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arXiv · 2610.32139

Coupled-channel extension of the effective-range expansion with left-hand cut

Bing Wu·Wen-Jia Wang·Meng-Lin Du·Feng-Kun Guo·Hao-Jie Jing
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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.

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Bing Wu, Wen-Jia Wang, Meng-Lin Du, Feng-Kun Guo, Hao-Jie Jing. 2026-10-23. Coupled-channel extension of the effective-range expansion with left-hand cut. https://arxiv.org/abs/2610.32139

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