Determination of $\alpha_s$ and heavy quark masses from recent measurements of $R(s)$

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 $\bar{\rm MS}$ charm quark mass. Our result for the strong coupling constant $\alpha_s^{(4)}(5 {GeV})=0.235^{+0.047}_{-0.047}$ corresponds to $\alpha_s^{(5)}(M_Z)=0.124^{+0.011}_{-0.014}$, 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.