Transmuting off-shell CHY integrals in the double-cover framework

• Published in: The European physical journal. C, Particles and fields Vol. 80; no. 11; pp. 1 - 14
• Main Authors: Zhou, Kang, Zhou, Guo-Jun
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-11-2020; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Amplitudes; Astronomy; Astrophysics and Cosmology; Color; Decoupling; Differential equations; Elementary Particles; Gravity; Hadrons; Heavy Ions; Integrals; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; String Theory
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-020-08624-1

In this paper, by defining off-shell amplitudes as off-shell CHY integrals, and redefining the longitudinal operator, we demonstrate that the differential operators which link on-shell amplitudes for a variety of theories together link off-shell amplitudes in a similar manner. Based on the algebraic property of the differential operator, we also generalize three relations among color-ordered on-shell amplitudes, including the color-ordered reversed relation, the photon decoupling relation, the Kleiss–Kuijf relation, to off-shell ones. The off-shell CHY integrals are chosen to be in the double-cover framework, thus, as a by product, our result also provides a verification for the double-cover construction.