Determination of ${\alpha }_s$ and heavy quark masses from recent measurements of $R(s)$

Abstract

In this paper we compare recent experimental data for the total cross section $\sigma (e^{+}{e}^{-}\to hadrons)$ with the up-to-date theoretical prediction of perturbative QCD for those energies where perturbation theory is reliable. The excellent agreement suggests the determination of the strong coupling ${\alpha }_s$ from the measurements in the continuum. The precise data from the charm threshold region, when combined with the recent evaluation of moments with three loop accurracy, lead to a direct determination of the short distance $\overline{\mathrm{MS}}$ charm quark mass. Our result for the strong coupling constant ${\alpha }_s^{(4)}(5GeV)=0.235_{-0.047}^{+0.047}$ corresponds to ${\alpha }_s^{(5)}(M_Z)=0.124_{-0.014}^{+0.011}$, for the charmed quark mass we find $m_c(m_c)=1.304(27)$. Applying the same approach to the bottom quark we obtain $m_b(m_b)=4.191(51)$ GeV. Whereas our result for ${\alpha }_s(M_Z)$ serves as a useful cross check for other more precise determinations, our values for the charm and bottom quark masses are more accurate than other recent analyses.

16 pages, minor change in numerical result for mb(mb)

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