Quartic mass corrections to Rhad at O(αs3)

The total cross section for the production of massive quarks in electron-positron annihilation can be predicted in perturbative QCD. After expansion in m(2)/s the quartic terms, i.e., those proportional to m(4)/s(2) are calculated up to order alpha(s)(3) for vector and axial current induced rates. predictions relevant for charm, bottom and top quarks production are presented. The alpha(s)(3) corrections are shown to be comparable to terms of order alpha(s) and alpha(s)(2). As a consequence, the predictions exhibit a sizeable dependence on the renormalization scale. The stability of the prediction 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 scheme independent invariant one (m) over cap. By combining these results with the prediction for massless case and the quadratic mass terms the cross section for massive quark production at electron-positron colliders is put under control in order alpha(s)(3) From the high energy region down to fairly low energies. (C) 2000 Elsevier Science B.V. All rights reserved.