1,061,860 research outputs found
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
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
Multidimensional integrable vacuum cosmology with two curvatures
The vacuum cosmological model on the manifold describing the evolution of Einstein spaces of non-zero
curvatures is considered. For the Einstein equations are reduced to the
Abel (ordinary differential) equation and solved, when dim dim. The Kasner-like behaviour of the
solutions near the singularity is considered ( is synchronous
time). The exceptional ("Milne-type") solutions are obtained for arbitrary .
For these solutions are attractors for other ones, when . For dim and certain two-parametric
families of solutions are obtained from ones using "curvature-splitting"
trick. In the case , a family of non-singular
solutions with the topology is found.Comment: 21 pages, LaTex. 5 figures are available upon request (hard copy).
Submitted to Classical and Quantum Gravit
Integration of D-dimensional 2-factor spaces cosmological models by reducing to the generalized Emden-Fowler equation
The D-dimensional cosmological model on the manifold describing the evolution of 2 Einsteinian factor spaces,
and , in the presence of multicomponent perfect fluid source is
considered. The barotropic equation of state for mass-energy densities and the
pressures of the components is assumed in each space. When the number of the
non Ricci-flat factor spaces and the number of the perfect fluid components are
both equal to 2, the Einstein equations for the model are reduced to the
generalized Emden-Fowler (second-order ordinary differential) equation, which
has been recently investigated by Zaitsev and Polyanin within discrete-group
analysis. Using the integrable classes of this equation one generates the
integrable cosmological models. The corresponding metrics are presented. The
method is demonstrated for the special model with Ricci-flat spaces
and the 2-component perfect fluid source.Comment: LaTeX file, no figure
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