268 research outputs found
QCD coupling below 1 GeV from quarkonium spectrum
In this paper we extend the work synthetically presented in Ref.[1] and give
theoretical details and complete tables of numerical results. We exploit
calculations within a Bethe-Salpeter (BS) formalism adjusted for QCD, in order
to extract an ``experimental'' strong coupling \alpha_s^{exp}(Q^2) below 1 GeV
by comparison with the meson spectrum. The BS potential follows from a proper
ansatz on the Wilson loop to encode confinement and is the sum of a
one-gluon-exchange and a confinement terms. Besides, the common perturbative
strong coupling is replaced by the ghost-free expression \alpha_E(Q^2)
according to the prescription of Analytic Perturbation Theory (APT). The
agreement of \alpha_s^{exp}(Q^2) with the APT coupling \alpha_E(Q^2) turns out
to be reasonable from 1 GeV down to the 200 MeV scale, thus confirming
quantitatively the validity of the APT prescription. Below this scale, the
experimental points could give a hint on the vanishing of \alpha_s(Q^2) as Q
approaches zero. This infrared behaviour would be consistent with some lattice
results and a ``massive'' generalization of the APT approach. As a main result,
we claim that the combined BS-APT theoretical scheme provides us with a rather
satisfactory correlated understanding of very high and rather low energy
phenomena from few hundreds MeV to few hundreds GeV.Comment: Preliminary revision. Typos corrected, comments and references adde
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.
Bound state approach to the QCD coupling at low energy scales
We exploit theoretical results on the meson spectrum within the framework of
a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an
``experimental'' coupling \alpha_s^{exp}(Q^2) below 1 GeV by comparison with
the data. Our results for \alpha_s^{exp}(Q^2) exhibit a good agreement with the
infrared safe Analytic Perturbation Theory (APT) coupling from 1 GeV down to
200 MeV. As a main result, we claim that the combined BS-APT theoretical scheme
provides us with a rather satisfactory correlated understanding of very high
and low energy phenomena.Comment: Revised version, to appear on Physical Review Letters. 7 pages, 2
figures, Revte
Multicomponent Consideration of Electron Fraction of ECR Source Plasma
The development of physical model and mathematical simulation methods of electron and ion accumulation and production in the ECR ion source is presented. New equations represent electrons in the ECR plasma as a multicomponent media. In the result any kind of experimental or analytical electron distribution function can be approximated with a series of Maxwellian distributions with different temperatures and partial weights. Main positive plasma potential is introduced into consideration in addition to the negative potential dip for highly charged ion confinement. This potential regulates the loss rate of primary cold electrons from the plasma volume and completes the total picture of ECR plasma behavior. The first test of new model and code with recent experimental data of RIKEN 18 GHz ECR source has shown some new opportunities for investigators to study the ECR ion sources
The massive analytic invariant charge in QCD
The low energy behavior of a recently proposed model for the massive analytic
running coupling of QCD is studied. This running coupling has no unphysical
singularities, and in the absence of masses displays infrared enhancement. The
inclusion of the effects due to the mass of the lightest hadron is accomplished
by employing the dispersion relation for the Adler D function. The presence of
the nonvanishing pion mass tames the aforementioned enhancement, giving rise to
a finite value for the running coupling at the origin. In addition, the
effective charge acquires a "plateau-like" behavior in the low energy region of
the timelike domain. This plateau is found to be in agreement with a number of
phenomenological models for the strong running coupling. The developed
invariant charge is applied in the processing of experimental data on the
inclusive lepton decay. The effects due to the pion mass play an
essential role here as well, affecting the value of the QCD scale parameter
extracted from these data. Finally, the massive analytic running
coupling is compared with the effective coupling arising from the study of
Schwinger-Dyson equations, whose infrared finiteness is due to a dynamically
generated gluon mass. A qualitative picture of the possible impact of the
former coupling on the chiral symmetry breaking is presented.Comment: 13 pages, 7 figures, revtex
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
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
Coupling running through the Looking-Glass of dimensional Reduction
The dimensional reduction, in a form of transition from four to two
dimensions, was used in the 90s in a context of HE Regge scattering. Recently,
it got a new impetus in quantum gravity where it opens the way to
renormalizability and finite short-distance behavior. We consider a QFT model
with running coupling defined in both the two domains of
different dimensionality; the \gbar(Q^2)\, evolutions being duly conjugated
at the reduction scale Beyond this scale, in the deep UV 2-dim
region, the running coupling does not increase any more. Instead, it {\it
slightly decreases} and tends to a finite value \gbar_2(\infty) \,< \,
\gbar_2(M^2)\, from above. As a result, the global evolution picture looks
quite peculiar and can propose a base for the modified scenario of gauge
couplings behavior with UV fixed points provided by dimensional reduction
instead of leptoquarks.Comment: 8 pages, 4 figures,Version to match the one which (besides the
Appendix) will appear in "Particles and Nuclei (PEPAN), Letters", v.7, No
6(162) 2010 pp 625-631. Slightly edited, one more reference and related
numerical estimate adde
Resolution of the Landau pole problem in QED
We present new numerical results for the renormalized mass and coupling in
non-compact lattice QED with staggered fermions. Implications for the continuum
limit and the role of the Landau pole are discussed.Comment: 3 pages, talk presented by H. St\"uben at Lattice '97, Edinburg
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