31 research outputs found

    The Bjorken Sum Rule in the Analytic Approach to Perturbative QCD

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    Results of applying analytic perturbation theory (APT) to the Bjorken sum rule are presented. We study the third-order QCD correction within the analytic approach and investigate its renormalization scheme dependence. We demonstrate that, in the framework of the method, theoretical predictions of the Bjorken sum rule are, practically, scheme independent for the entire interval of momentum transfer.Comment: 12 pages, 3 eps figures, uses elsart.cl

    Analytical calculations of the tenth order QED radiative corrections to lepton anomalies within the Mellin-Barnes representation

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    We investigate the radiative quantum electrodynamic (QED) corrections to the lepton (L=e, μL=e, ~\mu and τ\tau) anomalous magnetic moment due to the contributions of diagrams with insertions of the photon vacuum polarisation operator consisting solely of four closed lepton (l=e, μl=e, ~\mu and τ\tau) loops. Moreover, we focus on specific operators with two loops formed by leptons LL of the same type as the external one, the other two formed by leptons \ell different from LL. The approach is essentially based on the employment of the Mellin-Barnes representation of the xx-parametrization of the corresponding Feynman diagrams. This allows one to obtain, for the first time, exact analytical expressions for the radiative corrections of the tenth order w.r.t. the electromagnetic coupling constant ee. Analytically, the radiative corrections are expressed in terms of the ratio r=m/mLr=m_\ell/m_L of the internal to external lepton masses. The dependence on rr is investigated numerically in the whole interval of rr, 0<r<0 < r < \infty. To make comparisons with earlier published results possible, our exact analytical expressions are expanded about r=0r=0 and rr \to \infty and compared with the corresponding asymptotic expansions known in the literature.Comment: 20 pages, 4 figure

    Renormalization Scheme Dependence in Variational Approach to QCD

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    We present a detailed investigation of the renormalization scheme dependence for the Adler 29-function in the framework of the varia­tional approach to QCD

    The Adler Function for Light Quarks in Analytic Perturbation Theory

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    The method of analytic perturbation theory, which avoids the problem of ghost-pole type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the "light" Adler function corresponding to the non-strange vector channel of the inclusive decay of the τ\tau lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the ``experimental'' Adler function down to the lowest energy scale.Comment: 13 pages, one ps figure, REVTe

    The Gross--Llewellyn Smith Sum Rule in the Analytic Approach to Perturbative QCD

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    We apply analytic perturbation theory to the Gross--Llewellyn Smith sum rule. We study the Q2Q^2 evolution and the renormalization scheme dependence of the analytic three-loop QCD correction to this sum rule, and demonstrate that the results are practically renormalization scheme independent and lead to rather different Q2Q^2 evolution than the standard perturbative correction possesses.Comment: 17 pages, 9 eps figures, REVTe

    Remark on the perturbative component of inclusive τ\tau-decay

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    In the context of the inclusive τ\tau-decay, we analyze various forms of perturbative expansions which have appeared as modifications of the original perturbative series. We argue that analytic perturbation theory, which combines renormalization-group invariance and Q2Q^2-analyticity, has significant merits favoring its use to describe the perturbative component of τ\tau-decay.Comment: 5 pages, ReVTEX, 2 eps figures. Revised paper includes clarifying remarks and corrected references. To be published in Phys. Rev.

    Ten years of the Analytic Perturbation Theory in QCD

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    The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The Analytic Perturbation Theory constitutes the next step of the improvement of perturbative expansions. Specifically, it involves additional analyticity requirement which is based on the causality principle and implemented in the K\"allen--Lehmann and Jost--Lehmann representations. Eventually, this approach eliminates spurious singularities of the perturbative power series and enhances the stability of the latter with respect to both higher loop corrections and the choice of the renormalization scheme. The paper contains an overview of the basic stages of the development of the Analytic Perturbation Theory in QCD, including its recent applications to the description of hadronic processes.Comment: 26 pages, 9 figures, to be published in Theor. Math. Phys. (2007

    Radiative corrections to the cross section of e+pν+ne^-+p\to \nu+n and the crossed processes

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    Born cross section and the radiative corrections to its lowest order are considered in the frame work of QED with structureless nucleons including the emission of virtual and real photons. Result is generalized to take into account radiative corrections in higher orders of perturbation theory in the leading and next-to leading logarithmic approximation. Crossing processes are considered in the leading approximation.Comment: 11 pages, 1 figur
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