NNLO soft functions for heavy-quark pair production at hadron colliders
We generalise the SoftSERVE framework for the automated computation of soft functions involving final-state heavy quarks in back-to-back kinematics up to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our algorithm employs suitable phase-space parameterisations for both massive and mixed massless-massive contributions, allowing for an efficient numerical evaluation. Focusing on SCET$_\mathrm{I}$ observables that satisfy non-Abelian exponentiation, we present explicit results for the 0-jettiness soft function in hadronic top-quark pair production in the form of two-dimensional grids. We describe the renormalisation procedure in detail and discuss the singular behaviour of the tripole colour correlations in the threshold limit.