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

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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Cite

BibTeX RIS

BibTeX

@misc{wu2026coupledchannel,
  title = {{Coupled-channel extension of the effective-range expansion with left-hand cut}},
  author = {Bing Wu and Wen-Jia Wang and Meng-Lin Du and Feng-Kun Guo and Hao-Jie Jing},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32139},
  eprint = {2610.32139},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32139},
}

RIS

TY  - UNPB
TI  - Coupled-channel extension of the effective-range expansion with left-hand cut
AU  - Bing Wu
AU  - Wen-Jia Wang
AU  - Meng-Lin Du
AU  - Feng-Kun Guo
AU  - Hao-Jie Jing
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32139
UR  - https://arxiv.org/abs/2610.32139
AB  - 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.
ER  -

Abstract

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