Corrections of order αs3 to Rhad in pQCD with light gluinos

Abstract

By a completely independent analytic calculation made in general covariant gauge we confirm the known result for the massless O (α s 3) correction to R had 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) = 11 3 [1 + α s π + (1.409 − 0.346n g ) ( α s π ) 2 + (−12.805 − 3.006n g − 0.0466n g 2) ( α s π ) 3] where n g is the number of such colour octets. The gluino O (α s 3) contribution to the Z-boson hadronic decay rate proves to be relatively small while it is significant for τ-lepton semihadronic width.