We calculate the next-to-leading QCD corrections to the effective Hamiltonian for B → X s e + e − in the NDR and HV schemes. We give for the first time analytic expressions for the Wilson Coefficient of the operator Q 9 = (sb) V −A (ēe) V in the NDR and HV schemes. Calculating the relevant matrix elements of local operators in the spectator model we demonstrate the scheme independence of the resulting short distance contribution to the physical amplitude. Keeping consistently only leading and next-to-leading terms, we find an analytic formula for the differential dilepton invariant mass distribution in the spectator model. Numerical analysis of the m t , Λ MS and µ ≈ O(m b ) dependences of this formula is presented. We compare our results with those given in the literature. * Supported by the German Bundesministerium für Forschung und Technologie under contract 06 TM 743 and the CEC Science project SC1-CT91-0729.

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We analyze uncertainties in the theoretical prediction for the inclusive branching ratio BR[B → X s γ]. We find that the dominant uncertainty in the leading order expression comes from its µ-dependence. We discuss a next-to-leading order calculation of B → X s γ in general terms and check to what extent the µ-dependence can be reduced in such a calculation. We present constraints on the Standard and Two-Higgs-Doublet Model parameters coming from the measurement of b → sγ decay. The current theoretical uncertainties do not allow one to definitively restrict the Standard Model parameters much beyond the limits coming from other experiments. The bounds on the Two-Higgs-Doublet Model remain very strong, though significantly weaker than the ones present in the recent literature. In the Two-Higgs-Doublet Model case, the b → sγ, Z → bb and b → cτν τ processes are enough to give the most restrictive bounds in the M H ± − tanβ plane. † On leave of absence from Institute of Theoretical Physics, Warsaw University.

We derive an algorithm for automatic calculation of perturbative β-functions and anomalous dimensions in any local quantum field theory with canonical kinetic terms. The infrared rearrangement is performed by introducing a common mass parameter in all the propagator denominators. We provide a set of explicit formulae for all the necessary scalar integrals up to three loops.

The strange quark mass is calculated from QCD sum rules for the divergence of the vector as well as axial-vector current in the next-next-to-leading logarithmic approximation. The determination for the divergence of the axial-vector current is found to be unreliable due to large uncertainties in the hadronic parametrisation of the two-point function.From the sum rule for the divergence of the vector current, we obtain a value of m s ≡ m s (1 GeV) = 189 ± 32 MeV, where the error is dominated by the unknown perturbative O(α 3 s ) correction. Assuming a continued geometric growth of the perturbation series, we find m s = 178 ± 18 MeV. Using both determinations of m s , together with quark-mass ratios from chiral perturbation theory, we also give estimates of the light quark masses m u and m d .