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 pp̄ 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.