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We report on the calculation of the threshold soft function for heavy quarkpair production in e+ e- annihilation at two-loop order. Our main result is ageneralization of the familiar Drell-Yan threshold soft function to the case ofnon-zero primary quark mass. We set up a framework based on the method ofdifferential equations which allows for the straightforward calculation of thebare soft function to arbitrarily high orders in the dimensional regularizationparameter. Remarkably, we find that we can obtain the bare two-loop Drell-Yansoft function from the heavy quark soft function to the order in epsilonrequired for a two-loop calculation by making simple replacements. We expectthat our results will be of use, both as an important input for precisionphysics calculations at linear colliders and, more formally, as a first steptowards a better understanding of the connection between vacuum matrix elementsof massive soft Wilson lines and vacuum matrix elements of massless soft Wilsonlines.

The two-loop soft function for heavy quark pair production at future linear colliders