Limits on the production of narrow $t\overline{t}$ resonances in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$

We search for evidence of resonant top quark pair production in 955 ${\mathrm{pb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ recorded with the CDF II detector at the Fermilab Tevatron. For fully reconstructed candidate $t\overline{t}$ events triggered on leptons with large transverse momentum and containing at least one identified $b$-quark jet, we compare the invariant mass spectrum of $t\overline{t}$ pairs to the expected superposition of standard model $t\overline{t}$, non-$t\overline{t}$ backgrounds, and a simple resonance model based on a sequential $Z^{\prime }$ boson. We establish upper limits for $\sigma (p\overline{p}\to Z^{\prime })·Br(Z^{\prime }\to t\overline{t})$ in the $Z^{\prime }$ mass interval from $450\mathrm{GeV}/c^2$ to $900\mathrm{GeV}/c^2$. A topcolor leptophobic $Z^{\prime }$ is ruled out below $720\mathrm{GeV}/c^2$, and the cross section of any narrow $Z^{\prime }$-like state decaying to $t\overline{t}$ is found to be less than 0.64 pb at 95% C.L. for $M_{Z^{\prime }}$ above $700\mathrm{GeV}/c^2$.