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

We present a search for a new narrow, spin-1, high mass resonance decaying to $\mu^+\mu^- + X $, using a matrix element based likelihood and a simultaneous measurement of the resonance mass and production rate. In data with 4.6 fb$^{-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 is consistent with zero at 16\% confidence level. We therefore do not observe evidence for a high mass resonance, and place limits on models predicting spin-1 resonances, including $M > 1071$ GeV/$c^2$ at 95\% confidence level for a $Z'$ boson with the same couplings to fermions as the $Z$ boson.