Determination of light quark masses fromη→3π0

Abstract

We provide a model-independent determination of the quantity ${B}_{0}({m}_{d}\ensuremath{-}{m}_{u})$. 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 ${B}_{0}({m}_{d}\ensuremath{-}{m}_{u})=(4495\ifmmode\pm\else\textpm\fi{}440)\text{ }\text{ }{\mathrm{MeV}}^{2}$. The preceding value, combined with lattice determinations, leads to the values ${m}_{u}(2\text{ }\text{ }\mathrm{GeV})=(2.9\ifmmode\pm\else\textpm\fi{}0.8)\text{ }\text{ }\mathrm{MeV}$ and ${m}_{d}(2\text{ }\text{ }\mathrm{GeV})=(4.7\ifmmode\pm\else\textpm\fi{}0.8)\text{ }\text{ }\mathrm{MeV}$.