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 $B_0(m_d-m_u)=(4495\pm 440){\mathrm{MeV}}^2$. The preceding value, combined with lattice determinations, leads to the values $m_u(2\mathrm{GeV})=(2.9\pm 0.8)\mathrm{MeV}$ and $m_d(2\mathrm{GeV})=(4.7\pm 0.8)\mathrm{MeV}$.

• Received 26 March 2008

DOI:https://doi.org/10.1103/PhysRevD.78.034032