Об интегралах по фазовому пространству с тета-функцией Хевисайда
В общем-то, это о КХД, но, возможно, там есть что-то полезное и для широких кругов...
On phase-space integrals with Heaviside functions: https://arxiv.org/abs/2111.13594
Daniel Baranowski, Maximilian Delto, Kirill Melnikov, Chen-Yu Wang
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.
Comments: 46 pages; 2 appendices; one ancillary file
On phase-space integrals with Heaviside functions: https://arxiv.org/abs/2111.13594
Daniel Baranowski, Maximilian Delto, Kirill Melnikov, Chen-Yu Wang
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.
Comments: 46 pages; 2 appendices; one ancillary file