Study of the e+e- → ϕK+K- reaction within triangle dynamics and its implications for the ϕ(2170)
Abstract
We revisit the e+e- → ϕπ+π- reaction within the K1-K̅-K triangle dynamics framework, in which the e+e- pair annihilates through one-photon exchange approximation to produce a K1K̅ pair, followed by the K1 →ϕK decay and the final-state KK̅ → π+π- rescattering. With the same theoretical formalism and model parameters, the e+e- → ϕK+K- reaction is investigated, and it is found that the predicted total cross sections for the e+ e- → 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 K1K̅ 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- → 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 K1-K̅-K triangle loop.
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BibTeX
@misc{wei2026study,
title = {{Study of the $e^+e^- \to ϕK^+K^-$ reaction within triangle dynamics and its implications for the $ϕ(2170)$}},
author = {Xiang Wei and Cheng Chen and Si-Wei Liu and Zu-Xin Cai and Gang Li and Xiao-Hai Liu and Ju-Jun Xie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19951},
eprint = {2609.19951},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19951},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Study of the e^+e^- → ϕK^+K^- reaction within triangle dynamics and its implications for the ϕ(2170)
AU - Xiang Wei
AU - Cheng Chen
AU - Si-Wei Liu
AU - Zu-Xin Cai
AU - Gang Li
AU - Xiao-Hai Liu
AU - Ju-Jun Xie
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19951
UR - https://arxiv.org/abs/2609.19951
AB - We revisit the e^+e^- → ϕπ^+π^- reaction within the K_1-K̅-K triangle dynamics framework, in which the e^+e^- pair annihilates through one-photon exchange approximation to produce a K_1K̅ pair, followed by the K_1 →ϕK decay and the final-state KK̅ → π^+π^- rescattering. With the same theoretical formalism and model parameters, the e^+e^- → ϕK^+K^- reaction is investigated, and it is found that the predicted total cross sections for the e^+ e^- → 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_1K̅ 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^- → 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-K̅-K triangle loop.
ER -