Corrections of order αs3 to Rhad in pQCD with light gluinos

By a completely independent analytic calculation made in general covariant gauge we confirm the known result for the massless O(αs3) correction to Rhad and check explicitly its gauge independence. We extend the calculations to include contributions due to a hypothetical existence of a colour octet of (light) neutral fermions known also under the name of gluinos. In numerical form and for five active flavours we found (in MS scheme) that R(s) = 113[1 + αsπ + (1.409 − 0.346ng) (αsπ)2 + (−12.805 − 3.006ng − 0.0466ng2) (αsπ)3] where ng is the number of such colour octets. The gluino O(αs3) contribution to the Z-boson hadronic decay rate proves to be relatively small while it is significant for τ-lepton semihadronic width.