Search for Pair Production of Scalar Top Quarks Each Decaying to a $\tau$ Lepton and a $b$ Quark in 1.96-TeV $p\bar{p}$ Collisions

We present the results of a search for pair production of scalar top quarks ($\tilde{t}_{1}$) in an {\it R}-parity violating supersymmetry scenario, in 322 pb$^{-1}$ of $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV, collected by the Collider Detector at Fermilab (CDF). We assume each stop quark always decays into a $\tau$ lepton and a $b$ quark, and that the final state is either an electron or a muon from the leptonic $\tau$ decay, a hadronically decaying $\tau$ lepton, and two or more jets. Two candidate events pass our final selection criteria, consistent with the expectation from standard model sources. We set a 95\% confidence level limit $m(\tilde{t}_{1}) > 151$ GeV comparing with the next-to-leading order cross section. This limit is also fully applicable to the case of the third generation scalar leptoquark ($LQ_3$) assuming a 100\% branching ratio for the $LQ_3 \to \tau b$ decay mode.