Annihilation of S - wave quarkonia and the measurement of α s ∗

We analyze the relativistic corrections to annihilation rates of S-wave quarkonia within the framework of NRQCD. We show that order v2 corrections can be expressed in terms of the heavy quark pole mass and the quarkonium mass. The ratio of hadronic to radiative annihilation rates for ηb and ηc can therefore be predicted accurately. The contributions of color-octet operators to the hadronic decay rates of spin-triplet quarkonia are shown to be significant, even though they arise at order v4 in the velocity expansion. We provide a rough estimate of the color-octet contributions and extract the value of αs from the experimental data on Υ decays. Work supported in part by the U.S. Dept. of Energy under Grant no. DE-FG03-92-ER 40701. 1