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General amplitude of near-threshold hadron scattering for exotic hadrons

Katsuyoshi Sone ^* and Tetsuo Hyodo ^†,‡

Department of Physics, Tokyo Metropolitan University, Hachioji 192-0397, Japan

^*Contact author: sone-katsuyoshi@ed.tmu.ac.jp
^†Contact author: hyodo@tmu.ac.jp
^‡Present address: Research Center for Nuclear Physics (RCNP), Ibaraki, Osaka 567-0047, Japan.

Phys. Rev. C 112, 065207 – Published 19 December, 2025

DOI: https://doi.org/10.1103/qp1j-slqg

Abstract

We discuss the general behavior of the scattering amplitude with channel couplings near the two-body threshold. It is known that the Flatté amplitude, which is often used in the analysis of experimental data involving exotic hadrons, has some constraint in the near-threshold energy region. While the $M$ -matrix gives the general expression of the scattering amplitude, it is not smoothly connected to the Flatté amplitude, due to the property of the determinant of the amplitude in channel space. In this paper, based on the effective field theory, we propose new parametrization of the scattering amplitude which gives the general expression near the threshold and has a well-defined limit reproducing the Flatté amplitude. We show that the nonresonant background contribution exists in the general amplitude even in the first order in the momentum. Finally, we quantitatively evaluate the cross sections by changing the strength of the background contribution. We find that the interference with the background term may induce a dip structure of the cross section near the threshold, in addition to the peak and threshold cusp structures.

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Phys. Rev. C 112, 065207– Published 19 December, 2025

Vol. 112, Iss. 6 — December 2025

Received 20 May 2024
Revised 15 October 2025
Accepted 31 October 2025

DOI: https://doi.org/10.1103/qp1j-slqg

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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General amplitude of near-threshold hadron scattering for exotic hadrons

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