Novel method for determining the light quark mass ratio using $\eta'\to\eta \pi\pi$ decays

TL;DR

This paper introduces a new method using Dalitz plot mapping to a unit disk for extracting symmetry breaking effects from three-body decays, demonstrated by determining the light quark mass ratio Q with results consistent with previous studies.

Contribution

The paper presents a novel approach to isolate symmetry breaking effects in three-body decays by mapping Dalitz plots to a unit disk, enabling precise extraction of the quark mass ratio Q.

Findings

Extracted Q value of 22.3 ± 0.7 from BESIII data.

Method achieves comparable precision to previous determinations.

Potential for higher precision with larger data sets.

Abstract

We propose a novel approach for extracting symmetry breaking effects from symmetry conserved 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 $\eta'\to\eta\pi^+\pi^-$ and $\eta'\to\eta\pi^0\pi^0$. With the Dalitz plot distributions for these two decays reported by BESIII, we obtain $Q=22.3\pm0.7$, which is consistent with previous determinations and has a comparable uncertainty. With the full BESIII data set, which is eight times larger than the one used here, a significantly more precise determination of $Q$ will be achievable. This promising and novel method can be generalized to other three-body decays to extract symmetry breaking effects.