We present two variants of an approach for evaluation of observables in analytic QCD models. The approach is motivated by the skeleton expansion in a certain class of schemes. We then evaluate the Adler function at low energies in one variant of this approach, in various analytic QCD models for the coupling parameter, and compare with perturbative QCD predictions and the experimental results. We introduce two analytic QCD models for the coupling parameter which reproduce the measured value of the semihadronic τ decay ratio. Further, we evaluate the Bjorken polarized sum rule at low energies in both variants of the evaluation approach, using for the coupling parameter the analytic QCD model of Shirkov and Solovtsov, and compare with values obtained by the evaluation approach of Milton et al. and Shirkov. PACS numbers: 12.38.Cy, 12.38.Aw,12.40.Vv Consider an observable O(Q 2 ) depending on a single space-like scale Q 2 (≡ −q 2 ) > 0 and assume that the skeleton expansion for this observable exists:The observable is normalized such that O(Q 2 ) = a pt at first order in perturbation theory. The characteristic functions F A O are symmetric functions and have the following normalization:and s O i are the skeleton coefficients. The perturbative running coupling a pt (Q 2 ) ≡ α(Q 2 )/π obeys the renormalization group (RG) equation:In QCD, the first two coefficients β 0 = (1/4)(11 − 2n f /3) and β 1 = (1/16)(102 − 38n f /3) are scheme-independent in mass-independent schemes; n f is the number of active quarks flavors. The value of C depends on the value of the scale Λ in a pt (Λ 2 (C) = Λ 2 (0) e C ) [1]. In MS scheme C = C ≡ −5/3. The skeleton integrands and integrals are independent of C. Expansion (1) exists in QED if one excludes light-by-light subdiagrams [2,3]. In the QCD case, the leading skeleton part was investigated in Refs. [1,4]. We will assume that expansion (1) exists in a certain class of schemes.On the other hand, the RG-improved perturbation expansion for the observable O(Q 2 ) is given byExpanding a pt (te C Q 2 ) around t = e −C inside the integrals in Eq. (1) must give Eq. (4). The skeleton expansion is a reorganization of the perturbation series such that each term in (1) corresponds to the sum of an infinite number of Feynman diagrams. These sums, however, do not converge. Although it is possible to assign a value to these sums, this value is not unique, a renormalon ambiguity is present. In formulation (1) the ambiguities arise from the (nonphysical) Landau singularities of a pt (te C Q 2 ) in the non-perturbative space-like region 1 hep-ph/0601050v3 -one reference added; no other changes; version to appear in J. Phys. G.

Abstract:We obtain an improved determination of the normalization constant of the first infrared renormalon of the pole mass (and the singlet static potential). For N f = 3 it reads N m = 0.563(26). Charm quark effects in the bottom quark mass determination are carefully investigated. Finally, we determine the bottom quark mass using the NNNLO perturbative expression for the Υ(1S) mass. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to pole mass renormalon. Our result for the MS mass reads m b (m b ) = 4201(43) MeV.

Top-quark condensation, in particular the minimal framework in which the neutral Higgs scalar is (predominantly) an effective tt condensate of the standard model, is reviewed. Computational approaches are compared and similarities, differences, and deficiencies pointed out. Extensions of the minimal framework, including scenarios with two composite Higgs doublets, additional neutrino condensates, and tt condensation arising from four-fermion interactions with enlarged symmetries, are described. Possible renormalizable models of underlying physics potentially responsible for the condensation, including topcolor-assisted technicolor frameworks, are discussed. Phenomenological implications of top condensate models are outlined. Outstanding theoretical issues and problems for future investigation are pointed out. Progress in the field after this article was accepted has been briefly covered in a Note added at the end. [S0034-6861(99)

The product of the gluon dressing function and the square of the ghost dressing function in the Landau gauge can be regarded to represent, apart from the inverse power corrections 1/Q 2n , a nonperturbative generalization A(Q 2 ) of the perturbative QCD running coupling a(Q 2 ) (≡ αs(Q 2 )/π). Recent large volume lattice calculations for these dressing functions indicate that the coupling defined in such a way goes to zero as A(Q 2 ) ∼ Q 2 when the squared momenta Q 2 go to zero (Q 2 1 GeV 2 ). In this work we construct such a QCD coupling A(Q 2 ) which fulfills also various other physically motivated conditions. At high momenta it becomes the underlying perturbative coupling a(Q 2 ) to a very high precision. And at intermediate low squared momenta Q 2 ∼ 1 GeV 2 it gives results consistent with the data of the semihadronic τ lepton decays as measured by OPAL and ALEPH. The coupling is constructed in a dispersive way, resulting as a byproduct in the holomorphic behavior of A(Q 2 ) in the complex Q 2 -plane which reflects the holomorphic behavior of the spacelike QCD observables. Application of the Borel sum rules to τ -decay V + A spectral functions allows us to obtain values for the gluon (dimension-4) condensate and the dimension-6 condensate, which reproduce the measured OPAL and ALEPH data to a significantly better precision than the perturbative MS coupling approach.3 It is possible to show that pQCD renormalization schemes exist in which pQCD coupling a(Q 2 ) is holomorphic for Q 2 ∈ C\(−∞, −M 2 thr ] and at the same time reproduces the high-energy QCD phenomenology as well as the semihadronic τ -lepton decay physics [23][24][25]. 4 MiniMOM scheme is known at present to four loops [18][19][20]. 5 In this scheme, however, we rescale Q 2 from the Λ MM to the usual Λ MS convention. 6 In Ref. [29], the matching of A(Q 2 ) and dA(Q 2 )/d ln Q 2 at an IR/UV transition scale Q 2 0 ∼ 1 GeV 2 is imposed, fixing the values of A(0) > 0 and Q 2 0 . On the other hand, our coupling A(Q 2 ) will be holomorphic, no explicit IR/UV matching scale will exist. Instead of the matching, we will impose various physically motivated conditions which will affect simultaneously the behavior of A(Q 2 ) in the UV and IR regimes.10 In principle, we could construct A in any other scheme, e.g., in MS scheme, but then it would not be clear how such a coupling compares with A latt of Ref.[32] in the deep IR regime. For an application and discussion of the MiniMOM scheme in pQCD, see Ref.[56].