We present the results of a search for pair production of a heavy top-like (t) quark decaying to Wq final states using data corresponding to an integrated luminosity of 5.6 fb-1 collected by the CDF II detector in pp collisions at {surd}s = 1.96 TeV. We perform parallel searches for t to Wb and t to Wq (where q is a generic down-type quark) in events containing a lepton and four or more jets. By performing a fit to the two-dimensional distribution of total transverse energy versus reconstructed t quark mass, we set upper limits on the t bar{t} production cross section and exclude a standard model fourth-generation t quark decaying to W b (W q) with mass below 358 (340) GeV/c2 at 95% CL.
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