Resummation for $s$-channel single-top production

I present higher-order results for $s$-channel single-top-quark production that are derived from soft-gluon resummation. I show that the soft-gluon corrections provide the dominant contribution to the QCD corrections, and that they approximate very well the exact results through NNLO. Furthermore, approximate N$^3$LO corrections are computed by using the expansion of the resummed cross section to third order in the strong coupling. The calculation treats the final-state $b$-quarks as massless but I also show how to extend the formalism to the case of massive $b$-quarks. The higher-order corrections are large at LHC energies and they improve the theoretical accuracy.