On phase-space integrals with Heaviside functions

Abstract

We discuss peculiarities that arise in the computation of real-emission contributions to observables that contain Heaviside functions. A prominent example of such a case is the zero-jettiness soft function in SCET, whose calculation at next-to-next-to-next-to-leading order in perturbative QCD is an interesting problem. Since the zero-jettiness soft function distinguishes between emissions into different hemispheres, its definition involves $\theta$-functions of light-cone components of emitted soft partons. This prevents a direct use of multi-loop methods, based on reverse unitarity, for computing the zero-jettiness soft function in high orders of perturbation theory. We propose a way to bypass this problem and illustrate its effectiveness by computing various non-trivial contrbutions to the zero-jettiness soft function at NNLO and N3LO in perturbative QCD.

46 pages; 2 appendices; one ancillary file

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Cited by in corpus (6)

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• Same-hemisphere three-gluon-emission contribution to the zero-jettiness soft function at N3LO QCD
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
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• Thrust distribution in Higgs decays up to the fifth logarithmic order
• Double-Real-Virtual and Double-Virtual-Real Corrections to the Three-Loop Thrust Soft Function