Quartic mass corrections to R-had at O(alpha(3)(s))

The total cross section for the production of massive quarks in electron-po sitron annihilation can be predicted in perturbative QCD. After expansion i n m(2)/s the quartic terms, i.e., those proportional to m(4)/s(2) are calcu lated up to order alpha(s)(3) for vector and axial current induced rates. p redictions relevant for charm, bottom and top quarks production are present ed. The alpha(s)(3) corrections are shown to be comparable to terms of orde r alpha(s) and alpha(s)(2). As a consequence, the predictions exhibit a siz eable dependence on the renormalization scale. The stability of the predict ion is improved and, at the same time, the relative size of the large order terms decreases by replacing the running mass (m) over bar(mu) with the sc heme independent invariant one (m) over cap. By combining these results wit h the prediction for massless case and the quadratic mass terms the cross s ection for massive quark production at electron-positron colliders is put u nder control in order alpha(s)(3) From the high energy region down to fairl y low energies. (C) 2000 Elsevier Science B.V. All rights reserved.