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Effective range expansion with the left-hand cut: Higher order improvements

Wen-Jia Wang1,*, Bing Wu1,†, Meng-Lin Du1,‡, and Feng-Kun Guo2,3,4,§

  • *Contact author: wwenjia@std.uestc.edu.cn
  • †Contact author: wu.bing@uestc.edu.cn
  • ‡Contact author: du.ml@uestc.edu.cn
  • §Contact author: fkguo@itp.ac.cn
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Phys. Rev. D 114, 014003 – Published 6 July, 2026

DOI: https://doi.org/10.1103/tdyn-422c

Abstract

A model-independent parametrization of the low-energy scattering amplitude that incorporates the left-hand cut from one-particle exchange, an extension of the conventional effective range expansion (ERE), was recently proposed and successfully applied to the low-energy DD* system [, Effective-range expansion with a long-range force, Phys. Rev. Lett. 135, 011903 (2025)]. While the original formulation is based on a nonrelativistic approximation and is thus limited to a [1, 1] approximant for self-consistency, we extend the framework by explicitly including the higher order terms up to O(k6). We systematically investigate the reliability and robustness of the generalized ERE by incorporating relativistic kinematic effects. In addition, we develop a relativistic version of the ERE that accounts for the left-hand cut contributions. These results affirm the generalized ERE as a robust and systematically improvable framework for near-threshold scattering processes, providing both analytical and numerical reliability for applications in two-body scattering problems with a particle exchange.

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Phys. Rev. D 114, 014003– Published 6 July, 2026
  • Received 14 January 2026
  • Accepted 10 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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