Two-loop soft anomalous dimensions for single top quark associated production with a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>W</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>or<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>H</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>

I present results for the two-loop soft anomalous dimensions for associated production of a single top quark with a $W$ boson or a charged Higgs boson. The calculation uses expressions for the massive cusp anomalous dimension, which are presented in different forms, and it allows soft-gluon resummation at next-to-next-to-leading-logarithm (NNLL) accuracy. From the NNLL resummed cross section I derive approximate NNLO cross sections for $bg\ensuremath{\rightarrow}t{W}^{\ensuremath{-}}$ and $bg\ensuremath{\rightarrow}t{H}^{\ensuremath{-}}$ at LHC energies of 7, 10, and 14 TeV.

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