Sequential Discontinuities of Feynman Integrals and the Monodromy Group

TL;DR

This paper extends the understanding of Feynman integrals by relating sequential discontinuities to monodromy groups, providing new formulas and methods to analyze their analytic structure at all loop orders.

Contribution

It introduces a general framework for computing sequential discontinuities of Feynman integrals using monodromy groups, applicable to arbitrary momentum channels and all loop orders.

Findings

Derived new relations for sequential discontinuities using time-ordered perturbation theory.

Explained how to compute sequential discontinuities as monodromies of Feynman integrals.

Validated formulas through cross-checks in polylogarithmic examples, including all loop orders.

Abstract

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.