Threshold corrections in bottom and charm quark hadroproduction at next-to-next-to-leading order

We calculate threshold soft-gluon corrections to total cross sections and transverse momentum distributions for bottom and charm quark production in fixed target experiments, considering both pp and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\pi^- p$\end{document} interactions. We investigate the quality of the near-threshold soft-gluon approximation at next-to-leading order (NLO) and calculate next-to-next-to-leading order (NNLO) corrections through next-to-next-to-next-to-leading-logarithmic (NNNLL) accuracy, including some virtual terms. We find that the NNLO threshold corrections reduce the factorization and renormalization scale dependence of the cross sections.