Search for a heavy fourth generation $t\prime$\ quark in Lepton plus Jets channel at CDF

We present a search for a heavy $t^\prime$\ quark decaying to $Wq$\ final states in $p\bar{p}$\ collisions at $\sqrt{s}$ = 1.96 TeV, using 340 pb$^{-1}$\ of data collected by the CDFII detector at the Fermilab Tevatron. We select events with a high transverse momentum electron or muon, 4 or more jets, and missing $E_T$. We use the observed total transverse energy ($H_T$) spectrum and an artificial neural network to discriminate the $t^\prime$\ signal from background, and obtain limits on a $t^\prime$\ cross section as a function of hypothetical $t^\prime$\ mass. In addition to the status of the current search, we will present the prospects for the future.