Since 2003, plenty of resonant structures have been observed in the heavy quarkonium regime. Many of them are close to the thresholds of a few pairs of heavy hadrons. They are candidates of exotic hadrons and have attracted immense attentions. Based on a coupled-channel nonrelativistic effective field theory, we classify the near-threshold structures of a symmetry-related two-channel system by studying the evolution of the scattering amplitude line shapes and pole positions with the variation of the single-channel scattering length and channel coupling strength. We show that the evolution of the scattering amplitude line shapes can be understood from the pole trajectories in the complex energy plane, and the pole evolution can be traced back to the renormalization group fixed points. We provide a dictionary of correspondence between the evolution of line shapes and pole trajectories along with varying interaction and channel coupling strengths, which can be used to understand the experimental observations of the near-threshold structures.
A Study of Degenerate Two-Body and Three-Body Coupled-Channel Systems -Renormalized Effective AGS Equations and Near-Threshold Resonances-
由于存在质量接近两体和三体强子阈值的奇异强子候选者，我们研究了简并的两体和三体耦合通道系统.本文首先将非简并二体和三体耦合道的散射问题表示为一个有效的三体问题，即有效Alt-Grassberger-Sandhas（AGS）方程。接下来，我们研究的行为$S$矩阵极点附近的阈值时，两体和三体阈值退化。通过求解AGS方程核的本征值方程而不是AGS方程本身来获得$S$ -矩阵极点能量。然后，我们面临一个非物理奇异性问题：虽然物理跃迁振幅只有物理奇异性，但AGS方程的核具有非物理奇异性。然而，我们表明，这些非物理的奇异性可以通过适当的重组的散射方程和质量重整化。退化阈值附近的$S$矩阵极点的行为被发现是普遍的意义上的复极点能量，$E$，是由一个真正的参数，$c$，作为$c - E \log{\left( - E \right)} = 0$，或等价地，${\rm Im} E = - π{\rm Re} E / \log{\mid {\rm Re} E \mid}$。这种行为不同于二体或三体系统，是简并二体和三体耦合通道系统的特征。我们期望这类新的普遍行为可能在理解奇异强子方面发挥关键作用。
Amplified Isospin Breaking from Coupled-Channel Dynamics Near Threshold
Universität Bonn（波恩大学）；Helmholtz Institut für Strahlen- und Kernphysik（亥姆霍兹辐射与核物理研究所）；Cluster of Excellence “Color meets Flavor”（卓越集群“颜色遇见风味”）；Bethe Center for Theoretical Physics（贝特理论物理中心）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心（SCNT））；Forschungszentrum Jülich（于利希研究中心）；Institute for Advanced Simulation (IAS-4)（先进模拟研究所（IAS-4））
Unified coupled-channel description for the five near-threshold structures $ψ(3770)$, $G(3900)$, $R(3760)$, $R(3780)$ and $R(3810)$ from $e^+e^-$ annihilation
School of Physical Science and Technology, Lanzhou University（兰州大学物理科学与技术学院）；MoE Frontiers Science Center for Rare Isotopes, Lanzhou University（兰州大学教育部同位素前沿科学中心）；Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS（兰州大学及中国科学院近代物理研究所强子与重离子加速器物理研究中心）
