Eur. Phys. J. C (2025) 85: 1388
https://doi.org/10.1140/epjc/s10052-025-15109-6

Regular Article - Theoretical Physics

A combined analysis of Y(2240) in the $e^{+}{e}^{-}\to K^{+}{K}^{-}$ and $e^{+}{e}^{-}\to K_S^0{K}_L^0$ processes

¹ School of Physics, Southeast University, 210094, Nanjing, China
² School of Physics and Electromechanical Engineering, Hubei University of Education, 430205, Wuhan, China
³ Lanzhou Center for Theoretical Physics, Lanzhou University, 730000, Lanzhou, China
⁴ School of Physical Science, University of Science and Technology of China, 230026, Hefei, China
⁵ School of Physics and Technology, University of Jinan, 250022, Jinan, China

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Received: 13 October 2025
Accepted: 20 November 2025
Published online: 5 December 2025

Abstract

In the present work, we perform a combined analysis of the cross sections for $e^{+}{e}^{-}\to K^{+}{K}^{-}$ and $e^{+}{e}^{-}\to K_S^0{K}_L^0$ by including the interference between direct coupling process and resonance intermediate process. When setting the isospin factor as a free parameter, we can well reproduce the structures in the cross sections for $e^{+}{e}^{-}\to K^{+}{K}^{-}$ and $e^{+}{e}^{-}\to K_S^0{K}_L^0,$ however, the isospin factor deviates with the isospin symmetry conservation predicted value of one. By fixing the isospin factor to be one, we find the cross sections for $e^{+}{e}^{-}\to K^{+}{K}^{-}$ can be accurately fitted, while the same model parameters fail to adequately reproduce the observed cross section for the process $e^{+}{e}^{-}\to K_S^0{K}_L^0,$ which indicate that there should be contributions from other vector meson states, such as $\rho (2150)$ and $\omega (2220).$ The combined analysis with $\varphi (2170),$$\omega (2220)$ and $\rho (2150)$ indicate that the inclusion of $\rho (2150)$ can improve the descriptions of the cross sections for $e^{+}{e}^{-}\to K^{+}{K}^{-}$ and $e^{+}{e}^{-}\to K_S^0{K}_L^0.$