Measurement of $\bm{\sigma (p \bar p \to Z) \cdot}$Br$\bm{(Z \to \tau \tau)}$ at $\bm{\sqrt{s}=}$1.96 TeV

We present a measurement of the cross section for $Z$ production times the branching fraction to $\tau$ leptons, $\sigma \cdot$Br$(Z\to \tau^+ \tau^-)$, in $p \bar p$ collisions at $\sqrt{s}=$1.96 TeV in the channel in which one $\tau$ decays into $\mu \nu_{\mu} \nu_{\tau}$, and the other into $\rm {hadrons} + \nu_{\tau}$ or $e \nu_e \nu_{\tau}$. The data sample corresponds to an integrated luminosity of 226 pb$^{-1}$ collected with the D{\O}detector at the Fermilab Tevatron collider. The final sample contains 2008 candidate events with an estimated background of 55%. From this we obtain $\sigma \cdot$Br$(Z \to \tau^+ \tau^-)=237 \pm 15$(stat)$\pm 18$(sys)$ \pm 15$(lum) pb, in agreement with the standard model prediction.