Sequential discontinuities of Feynman integrals and the monodromy group
Jacob Bourjaily (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen Ø, DK-2100, Denmark, Institute for Gravitation and the Cosmos, Department of Physics, Pennsylvania State University, University Park, PA, 16892, USA); Holmfridur Hannesdottir (Department of Physics, Harvard University, Cambridge, MA, 02138, USA); Andrew McLeod (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen Ø, DK-2100, Denmark); Matthew Schwartz (Department of Physics, Harvard University, Cambridge, MA, 02138, USA); Cristian Vergu (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen Ø, DK-2100, Denmark)
We generalize the relation between discontinuities of scattering amplitudes and cut diagrams to cover sequential discontinuities (discontinuities of discontinuities) in arbitrary momentum channels. The new relations are derived using time-ordered perturbation theory, and hold at phase-space points where all cut momentum channels are simultaneously accessible. As part of this analysis, we explain how to compute sequential discontinuities as monodromies and explore the use of the monodromy group in characterizing the analytic properties of Feynman integrals. We carry out a number of cross-checks of our new formulas in polylogarithmic examples, in some cases to all loop orders.
