A general algorithm to build mixed real and virtual antenna functions for higher-order calculations

• Published in: The journal of high energy physics Vol. 2023; no. 11; pp. 179 - 43
• Main Authors: Braun-White, Oscar, Glover, Nigel, Preuss, Christian T.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 24.11.2023; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Antennas; Automation; Classical and Quantum Gravitation; Elementary Particles; High energy physics; Higher-Order Perturbative Calculations; Large Hadron Collider; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Radiation; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Subtraction; Automation; Higher-Order Perturbative Calculations
• ISSN: 1029-8479; 1126-6708; 1127-2236; 1029-8479
• DOI: 10.1007/JHEP11(2023)179

A bstract The antenna-subtraction technique has demonstrated remarkable effectiveness in providing next-to-next-to-leading order in α s (NNLO) predictions for a wide range of processes relevant for the Large Hadron Collider. In a previous paper [1], we demonstrated how to build real-radiation antenna functions for any number of real emissions directly from a specified list of unresolved limits. Here, we extend this procedure to the mixed case of real and virtual radiation, for any number of real and virtual emissions. A novel feature of the algorithm is the requirement to match the antenna constructed with the correct unresolved limits to the other elements of the subtraction scheme. We discuss how this can be achieved and provide a full set of real-virtual NNLO antenna functions (together with their integration over the final-final unresolved phase space). We demonstrate that these antennae can be combined with the real-radiation antennae of ref. [1] to form a consistent NNLO subtraction scheme that cancels all explicit and implicit singularities at NNLO. We anticipate that the improved antenna functions should be more amenable to automation, thereby making the construction of subtraction terms for more complicated processes simpler at NNLO.