We report on a search for charged massive resonances decaying to top ($t$) and bottom ($b$) quarks in the full data set of proton-antiproton collisions at center-of-mass energy of $sqrt{s} = 1.96$ TeV collected by the CDF~II detector at the Tevatron, corresponding to an integrated luminosity of 9.5 $fb^{-1}$. No significant excess above the standard model (SM) background prediction is observed. We set 95% Bayesian credibility mass-dependent upper limits on the heavy charged particle production cross section times branching ratio to $t b$. Using a SM extension with a $W^{prime}$ and left-right-symmetric couplings as a benchmark model, we constrain the $W^{prime}$ mass and couplings in the 300 to 900 GeV/$c^2$ range. The limits presented here are the most stringent for a charged resonance with mass in the range 300 -- 600 GeV/$c^2$ decaying to top and bottom quarks.
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