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Understanding the nontrivial isoscalar pseudoscalar structures in the $K_{S} K_{S} π^{0}$ spectra in the $J / ψ$ radiative decay

Yin Cheng ^1,2,3,*, Lin Qiu ^1,2,†, and Qiang Zhao ^1,2,4,‡

¹Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
²University of Chinese Academy of Sciences, Beijing 100049, China
³Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
⁴Center for High Energy Physics, Henan Academy of Sciences, Zhengzhou 450046, China

^*Contact author: chengyin@itp.ac.cn
^†Contact author: qiulin@ihep.ac.cn
^‡Contact author: zhaoq@ihep.ac.cn

Phys. Rev. D 111, 114015 – Published 17 June, 2025

DOI: https://doi.org/10.1103/8hbx-79qp

Abstract

Initiated by the recent observation of a flattened line shape of $I J^{P C} = 0 0^{- +}$ around 1.4–1.5 GeV in the $K_{S} K_{S} π^{0}$ invariant mass spectrum by BESIII, we make a systematic partial wave analysis of $J / ψ \to γ η_{X} \to γ K \bar{K} π$ based on an isobaric approach. We demonstrate that in the scenario of the first radial excitations of the isoscalar pseudoscalar from the $K \bar{K} π$ threshold to about 1.6 GeV the non-trivial $K_{S} K_{S} π^{0}$ invariant mass spectrum can be explained by the coupled-channel effects with the presence of the triangle singularity mechanism. It shows that a combined fit of the Dalitz plots, three-body and two-body spectra can be achieved, which suggests that the one-state solution around 1.4–1.5 GeV proposed before still holds well. In particular, we show that the coupled-channel effects between the three important quasi-two-body decay channels, $K^{*} \bar{K} + c . c .$ , $κ \bar{K} + c . c .$ and $a_{0} (980) π$ , can be well described by taking into account the one-loop corrections in the isobaric approach. This is because the isoscalar pseudoscalar states are coupled to the $K^{*} \bar{K} + c . c .$ and $a_{0} (980) π$ ( $κ \bar{K} + c . c .$ ) channels via the $P$ and $S$ waves, respectively. As a consequence, the coupled-channel effects can be largely absorbed into the redefinition of the tree-level effective couplings with the transition amplitudes computed to the order of one-loop corrections. Then, the coupled-channel effects can be estimated by the contributions from the one-loop rescattering amplitudes in comparison with the tree-level ones, where we find that the rescattering contributions from the $P$ wave into the $S$ wave, or vice versa, are apparently suppressed in the kinematic region near threshold.

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In Ref. [42] the two-body invariant mass spectra $K \bar{K}$ and $K π$ are extracted by an isobaric parametrization which is an assumption made in the data analysis. Because of this treatment some model-dependent features with the two-body spectra may be inevitable. Although it may raise concerns about the output of fitting the two-body spectra, it is actually a proof that the one-state isobaric picture around 1.4 GeV can be accommodated by the data. It also implies that the three-body unitarity approach would not drastically change such a phenomenon. We will report the full analysis with three-body unitarity in a forthcoming work.
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Phys. Rev. D 111, 114015– Published 17 June, 2025

Vol. 111, Iss. 11 — 1 June 2025

Received 19 July 2024
Accepted 19 April 2025

DOI: https://doi.org/10.1103/8hbx-79qp

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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Understanding the nontrivial isoscalar pseudoscalar structures in the $K_{S} K_{S} π^{0}$ spectra in the $J / ψ$ radiative decay

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Understanding the nontrivial isoscalar pseudoscalar structures in the KSKSπ0 spectra in the J/ψ radiative decay

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Understanding the nontrivial isoscalar pseudoscalar structures in the $K_{S} K_{S} π^{0}$ spectra in the $J / ψ$ radiative decay