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 m2/s the quartic terms, i.e., those proportional to m4/s2 , are calculated up to order αs3 for vector and axial current induced rates. Predictions relevant for charm, bottom and top quarks production are presented. The αs3 corrections are shown to be comparable to terms of order αs and αs2 . 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(μ) with the scheme independent invariant one m̂ . 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 αs3 from the high energy region down to fairly low energies.