)=1. The corresponding contour in the nu_e->nu_tau oscillation hypothesis results in sin^2(2theta)<1.5 x 10^{-2} at large Delta m^2 and Delta m^2 < 5.9 eV^2/c^4 at sin^2(2theta)=1. We also derive limits on effective couplings of the tau lepton to nu_mu or nu_e.