2021/11/26 by Daniel Baranowski, Maximilian Delto, Kirill Melnikov +1
Mathematics · Physics and Astronomy · #Algorithm #Computation #Function (biology) #Heaviside step function #High-Energy Particle Collisions Research #Mathematical analysis #Mathematics #Observable #Particle physics #Particle physics theoretical and experimental studies #Parton #Perturbation theory (quantum mechanics) #Perturbative QCD #Phase space #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Unitarity #hep-ph
paper · pdf · doi:10.1007/jhep02(2022)081
46 pages; 2 appendices; one ancillary file
arxiv created 2021/11/26 · openalex publication_date 2022/02/01 · arxiv updated 2022/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 θ-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.