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Novel method for determining the light quark mass ratio using $η^{'} \to η π π$ decays

Adolfo Guevara ^1,2,*, Feng-Kun Guo ^1,3,4,†, and Hao-Jie Jing ^3,5,‡

¹Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
²Área Académica de Matemáticas y Física, Universidad Autónoma del Estado de Hidalgo, Ciudad del conocimiento, Carr. Pachuca-Tulancingo Km. 4.5, Mineral de la Reforma, Hidalgo, 42184, Mexico
³School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
⁴Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, Huizhou 516000, China
⁵College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China

^*Contact author: adolfo_guevara@uaeh.edu.mx
^†Contact author: fkguo@itp.ac.cn
^‡Contact author: jinghaojie@sxu.edu.cn

Phys. Rev. D 114, 014021 – Published 8 July, 2026

DOI: https://doi.org/10.1103/j982-c64r

Abstract

We propose a novel approach for extracting symmetry breaking effects from symmetry conserving three-body decays. The method is based on mapping the Dalitz plot to a unit disk, and the difference of the disk distributions of two related decays isolates purely symmetry breaking effects. We demonstrate this method by extracting the fundamental parameter $Q$ , an isospin breaking ratio of light quark masses defined as $Q^{2} \equiv (m_{s}^{2} - {\hat{m}}^{2}) / (m_{d}^{2} - m_{u}^{2})$ with $\hat{m}$ the average of up and down quark masses, from the decays $η^{'} \to η π^{+} π^{-}$ and $η^{'} \to η π^{0} π^{0}$ . With the Dalitz plot distributions for these two decays reported by BESIII, we illustrate the method and obtain $Q = 22.5 \pm 1.0$ , which is consistent with previous determinations and has a comparable uncertainty. With the full BESIII dataset, which is eight times larger than the one used here, a more precise determination of $Q$ should become possible. This promising and novel method can be generalized to other three-body decays to extract symmetry breaking effects.

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Phys. Rev. D 114, 014021– Published 8 July, 2026

Vol. 114, Iss. 1 — 1 July 2026

Received 17 February 2025
Accepted 19 May 2026

DOI: https://doi.org/10.1103/j982-c64r

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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Novel method for determining the light quark mass ratio using $η^{'} \to η π π$ decays

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Novel method for determining the light quark mass ratio using η′→ηππ decays

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Novel method for determining the light quark mass ratio using $η^{'} \to η π π$ decays