Zero-Jettiness Soft Function to Third Order in Perturbative QCD

We present the high-precision result for the zero-jettiness soft function at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. At this perturbative order, the soft function is the last missing ingredient required for the computation of a hadronic color singlet production or a color singlet decay into two jets using the zero-jettiness variable as the slicing parameter. Furthermore, the knowledge of the N3LO soft function enables the resummed description of the thrust distribution in the process e+e−→hadrons through next-to-next-to-next-to-leading logarithmic order, which is important for the extraction of the strong coupling constant using this shape variable. On the methodological side, the complexity of the zero-jettiness variable forced us to develop a new semi-analytic method for phase-space integration in the presence of constraints parameterized through Heaviside functions which, hopefully, will be useful for further development of the N-jettiness slicing scheme.