Abstract :
We determine the strange quark running mass of the MS-scheme by simulating τ-like inclusive processes for the old Das-Mathur-Okubo sum rule relating the e+e− into I = 0 and I = 1 hadrons total cross-sections data. We obtain to three-loop accuracy: ms(1 GeV) = (197 ± 29) MeV. By combining this result with the pseudoscalar sum rule estimate of (md + mu) and the standard current algebra values of the light quark mass ratios, we deduce: md(1 GeV) = (10 ± 1) MeV, mu(1 GeV) = (4 ± 1) MeV, and built12〈uu + dd〉(1 GeV) = − [(229 ± 9) MeV]3. Using also this new value of ms, we also re-estimate the (pseudo) scalar two-point correlator subtraction constants, from which we deduce a deviation of about 34% from kaon PCAC and a value of 0.7−0.3+0.1 for the ratio 〈ss〉〈uu〉 of the normal-ordered condensates, which, therefore, confirm previous findings from QCD spectral sum rules. Finally, using the recent two-loop value of mb from the ϒ-sum rules, we obtain the scale independent quark-mass ratio: mbms = 34 ± 4.
