Search for Flavor Changing Neutral Currents in Top Quark Decays at CDF

In the CDF~II detector at the Fermilab Tevatron, $t\bar{t}$ pairs are produced in $p\bar{p}$ collisions at 1.96 TeV. We have performed a search for the flavor-changing neutral current (FCNC) decay of the top quark $t \rightarrow Zq$. This decay is extremely rare in the standard model, and any signal at the Tevatron would be an indication of new physics. For the summer 2007 conferences, using 1.12\,fb$^{-1}$ of data we presented the world's best limit on the branching fraction $\mathcal{B}$ $\left (t \rightarrow Zq\right)$ of 10.6\% at 95\% C.L. In this talk, we show the updated analysis with 1.9\,fb$^{-1}$ of data. We discriminate signal from background by exploring kinematic constraints present in FCNC events. We construct a mass $\chi^2$ variable and fit templates to the data, taking into account shape systematic uncertainties of the $\chi^2$ distribution. Using a Feldman-Cousins limit technique, we expect to set an improved limit on the branching fraction $\mathcal{B}$ $\left (t \rightarrow Zq \right)$.