Higher-order soft gluon corrections in single top quark production at the CERN LHC

I present a calculation of soft-gluon corrections to single top-quark production in pp collisions at the LHC via the standard model partonic processes in the t and s channels and associated top quark and W boson production. Higher-order soft-gluon corrections through next-to-next-to-next-to-leading order (NNNLO) are calculated at next-to-leading logarithmic (NLL) accuracy. The soft-gluon corrections in the s channel and in tW production are large and dominant, while in the t channel they are not a good approximation of the complete QCD corrections.