A note on the determination of light quark masses

TL;DR

This paper presents a model-independent method to determine light quark mass differences using eta decay data and chiral symmetry, resulting in precise estimates for u and d quark masses.

Contribution

It introduces a novel approach that relates quark mass differences to decay data without relying on specific models, improving accuracy of light quark mass estimates.

Findings

Determined B_0(m_d-m_u) as 4495±440 MeV^2.

Estimated light quark masses: m_u(2 GeV)=2.9±0.8 MeV, m_d(2 GeV)=4.7±0.8 MeV.

Abstract

We provide a model-independent determination of the quantity B_0(m_d-m_u). Our approach rests only on chiral symmetry and data from the decay of the eta into three neutral pions. Since the low-energy prediction at next-to-leading order fails to reproduce the experimental results, we keep the strong interaction correction as an unknown parameter. As a first step, we relate this parameter to the quark mass difference using data from the Dalitz plot. A similar relation is obtained using data from the decay width. Combining both relations we obtain B_0(m_d-m_u)=(4495+/-440) MeV^2. The preceding value, combined with lattice determinations, leads to the values m_u(2 GeV)=(2.9+/-0.8) MeV and m_d(2 GeV)=(4.7+/-0.8) MeV.