Heavy flavour contributions to the deep inelastic scattering sum rules

We have calculated the first and second order corrections to several deep i nelastic sum rules which are due to heavy flavour contributions. A comparis on is made with the existing perturbation series which has been computed up to third order for massless quarks only. In general it turns out that the effects of heavy quarks are very small except when Q similar to m or Q >> m . Here Q and m denote the virtual mass of the vector boson and the mass of the heavy quark, respectively. For Q >> m the radiative corrections reveal large logarithms of the type lnQ(2)/m(2) which have to be absorbed in the r unning coupling constant so that the number of light flavours n(f) is enhan ced by one unit. However this has to happen at much larger values of Q i.e. Q similar to 6.5 m than one usually assumes for the flavour thresholds whi ch appear in the running coupling constant. An alternative description for the heavy flavour dependence of the running coupling constant in the contex t of the MOM-scheme is discussed. (C) 1999 Elsevier Science B.V. All rights reserved.