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We present a search for a new narrow, spin-1, high mass resonance decaying to$\mu^+\mu^- + X $, using a matrix element based likelihood and a simultaneousmeasurement of the resonance mass and production rate. In data with 4.6fb$^{-1}$ of integrated luminosity collected by the CDF detector in $p\bar{p}$collisions at $\sqrt{s}=1960$ GeV, the most likely signal cross section isconsistent with zero at 16\% confidence level. We therefore do not observeevidence for a high mass resonance, and place limits on models predictingspin-1 resonances, including $M > 1071$ GeV/$c^2$ at 95\% confidence level fora $Z'$ boson with the same couplings to fermions as the $Z$ boson.

Search for High Mass Resonances Decaying to Muon Pairs in $\sqrt{s}=1.96$ TeV $p\bar{p}$ Collisions