发表机构
State Key Laboratory of Heavy Ion Science and Technology, Institute of Modern Physics, Chinese Academy of Sciences; School of Nuclear Science and Technology, University of Chinese Academy of Sciences; College of Physics and Engineering, Qufu Normal University; Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（中国科学院近代物理研究所; 中国科学院大学核科学与技术学院; 曲阜师范大学物理工程学院; 天津大学理学院量子联合研究中心与物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在三角动力学框架下研究 $e^+e^- \to \phi K^+K^-$ 反应，发现三角奇点被抑制且干涉消除信号，从而解释了无 $\phi(2170)$ 信号，并验证了与 $\phi \pi^+\pi^-$ 反应相同的产生机制。
AI 中文摘要
我们在 $K_1$-$\bar{K}$-$K$ 三角动力学框架内重新审视了 $e^+e^- \to \phi \pi^+\pi^-$ 反应，其中 $e^+e^-$ 对通过单光子交换近似湮灭产生 $K_1\bar{K}$ 对，随后 $K_1 \to \phi K$ 衰变，末态 $K\bar{K} \to \pi^+\pi^-$ 发生再散射。采用相同的理论形式和模型参数，我们研究了 $e^+e^- \to \phi K^+K^-$ 反应，发现预测的 $e^+e^- \to \phi K^+K^-$ 反应总截面与现有 BESIII 测量结果吻合良好。我们的研究表明，$\phi K^+K^-$ 道中的三角奇点被强烈抑制，因为较高的 $K^+K^-$ 质量阈值使运动学偏离三角奇点条件，且 $K_1\bar{K}$ 阈值附近的相空间非常有限。此外，树级振幅与圈振幅之间的干涉消除了剩余信号。这些综合效应自然地解释了 $e^+e^- \to \phi K^+K^-$ 反应中缺乏明显的 $\phi(2170)$ 信号，为模型提供了强有力的检验，并强化了两种反应由相同潜在机制支配的观点，即 $\phi(2170)$ 态在 $e^+e^-$ 湮灭中通过 $K_1$-$\bar{K}$-$K$ 三角圈产生。
英文摘要
We revisit the $e^+e^- \to ϕπ^+π^-$ reaction within the $K_1$-$\bar{K}$-$K$ triangle dynamics framework, in which the $e^+e^-$ pair annihilates through one-photon exchange approximation to produce a $K_1\bar{K}$ pair, followed by the $K_1 \toϕK$ decay and the final-state $K\bar{K} \to π^+π^-$ rescattering. With the same theoretical formalism and model parameters, the $e^+e^- \to ϕK^+K^-$ reaction is investigated, and it is found that the predicted total cross sections for the $e^+ e^- \to ϕK^+ K^-$ reaction are in good agreement with the existing BESIII measurements. Our study shows that the triangle singularity in the $ϕK^+K^-$ channel is strongly suppressed, because the higher $K^+K^-$ mass threshold shifts the kinematics away from the triangle singularity condition and the phase space near the $K_1\bar{K}$ threshold is very limited. Moreover, the interference between the tree-level and loop amplitudes eliminates the remaining signal. These combined effects naturally explain the absence of a distinct $ϕ(2170)$ signal in the $e^+ e^- \to ϕK^+ K^-$ reaction, provide a strong test of the model, and reinforce the picture that both reactions are governed by the same underlying mechanism, in which the $ϕ(2170)$ state is produced in the $e^+ e^-$ annihilation from the $K_1$-$\bar{K}$-$K$ triangle loop.
Comments7 pages, 4 figures
