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At high values of the pair invariant mass the differential cross section fortop-quark pair production at hadron colliders factorizes into soft, hard, andfragmentation functions. In this paper we calculate thenext-to-next-to-leading-order (NNLO) corrections to the soft function appearingin this factorization formula, thus providing the final piece needed toevaluate at NNLO the differential cross section in the virtual plus softapproximation in the large invariant-mass limit. Technically, this amounts toevaluating the vacuum expectation value of a soft Wilson loop operator builtout of light-like Wilson lines for each of the four partons participating inthe hard scattering process, with a certain constraint on the total energy ofthe soft radiation. Our result turns out to be surprisingly simple, because inthe sum of all graphs the three and four parton contributions multiply colorstructures whose coefficients are governed by the non-abelian exponentiationtheorem.

The NNLO soft function for the pair invariant mass distribution of boosted top quarks