ScalarKπform factor and light-quark masses

Abstract

Recent experimental improvements on $K$-decay data allow for a precise extraction of the strangeness-changing scalar $K\ensuremath{\pi}$ form factor and the related strange scalar spectral function. On the basis of this scalar as well as the corresponding pseudoscalar spectral function, the strange quark mass is determined to be ${m}_{s}(2\text{ }\text{ }\mathrm{GeV})=92\ifmmode\pm\else\textpm\fi{}9\text{ }\text{ }\mathrm{MeV}$. Further taking into account chiral perturbation theory mass ratios, the light up and down quark masses turn out to be ${m}_{u}(2\text{ }\text{ }\mathrm{GeV})=2.7\ifmmode\pm\else\textpm\fi{}0.4\text{ }\text{ }\mathrm{MeV}$ as well as ${m}_{d}(2\text{ }\text{ }\mathrm{GeV})=4.8\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{ }\mathrm{MeV}$. As a by-product, we also find a value for the Cabibbo angle $|{V}_{us}|=0.2236(29)$ and the ratio of meson decay constants ${F}_{K}/{F}_{\ensuremath{\pi}}=1.203(16)$. Performing a global average of the strange mass by including extractions from other channels as well as lattice QCD results yields ${m}_{s}(2\text{ }\text{ }\mathrm{GeV})=94\ifmmode\pm\else\textpm\fi{}6\text{ }\text{ }\mathrm{MeV}$.