Year: 2026
Type: preprint
Abstract: We generalize the recently proposed effective-range expansion with a left-hand cut [Phys. Rev. Lett. 135, 011903 (2025)] to a coupled-channel framework. By systematically analyzing the singularity structure of the $S$-wave coupled-channel one-particle exchange (OPE) potential under various mass configurations, we derive an analytical parametrization of the coupled-channel scattering amplitude that incorporates the OPE left-hand cut for multiple channels. Taking the two-channel case as an illustration, we benchmark this parametrization against the Lippmann--Schwinger equation (LSE) by comparing the amplitudes and their inverses at different expansion orders. Even at the lowest order, with only six parameters, the coupled-channel parametrization faithfully reproduces the LSE results and enables precise extraction of the coupling constants, demonstrating its reliability for two-body coupled-channel scattering problems involving particle exchange.
Source: arXiv (Cornell University)
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223667735