====== TTP08-28 The Strong Coupling Constant at Low and High Energies ======
 
 
<hidden TTP08-28  The Strong Coupling Constant at Low and High Energies > Recent results for the
 cross section of electron-positron annihilation into hadrons and for the
 decay rates of the $Z$ boson and the  $\tau$ lepton into hadrons including
 corrections of order  $\alpha_s^4$ are reviewed.
 The consistency between two values  of $\alpha_s$ measured
 at vastly different energies constitutes
 a striking test of asymptotic freedom and requires the proper matching
 conditions
 at charm and bottom thresholds.
 Combining the results from $Z$ and $\tau$ decays
 leads to $\alpha_s(M_Z)=0.1198 \pm  0.0015$ as one of the most precise and
 presently only
 NNNLO result for the strong coupling constant. We report a recent
 determination of $\alpha_s$
 which is based on a lattice evaluation of the pseudoscalar correlator for
 the charm quarks combined
 with continuum perturbation theory.
 </hidden>
|**J.H. K&uuml;hn**  | 
|**      Contribution to "Continuous Advances in QCD, 2008" Minnepolis, USA, May 15 - 18, 2008; to be published in the proceedings **  |
| {{preprints:2008:ttp08-28.pdf|PDF}} {{preprints:2008:ttp08-28.ps|PostScript}}   |
| |