Strange quark mass from e+e- revisited and present status of light quark masses

We reconsider the determinations of the strange quark mass m_s from e⁺e^- into hadrons data using a new combination of finite energy sum rules (FESR) and revisiting the existing τ-like sum rules by including nonresonant contributions to the spectral functions. To order α_s³ and including the tachyonic gluon mass λ² contribution, which phenomenologically parametrizes the UV renormalon effect into the perturbative series, we obtain the invariant mass m^_s=(119±17)MeV leading to m¯_s(2GeV)=(104±15)MeV. Combining this value with the recent and independent phenomenological determinations from some other channels, to order α_s³ and including λ², we deduce the weighted average m¯_s(2GeV)=(96.1±4.8)MeV. The positivity of the spectral functions in the (pseudo)scalar (resp. vector) channels leads to the lower (resp. upper) bounds of m¯_s(2GeV): (71±4)MeV≤m¯_s(2GeV)≤(151±14)MeV, to order α_s³. Using the chiral perturbation theory (ChPT) mass ratio r₃≡2m_s/(m_u+m_d)=24.2±1.5, and the average value of m_s, we deduce (m¯_u+m¯_d)(2GeV)=(7.9±0.6)MeV, consistent with the pion sum rule result, which, combined with the ChPT value for m_u/m_d, gives m¯_d(2GeV)=(5.1±0.4)MeV and m¯_u(2GeV)=(2.8±0.2)MeV. Finally, using (m¯_u+m¯_d) from the pion sum rule and the average value of m¯_s (without the pion sum rule), the method gives r₃=23.5±5.8, in perfect agreement with the ChPT ratio, indicating the self-consistency of the sum rule results. Using the value m¯_b(m¯_b)=(4.23±0.06)GeV, we also obtain the scale-independent mass ratio m_b/m_s=50±3, which is useful for model-buildings. Absolute values of the light quark masses from QCD spectral sum rules reported in this paper are the most accurate determinations to date.