Single top quark production at the Fermilab Tevatron: Threshold resummation and finite-order soft gluon corrections

I present a calculation of threshold soft-gluon corrections to single top-quark production in $p\overline{p}$ collisions via all partonic processes in the $t$ and $s$ channels and via associated top quark and $W$ boson production. The soft-gluon corrections are formally resummed to all orders, and finite-order expansions of the resummed cross section are calculated through next-to-next-to-next-to-leading-order (NNNLO) at next-to-leading logarithmic (NLL) accuracy. Numerical results for single top-quark production at the Tevatron are presented, including the dependence of the cross sections on the top-quark mass and on the factorization and renormalization scales. The threshold corrections in the $t$ channel are small while in the $s$ channel they are large and dominant. Associated $tW$ production remains relatively minor due to the small leading-order cross section even though the $K$ factors are large.