The strange quark mass from QCD sum rules

The strange quark mass is calculated from QCD sum rules for the divergence of the vector as well as axial-vector current in the next-next-to-leading logarithmic approximation. The determination for the divergence of the axial-vector current is found to be unreliable due to large uncertainties in the hadronic parametrisation of the two-point function. From the sum rule for the divergence of the vector current, we obtain a value of m_s\equiv\mb_s(1\,\gev)=189\pm32\, \mev, where the error is dominated by the unknown perturbative {\cal O}(\alpha_s^3) correction. Assuming a continued geometric growth of the perturbation series, we find m_s=178\pm18\,\mev. Using both determinations of m_s, together with quark-mass ratios from chiral perturbation theory, we also give estimates of the light quark masses m_u and m_d.