Triple real-emission contribution to the zero-jettiness soft function at N3LO in QCD

Recently, we have presented the result for the zero-jettiness soft function at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD [1], without providing technical details of the calculation. The goal of this paper is to describe the most important element of that computation, the triple real-emission contribution. We present a detailed discussion of the many technical aspects of the calculation, for which a number of methodological innovations was required. Although some elements of the calculation were discussed earlier [2–6], this paper is intended to provide a complete summary of the methods used in the computation of the triple real-emission contribution to the soft function.