75 research outputs found
Fractional Analytic QCD beyond Leading Order in timelike region
In this paper we show that, as in the spacelike case, the inverse logarithmic
expansion is applicable for all values of the argument of the analytic coupling
constant. We present two different approaches, one of which is based primarily
on trigonometric functions, and the latter is based on dispersion integrals.
The results obtained up to the 5th order of perturbation theory, have a
compact form and their acquiring is much easier than the methods that have been
used before. As an example, we apply our results to study the Higgs boson decay
into a bb pair.Comment: 30 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:2203.0930
On Fractional Analytic QCD
We present a brief overview of fractional analytic QCD.Comment: 7 pages, 1 figure, contribution to the proceedings of the XXVth
International Baldin Seminar on High Energy Physics Problems Relativistic
Nuclear Physics and Quantum Chromodynamics (September 18-23, Dubna, Russia
Investigation of the Method of Dynamic Microwave Power Redistribution in a Resonator-Type Plasmatron
The investigation results of a dynamic microwave power fmicrowave = 2, 45 ± 0,05 GHz redistribution in a 9000 cm3 reaction-discharge chamber of a microwave resonator-type plasmatron are presented. In order to redistribute the microwave power, a rotating metallic four-blade L-form dissector placed above the reaction-discharge chamber was used. The microwave power in the local points at the axis of the chamber with plasma and without it was measured applying the "active probe" method. During the experiments the chamber contained silicon plates. Periodical interchange of maximum and minimum microwave power values along the chamber axis was established experimentally. Note, when the dissector was rotating, the range of maximum and minimum "active probe" values dispersion decreased. It has been established that during the dissector rotation the microwave power in the local discharge areas changes with periodic repetition every quarter of revolution
Neutron star inner crust: reduction of shear modulus by nuclei finite size effect
The elasticity of neutron star crust is important for adequate interpretation
of observations. To describe elastic properties one should rely on theoretical
models. The most widely used is Coulomb crystal model (system of point-like
charges on neutralizing uniform background), in some works it is corrected for
electron screening. These models neglect finite size of nuclei. This
approximation is well justified except for the innermost crustal layers, where
nuclei size becomes comparable with the inter-nuclear spacing. Still, even in
those dense layers it seems reasonable to apply the Coulomb crystal result, if
one assumes that nuclei are spherically symmetric: Coulomb interaction between
them should be the same as interaction between point-like charges. This
argument is indeed correct, however, as we point here, shear of crustal lattice
generates (microscopic) quadrupole electrostatic potential in a vicinity of
lattice cites, which induces deformation on the nuclei. We analyze this problem
analytically within compressible liquid drop model, using ionic spheroid model
(which is generalization of well known ion sphere model). In particular, for
ground state crust composition the effective shear modulus is reduced for a
factor of , where u is the filling factor (ratio
of the nuclei volume to the volume of the cell). This result is universal and
does not depend on the applied nucleon interaction model. For the innermost
layers of inner crust u~0.2 leading to reduction of the shear modulus by ~25%,
which can be important for correct interpretation of quasi-periodic
oscillations in the tails of magnetar flares.Comment: 7 pages, submitted to MNRAS on Sept.
Bjorken sum rule with analytic coupling at low Q2 values
The experimental data obtained for the polarized Bjorken sum rule
\Gamma^{(p-n)}_1(Q^2) for small values of Q2 are approximated by the
predictions obtained in the framework of analytic QCD up to the 5th order
perturbation theory, whose coupling constant does not contain the Landau pole.
We found an excellent agreement between the experimental data and the
predictions of analytic QCD, as well as a strong difference between these data
and the results obtained in the framework of standard QCD.Comment: 9 pages, 1 figur
A series of coverings of the regular n-gon
We define an infinite series of translation coverings of Veech's double-n-gon
for odd n greater or equal to 5 which share the same Veech group. Additionally
we give an infinite series of translation coverings with constant Veech group
of a regular n-gon for even n greater or equal to 8. These families give rise
to explicit examples of infinite translation surfaces with lattice Veech group.Comment: A missing case in step 1 in the proof of Thm. 1 b was added. (To
appear in Geometriae Dedicata.
Diffractive orbits in isospectral billiards
Isospectral domains are non-isometric regions of space for which the spectra
of the Laplace-Beltrami operator coincide. In the two-dimensional Euclidean
space, instances of such domains have been given. It has been proved for these
examples that the length spectrum, that is the set of the lengths of all
periodic trajectories, coincides as well. However there is no one-to-one
correspondence between the diffractive trajectories. It will be shown here how
the diffractive contributions to the Green functions match nevertheless in a
''one-to-three'' correspondence.Comment: 20 pages, 6 figure
Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces
We establish the background for the study of geodesics on noncompact
polygonal surfaces. For illustration, we study the recurrence of geodesics on
-periodic polygonal surfaces. We prove, in particular, that almost all
geodesics on a topologically typical -periodic surface with boundary are
recurrent.Comment: 34 pages, 13 figures. To be published in V. V. Kozlov's Festschrif
A pseudointegrable Andreev billiard
A circular Andreev billiard in a uniform magnetic field is studied. It is
demonstrated that the classical dynamics is pseudointegrable in the same sense
as for rational polygonal billiards. The relation to a specific polygon, the
asymmetric barrier billiard, is discussed. Numerical evidence is presented
indicating that the Poincare map is typically weak mixing on the invariant
sets. This link between these different classes of dynamical systems throws
some light on the proximity effect in chaotic Andreev billiards.Comment: 5 pages, 5 figures, to appear in PR
Hexagonal dielectric resonators and microcrystal lasers
We study long-lived resonances (lowest-loss modes) in hexagonally shaped
dielectric resonators in order to gain insight into the physics of a class of
microcrystal lasers. Numerical results on resonance positions and lifetimes,
near-field intensity patterns, far-field emission patterns, and effects of
rounding of corners are presented. Most features are explained by a
semiclassical approximation based on pseudointegrable ray dynamics and boundary
waves. The semiclassical model is also relevant for other microlasers of
polygonal geometry.Comment: 12 pages, 17 figures (3 with reduced quality
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