N³LO soft-gluon corrections in single-particle-inclusive kinematics and H^+ H^- production

We calculate the complete soft-gluon corrections for the production of colorless final states through N³LO in single-particle-inclusive kinematics. We present explicit analytical results and use them to study higher-order QCD corrections for the production of a heavy charged Higgs pair (H^+ H^-) via quark-antiquark annihilation in the Two-Higgs-Doublet Model at LHC energies. We calculate the NNLO soft-gluon and virtual QCD corrections as well as the N³LO soft-gluon corrections to the total cross section and the charged-Higgs rapidity distribution. This is the first calculation of complete N³LO soft-gluon corrections for a process in single-particle-inclusive kinematics, and the results can be applied to other processes with colorless final states.