Model-independent determination of [formula omitted] from τ-like decays in e+e− and implications for chiral symmetry

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: m s(1 GeV) = (197 ± 29) MeV. By combining this result with the pseudoscalar sum rule estimate of ( m d + m u ) and the standard current algebra values of the light quark mass ratios, we deduce: m d(1 GeV) = (10 ± 1) MeV, m u(1 GeV) = (4 ± 1) MeV, and built1 2 〈 uu + dd〉(1 GeV) = − [(229 ± 9) MeV] 3 . Using also this new value of m s , 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 m b from the ϒ-sum rules, we obtain the scale independent quark-mass ratio: m b m s = 34 ± 4 .