50 research outputs found
Analytic perturbation theory in QCD and Schwinger's connection between the beta-function and the spectral density
We argue that a technique called analytic perturbation theory leads to a
well-defined method for analytically continuing the running coupling constant
from the spacelike to the timelike region, which allows us to give a
self-consistent definition of the running coupling constant for timelike
momentum. The corresponding -function is proportional to the spectral
density, which confirms a hypothesis due to Schwinger.Comment: 11 pages, 2 figure
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
A novel integral representation for the Adler function
New integral representations for the Adler D-function and the R-ratio of the
electron-positron annihilation into hadrons are derived in the general
framework of the analytic approach to QCD. These representations capture the
nonperturbative information encoded in the dispersion relation for the
D-function, the effects due to the interrelation between spacelike and timelike
domains, and the effects due to the nonvanishing pion mass. The latter plays a
crucial role in this analysis, forcing the Adler function to vanish in the
infrared limit. Within the developed approach the D-function is calculated by
employing its perturbative approximation as the only additional input. The
obtained result is found to be in reasonable agreement with the experimental
prediction for the Adler function in the entire range of momenta .Comment: 11 pages, 3 figure
Rational approximations in Analytic QCD
We consider the ``modified Minimal Analytic'' (mMA) coupling that involves an
infrared cut to the standard MA coupling. The mMA coupling is a Stieltjes
function and, as a consequence, the paradiagonal Pade approximants converge to
the coupling in the entire -plane except on the time-like semiaxis below
the cut. The equivalence between the narrow width approximation of the
discontinuity function of the coupling, on the one hand, and this Pade
(rational) approximation of the coupling, on the other hand, is shown. We
approximate the analytic analogs of the higher powers of mMA coupling by
rational functions in such a way that the singularity region is respected by
the approximants.Several comparisons, for real and complex arguments ,
between the exact and approximate expressions are made and the speed of
convergence is discussed. Motivated by the success of these approximants, an
improvement of the mMA coupling is suggested, and possible uses in the
reproduction of experimental data are discussed.Comment: 12 pages,9 figures (6 double figures); figs.6-8 corrected due to a
programming error; analysis extended to two IR cutoffs; Introduction
rewritten; to appear in J.Phys.
Analytic Perturbation Theory for Practitioners and Upsilon Decay
Within the ghost-free Analytic Perturbation Theory (APT), devised in the last
decade for low energy QCD, simple approximations are proposed for 3-loop
analytic couplings and their effective powers, in both the space-like
(Euclidean) and time-like (Minkowskian) regions, accurate enough in the large
range (1--100 GeV) of current physical interest.\par Effectiveness of the new
Model is illustrated by the example of decay where the
standard analysis gives value that is
inconsistent with the bulk of data for .
Instead, we obtain that
corresponds to that is close to the world
average.\par The issue of scale uncertainty for decay is also
discussed.Comment: 12 pages, 0 figures. Model slightly modified to increase its
accuracy. Numerical results upgraded, references added. The issue of scale
uncertainty is discusse
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
Infrared enhanced analytic coupling and chiral symmetry breaking in QCD
We study the impact on chiral symmetry breaking of a recently developed model
for the QCD analytic invariant charge. This charge contains no adjustable
parameters, other than the QCD mass scale , and embodies asymptotic
freedom and infrared enhancement into a single expression. Its incorporation
into the standard form of the quark gap equation gives rise to solutions for
the dynamically generated mass that display a singular confining behaviour at
the origin. Using the Pagels-Stokar method we relate the obtained solutions to
the pion decay constant , and estimate the scale parameter ,
in the presence of four active quarks, to be about 880 MeV.Comment: 14 pages, 3 figures; to appear in J. Phys.
Leptonic constants of heavy quarkonia in potential approach of NRQCD
We consider a general scheme for calculating the leptonic constant of heavy
quarkonium QQ-bar in the framework of nonrelativistic quantum chromodynamics,
NRQCD, operating as the effective theory of nonrelativistic heavy quarks. We
explore the approach of static potential in QCD, which takes into account both
the evolution of effective charge in the three-loop approximation and the
linearly raising potential term, which provides the quark confinement. The
leptonic constants of bb-bar and cc-bar systems are evaluated by making use of
two-loop anomalous dimension for the current of nonrelativistic quarks, where
the factor for the normalization of matrix element is introduced in order to
preserve the renormalization group invariance of estimates.Comment: 18 pages, 6 eps-figures, discussion and references added, vNRQCD
analysis considere
Renorm-group, Causality and Non-power Perturbation Expansion in QFT
The structure of the QFT expansion is studied in the framework of a new
"Invariant analytic" version of the perturbative QCD. Here, an invariant
(running) coupling is transformed
into a "--analytized" invariant coupling which, by constuction, is free of ghost singularities due to
incorporating some nonperturbative structures.
Meanwhile, the "analytized" perturbation expansion for an observable , in
contrast with the usual case, may contain specific functions , the "n-th power of analytized as a whole", instead
of . In other words, the pertubation series for , due to
analyticity imperative, may change its form turning into an {\it asymptotic
expansion \`a la Erd\'elyi over a nonpower set} .
We analyse sets of functions and discuss properties of
non-power expansion arising with their relations to feeble loop and scheme
dependence of observables.
The issue of ambiguity of the invariant analytization procedure and of
possible inconsistency of some of its versions with the RG structure is also
discussed.Comment: 12 pages, LaTeX To appear in Teor. Mat. Fizika 119 (1999) No.
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