QED, Hadronic, and Electroweak Standard Model contributions to the muon anomalous magnetic moment, a µ ≡ (g µ − 2)/2, and their theoretical uncertainties are scrutinized. The status and implications of the recently reported 2.6 sigma experiment vs. theory deviation a exp µ − a SM µ = 426(165) × 10 −11 are discussed. Possible explanations due to supersymmetric loop effects with m SUSY ≃ 55 √ tan β GeV, radiative mass mechanisms at the 1-2 TeV scale and other "New Physics" scenarios are examined.

Combining our results for various O(alpha[s]) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find B(B[over ]-->X[s]gamma)=(3.15+/-0.23) x 10(-4) for Egamma>1.6 GeV in the B[over ]-meson rest frame. The four types of uncertainties:nonperturbative (5%), parametric (3%), higher-order (3%), and m(c)-interpolation ambiguity (3%) have been added in quadrature to obtain the total error.

Effects of strong interactions on the two loop electroweak radiative corrections to the muon anomalous magnetic moment, a µ = (g µ − 2)/2, are examined. Short-distance logs are shown to be unaffected. Computation of long-distance contributions is improved by use of an effective field theory approach that preserves the chiral properties of QCD and accounts for constraints from the operator product expansion. Small, previously neglected, two loop contributions, suppressed by a 1 − 4 sin 2 θ W factor, are computed and the complete three loop leading short-distance logs are reevaluated. These refinements lead to a reduction in uncertainties and a slight shift in the total electroweak contribution to a EW µ = 154(1)(2) × 10 −11 where the first error corresponds to hadronic uncertainties and the second is primarily due to the allowed Higgs mass range.

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We present the O(α 2 s ) corrections to the cross section for the reaction e + e − → γ * → QQ in the energy region close to the threshold. We assume that the energy of the reaction is such that both the perturbative expansion in the strong coupling constant α s and expansion in the velocity β of the heavy quarks can be used. We explicitly obtain terms O(α 2 s /β 2 , α 2 s /β, α 2 s ) in the relative correction to the threshold cross section. Using the ideas of asymptotic expansions, we demonstrate how an expansion of Feynman diagrams in the threshold region is constructed. From this analysis we obtain a matching relation between the vector current in full QCD and the quark-antiquark current in NRQCD at leading order in 1/m and the second order in the strong coupling constant.Theoretical predictions for the cross section of the reaction e + e − → QQ in the energy region close to the QQ threshold are of considerable interest for various phenomena. They are important for determinations of the b and c quark masses, as well as the value of the QCD coupling constant α s (µ), with µ ∼ 1 − 2 GeV, if one uses the sum rule approach for Υ and J/ψ hadrons proposed in [1]; achievement of the O(α 2 s ) accuracy is considered very important for these quantities. One should also mention the ongoing efforts to determine the decay rates of the heavy quarkonia to leptons with the O(α 2 s ) accuracy [2]. Also, for the future e + e − or µ + µ − colliders one is considering precision measurements of the top quark properties by studying its threshold production region. It is well known that for these and other applications, where the threshold region is of interest, the fixed order perturbative calculations break down and a resummation of the terms singular at threshold is mandatory. In the leading order, such resummation yields the well known Sommerfeld-Sakharov factor for the threshold production cross section. Aiming at the O(α 2 s ) accuracy for the threshold cross section, the first thing to be calculated is the perturbative expression for the cross 1