31 research outputs found
The Bjorken Sum Rule in the Analytic Approach to Perturbative QCD
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
We investigate the radiative quantum electrodynamic (QED) corrections to the
lepton ( and ) anomalous magnetic moment due to the
contributions of diagrams with insertions of the photon vacuum polarisation
operator consisting solely of four closed lepton ( and )
loops. Moreover, we focus on specific operators with two loops formed by
leptons of the same type as the external one, the other two formed by
leptons different from . The approach is essentially based on the
employment of the Mellin-Barnes representation of the -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 . Analytically, the
radiative corrections are expressed in terms of the ratio of the
internal to external lepton masses. The dependence on is investigated
numerically in the whole interval of , . To make comparisons
with earlier published results possible, our exact analytical expressions are
expanded about and and compared with the corresponding
asymptotic expansions known in the literature.Comment: 20 pages, 4 figure
Renormalization Scheme Dependence in Variational Approach to QCD
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
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 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
We apply analytic perturbation theory to the Gross--Llewellyn Smith sum rule.
We study the 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 evolution than the standard perturbative correction possesses.Comment: 17 pages, 9 eps figures, REVTe
Remark on the perturbative component of inclusive -decay
In the context of the inclusive -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 -analyticity, has significant merits
favoring its use to describe the perturbative component of -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
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 and the crossed processes
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