Scattering amplitudes with massive fermions using BCFW recursion

We study the QCD scattering amplitudes for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\bar{q}q\to{gg}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\bar{q}q\to{ggg}$\end{document} where q is a massive fermion. Using a particular choice of massive fermion spinor we derive compact expressions for the partial spin amplitudes for the 2→2 process. We then investigate the corresponding 2→3 amplitudes using the BCFW recursion technique. For the helicity conserving partial amplitudes we present new expressions, but we were unable to treat the helicity-flip amplitudes recursively, except for the case where all the gluon helicities are the same. We therefore evaluate the remaining partial amplitudes using standard Feynman diagram techniques.