Next-to-Leading Order Corrections to Single Top Quark Production and Decay at the Tevatron: 2. $t$-channel Process

We present a study of the $t$-channel mode of single top quark production at the upgraded Tevatron $p\bar{p}$ collider, including the next-to-leading order (NLO) QCD corrections to the production and the decay of a single top quark. The narrow width approximation was adopted in order to preserve the spin of the top quark in its production and decay. We discuss the effects of different $O({\alpha }_s)$ contributions on the inclusive cross section as well as various kinematic distributions after imposing the relevant cuts to select $t$-channel single top signal events.