Precise Determination of the Strong Coupling Constant at NNLO in QCD from the Three-Jet Rate in Electron-Positron Annihilation at LEP

We present the first determination of the strong coupling constant from the three-jet rate in e(+)e(-) annihilation at LEP, based on a next-to-next-to-leading-order (NNLO) perturbative QCD prediction. More precisely, we extract alpha(s)(M-Z) by fitting perturbative QCD predictions at O(alpha(3)(s)) to data from the ALEPH experiment at LEP. Over a large range of the jet-resolution parameter y(cut), this observable is characterized by small nonperturbative corrections and an excellent stability under renormalization scale variation. We find alpha(s)(M-Z) = 0.1175 +/- 0.0020(expt) +/- 0.0015(theor), which is more accurate than the values of alpha(s)(M-Z) from e(+)e(-) event-shape data currently used in the world average.