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$a_{0} (980)$ and $f_{0} (980)$ excitation in the $D^{+} \to π^{+} η η$ decay

Jing Song ^1,2,3,*, Yi-Yao Li ^4,5,6,3,†, Melahat Bayar ^7,3,‡, and Eulogio Oset ^3,8,§

¹Center for Theoretical Physics, School of Physics and Optoelectronic Engineering, Hainan University, Haikou 570228, People’s Republic of China
²School of Physics, Beihang University, Beijing, 102206, People’s Republic of China
³Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC Institutos de Investigación de Paterna, 46071 Valencia, Spain
⁴State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, People’s Republic of China
⁵Key Laboratory of Atomic and Subatomic Structure and Quantum Control (MOE), Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Guangzhou 510006, People’s Republic of China
⁶Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science, Guangzhou 510006, People’s Republic of China
⁷Department of Physics, Kocaeli University, 41380, Izmit, Turkey
⁸Department of Physics, Guangxi Normal University, Guilin 541004, People’s Republic of China

^*Contact author: Song-Jing@buaa.edu.cn
^†Contact author: liyiyao@m.scnu.edu.cn
^‡Contact author: melahat.bayar@kocaeli.edu.tr
^§Contact author: oset@ific.uv.es

Phys. Rev. D 113, 114039 – Published 22 June, 2026

DOI: https://doi.org/10.1103/y5vp-vhbs

Abstract

We have made a thorough study of the $D^{+} \to π^{+} η η$ reaction, recently measured by the Beijing Spectrometer III Collaboration, which shows an abnormal strength at high invariant masses in the $π η$ mass distribution. We studied in detail the triangle mechanism and the $f_{0} (1370)$ excitation modes that have been suggested to explain this abnormal feature, and concluded that they are too small to have any important role in the solution to that problem. We have also studied other possible solutions, evaluating the contribution of excitations of other $f_{0}$ , $a_{0}$ and $f_{2}$ resonances, and reached the same conclusion. Unexpectedly, the solution to the problem is found considering the $f_{0} (980)$ excitation, with the $f_{0} (980)$ decaying to two $η$ , which is tied to the $a_{0} (980)$ production, and well under control. At the same time, the consideration of the $f_{0} (980)$ excitation solves another nonreported problem, which is the $η η$ mass distribution that comes when only the $a_{0} (980)$ resonance is allowed to be excited, which produces a large deficiency at low invariant masses compared with experiments.

Physics Subject Headings (PhySH)

Particle interactions

Article Text

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Phys. Rev. D 113, 114039– Published 22 June, 2026

Vol. 113, Iss. 11 — 1 June 2026

Received 12 November 2025
Accepted 29 January 2026

DOI: https://doi.org/10.1103/y5vp-vhbs

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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$a_{0} (980)$ and $f_{0} (980)$ excitation in the $D^{+} \to π^{+} η η$ decay

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a0(980) and f0(980) excitation in the D+→π+ηη decay

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$a_{0} (980)$ and $f_{0} (980)$ excitation in the $D^{+} \to π^{+} η η$ decay