Discontinuity calculus and applications to two-body coupled-channel scattering

TL;DR

This paper introduces a new mathematical method called discontinuity calculus to analyze the complex analytic structure of two-body coupled-channel scattering amplitudes, providing deeper insights into their Riemann surfaces and analytic continuation.

Contribution

The paper develops a novel discontinuity calculus framework for systematically studying the analytic structure of coupled-channel scattering amplitudes.

Findings

Enables systematic investigation of Riemann surface topology

Provides new tools for analyzing analytic continuation in quantum scattering

Offers a unified approach to coupled-channel scattering problems

Abstract

We present a novel method, termed discontinuity calculus, for computing discontinuities of complex functions. This framework enables a systematic investigation of both analytic continuation and the topological structure of Riemann surfaces. We apply this calculus to analyze the analytic continuation of partial-wave amplitudes in two-body coupled-channel scattering problems and discuss their uniformization of the corresponding Riemann surfaces. This methodology offers new perspectives and tools for analyzing coupled-channel scattering problems in quantum scattering theory.