Model-independent determination of ${\overline{m}}_s$ from $\tau$-like inclusive decays in $e^{+}{e}^{-}$ and implications for the $\chi SB$-parameters

Abstract

We determine the strange quark running mass of the $\overline{MS}$-scheme by $simulating$ $\tau$-$like$ 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: ${\overline{m}}_s$(1 GeV)=($196.7\pm 29.1$) MeV. By combining this result with the pseudoscalar sum rule estimate of $({\overline{m}}_d+{\overline{m}}_u)$ and the standard current algebra values of the light quark mass ratios, we deduce the $average$: ${\overline{m}}_d$(1 GeV)=$(10.3\pm 1.5)$ MeV, ${\overline{m}}_u$(1 GeV)=$(5.0\pm 1.5)$ MeV and $\frac{1}{2}\text{la}\bar{u}u+\bar{d}d\text{ra}$ (1 GeV) $\simeq -[(228.6\pm 9.1)\text{mbox}MeV{]}^3$. Using also our value of $m_s$, we update the estimates of the $K^{\prime }(1.46)$ and $K_0^{\ast }(1.43)$ decay constants and of the (pseudo)scalar two-point correlator subtraction constants. Then, we deduce a deviation of about 34\% from kaon PCAC and the ratio of the {\it normal-ordered} condensates: $\text{la}\bar{s}s\text{ra}/\text{la}\bar{u}u\text{ra}=0.68_{-0.29}^{+0.15}$, which confirm previous findings from QCD spectral sum rules. Finally, using the recent value of the ${\overline{m}}_b$ from the ${\rm Y}$-sum rules, we deduce the scale independent quark-mass ratio: $m_b/m_s=34\pm 4$.

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