Search for Scalar and Vector Third Generation Leptoquarks with one $\tau$ Decaying to a Muon

At Run II of the Fermilab Tevatron, the CDF experiment provides good sensitivity for either discovery or setting limits on 3rd generation scalar and vector leptoquark ($LQ_3$) pair-production, where each leptoquark decays $LQ_3 \to \tau b$. The estimated cross section at the Tevatron for this process is 1 pb for scalar (vector) $LQ_3$ masses of 135 ($\sim$200, depending on coupling) GeV/c$^2$. We perform a search for such production in the $(\tau \to \mu) + \tau_h$ channel using about 400 pb$^{-1}$ of data taken at $\sqrt{s}$ = 1.96 TeV.