We report on the analytical calculation of NNNLO (O(α 3 s )) conversion factor between the MS quark mass and the one defined in the so-called "Regularization Invariant" scheme. The NNNLO contribution in the conversion factor turns out to be relatively large and comparable to the known NNLO term.

We derive explicit transformation formulae relating the renormalized quark mass and field as defined in the MS-scheme with the corresponding quantities defined in any other scheme. By analytically computing the three-loop quark propagator in the high-energy limit (that is keeping only massless terms and terms of first order in the quark mass) we find the NNNLO conversion factors transforming the MS quark mass and the renormalized quark field to those defined in a "Regularization Invariant" (RI) scheme which is more suitable for lattice QCD calculations. The NNNLO contribution in the mass conversion factor turns out to be large and comparable to the previous NNLO contribution at a scale of 2 GeV -the typical normalization scale employed in lattice simulations. Thus, in order to get a precise prediction for the MS masses of the light quarks from lattice calculations the latter should use a somewhat higher scale of around, say, 3 GeV where the (apparent) convergence of the perturbative series for the mass conversion factor is better.We also compute two more terms in the high-energy expansion of the MS renormalized quark propagator. The result is then used to discuss the uncertainty caused by the use of the high energy limit in determining the MS mass of the charmed quark. As a by-product of our calculations we determine the four-loop anomalous dimensions of the quark mass and field in the Regularization Invariant scheme. Finally, we discuss some physical reasons lying behind the striking absence of ζ(4) in these computed anomalous dimensions.

We present the analytic next-to-next-to-leading QCD calculation of some higher moments of deep inelastic structure functions in the leading twist approximation. We give results for the moments N =1,3,5,7,9,11,13 of the structure function F3. Similarly we present the moments N =10,12 for the flavour singlet and N =12,14 for the non-singlet structure functions F2 and FL. We have calculated both the three-loop anomalous dimensions of the corresponding operators and the three-loop coefficient functions of the moments of these structure functions.

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