162 research outputs found
The analytical singlet QCD contributions into the -annihilation Adler function and the generalized Crewther relations
The generalized Crewther relations in the channels of the non-singlet and
vector quark currents are considered. They follow from the double application
of the operator product expansion approach to the same axial
vector-vector-vector triangle amplitude in two regions, adjoining to the angle
sides (or ). We assume that the generalized Crewther relations
in these two kinematic regimes result in the existence of the same perturbation
expression for two products of the coefficient functions of annihilation and
deep-inelastic scattering processes in the non-singlet and vector channels.
Taking into account the 4-th order result for and the perturbative
effects of the violation of the conformal symmetry in the generalized Crewther
relation, we obtain the analytical contribution to the singlet
correction to the -function. Its a-posteriori comparison with the
recent result of direct diagram-by-diagram evaluation of the singlet 4-th order
corrections to - function demonstrates the coincidence of the
predicted and obtained -contributions to the singlet term. They can
be obtained in the conformal invariant limit from the original Crewther
relation. On the contrary to previous belief, the appearance of -terms
in perturbative series in gauge models does not contradict to the property of
conformal symmetry and can be considered as ragular feature. The Banks-Zaks
motivated relation between our predicted and obtained 4-th order corrections is
mentioned. This confirms Baikov-Chetyrkin-Kuhn expectation that the generalized
Crewther relation in the channel of vector currents receives additional singlet
contribution, which in this order of perturbation theory is proportional to the
first coefficient of the QCD -function.Comment: Concrete new foundations explained, abstract updated, presentation
improved, 2 references added, extra acknowledgements added. This work is
dedicated to K. G. Chetyrkin on the occasion of his 60th anniversary, to be
published in Jetp. Lett supposedly in vol.94, issue 1
from decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion
We consider the determination of from hadronic decays, by
investigating the contour-improved (CI) and the fixed-order (FO)
renormalization group summations in the frame of a new perturbation expansion
of QCD, which incorporates in a systematic way the available information about
the divergent character of the series. The new expansion functions, which
replace the powers of the coupling, are defined by the analytic continuation in
the Borel complex plane, achieved through an optimal conformal mapping. Using a
physical model recently discussed by Beneke and Jamin, we show that the new
CIPT approaches the true results with great precision when the perturbative
order is increased, while the new FOPT gives a less accurate description in the
regions where the imaginary logarithms present in the expansion of the running
coupling are large. With the new expansions, the discrepancy of 0.024 in
between the standard CI and FO summations is reduced to
only 0.009. From the new CIPT we predict , which practically coincides with the result of the
standard FOPT, but has a more solid theoretical basis
Energy of Bardeen Model Using Approximate Symmetry Method
In this paper, we investigate the energy problem in general relativity using
approximate Lie symmetry methods for differential equations. This procedure is
applied to Bardeen model (the regular black hole solution). Here we are forced
to evaluate the third-order approximate symmetries of the orbital and geodesic
equations. It is shown that energy must be re-scaled by some factor in the
third-order approximation. We discuss the insights of this re-scaling factor.Comment: 14 pages, no figure, accepted for publication in Physica Script
Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems
We investigate the scalar K pi form factor at low energies by the method of
unitarity bounds adapted so as to include information on the phase and modulus
along the elastic region of the unitarity cut. Using at input the values of the
form factor at t=0 and the Callan-Treiman point, we obtain stringent
constraints on the slope and curvature parameters of the Taylor expansion at
the origin. Also, we predict a quite narrow range for the higher order ChPT
corrections at the second Callan-Treiman point.Comment: 5 pages latex, uses EPJ style files, 3 figures, replaced with version
accepted by EPJ
Theory of unitarity bounds and low energy form factors
We present a general formalism for deriving bounds on the shape parameters of
the weak and electromagnetic form factors using as input correlators calculated
from perturbative QCD, and exploiting analyticity and unitarity. The values
resulting from the symmetries of QCD at low energies or from lattice
calculations at special points inside the analyticity domain can beincluded in
an exact way. We write down the general solution of the corresponding Meiman
problem for an arbitrary number of interior constraints and the integral
equations that allow one to include the phase of the form factor along a part
of the unitarity cut. A formalism that includes the phase and some information
on the modulus along a part of the cut is also given. For illustration we
present constraints on the slope and curvature of the K_l3 scalar form factor
and discuss our findings in some detail. The techniques are useful for checking
the consistency of various inputs and for controlling the parameterizations of
the form factors entering precision predictions in flavor physics.Comment: 11 pages latex using EPJ style files, 5 figures; v2 is version
accepted by EPJA in Tools section; sentences and figures improve
A class of nonlinear wave equations containing the continuous Toda case
We consider a nonlinear field equation which can be derived from a binomial
lattice as a continuous limit. This equation, containing a perturbative
friction-like term and a free parameter , reproduces the Toda case (in
absence of the friction-like term) and other equations of physical interest, by
choosing particular values of . We apply the symmetry and the
approximate symmetry approach, and the prolongation technique. Our main purpose
is to check the limits of validity of different analytical methods in the study
of nonlinear field equations. We show that the equation under investigation
with the friction-like term is characterized by a finite-dimensional Lie
algebra admitting a realization in terms of boson annhilation and creation
operators. In absence of the friction-like term, the equation is linearized and
connected with equations of the Bessel type. Examples of exact solutions are
displayed, and the algebraic structure of the equation is discussed.Comment: Latex file + [equations.sty], 22 p
New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models
We propose a hypothesis on the detailed structure for the representation of
the conformal symmetry breaking term in the basic Crewther relation generalized
in the perturbation theory framework in QCD renormalized in the scheme. We establish the validity of this representation in the
approximation. Using the variant of the generalized Crewther
relation formulated here allows finding relations between specific
contributions to the QCD perturbation series coefficients for the flavor
nonsinglet part of the Adler function for the electron-positron
annihilation in hadrons and to the perturbation series coefficients for the
Bjorken sum rule for the polarized deep-inelastic lepton-nucleon
scattering. We find new relations between the coefficients of
and . Satisfaction of one of them serves as an
additional theoretical verification of the recent computer analytic
calculations of the terms of order in the expressions for these
two quantities.Comment: 12 pages, Title modified, abstract modified, improved and extended
variant of the talks, presented at Int. Seminar "Quarks-2010" (6-12 June,
2010, Kolomna) and Int. Workshop Hadron Structure and QCD: From Low to High
Energies (5-9 July 2010, Gatchina
Improving the energy efficiency of wind turbines for charging batteries
The article describes the method for determining the optimal angular velocity and the number of turns of the generator winding on permanent magnets powered by a wind turbine operating in specific operating conditions according to the wind speed regime. The optimization criterion is the maximum potential of energy that can be used to charge the battery. The permissible power of the generator and wind turbine, current and battery charging voltage are accepted as limiting factors. The restriction is provided by connecting a ballast resistor to the generator output. The power developed by the turbine is determined taking into account the wind energy utilization factor, which depends on the angular velocity of its shaft and wind speed. Two variants of power limitation are compared: by limiting the angular velocity by aerodynamic means and by stopping the wind turbine. The return of energy to charging in both cases is determined taking into account the distribution of wind speeds, obeying the Weibull probability distribution law. As an example, the calculation of the possible annual power generation for charging a battery with a capacity of 200 A∙h with a voltage of 24 volts from a synchron generator with a number of poles of 48 driven by a wind turbine with a radius of 2 meters, operating in an area with an average wind speed of 5 m/s. The calculation shows that for the parameters and operating conditions of the electrical installation used in the example, the maximum annual energy output (3.3 × 103 kWh) is observed at optimal 11 turns of the winding at each of the poles of the generator. The deviation of the number of turns from the optimal one in both directions by 2 times leads, with the same dimensions of the wind turbine, to a decrease in annual energy output by 3...5 times, which is a clear proof of the need to carry out such a calculation for each specific wind turbine
Calculation of gluon and four-quark condensates from the operator expansion
The magnitudes of gluon and four-quark condensates are found from the
analysis of vector mesons consisting of light quarks (the families of
and mesons) in the 3 loops approximation. The QCD model with infinite
number of vector mesons is used to describe the function . This model
describes well the experimental function . Polarization operators
calculated with this model coincide with the Wilson operator expansion at large
. The improved perturbative theory, such that the polarization operators
have correct analytical properties, is used. The result is . The electronic widths of and
are calculated.Comment: 18 pages, latex, changed content slightl
Standard Model Higgs-Boson Branching Ratios with Uncertainties
We present an update of the branching ratios for Higgs-boson decays in the
Standard Model. We list results for all relevant branching ratios together with
corresponding uncertainties resulting from input parameters and missing
higher-order corrections. As sources of parametric uncertainties we include the
masses of the charm, bottom, and top quarks as well as the QCD coupling
constant. We compare our results with other predictions in the literature.Comment: 32 pages, 4 figures, contribution to LHC Higgs Cross Section Working
Group https://twiki.cern.ch/twiki/bin/view/LHCPhysics/CrossSections,
theoretical uncertainties for H->\mu\mu{} added, version to appear in
European Physical Journal
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