74 research outputs found
Analytic Approach to Perturbative QCD and Renormalization Scheme Dependence
We further develop the approach recently used to construct an analytic
ghost-free model for the QCD running coupling based on the requirement of the
-analyticity and apply it to the process of annihilation into
hadrons to study the renormalization scheme dependence of the
cross-section ratio. \par By transforming the relevant QCD corrections up to
the three-loop level into the "analytized" form we show that the
expression thus obtained is remarkably stable (as compared to the conventional
perturbative approach) with respect to the renormalization scheme dependence
for the whole low-energy region.Comment: 6 pages, LaTeX with psfig.sty, PostScript figur
Analytic Properties of the QCD Running Coupling Constant and Decay
A non-perturbative expansion method which gives a well-defined analytic
continuation of the running coupling constant from the spacelike to the
timelike region is applied to the inclusive semileptonic decay of the
--lepton. The method allows us to evaluate by integration over
the non-perturbative physical region, rather than by using Cauchy's theorem,
and hence to incorporate threshold effects in a very direct way. Within our
framework the difference between the effective coupling constants in the
timelike and spacelike domains can be substantial and is not simply a matter of
the standard terms.Comment: LaTeX, 11 page
QCD Running Coupling Constant in the Timelike Region
By using a non-perturbative expansion and the dispersion relation for the
Adler --function we propose a new method for constructing the QCD effective
coupling constant in the timelike region.Comment: LaTeX, 11 pages, 4 figure
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.
Hadronic decay, the renormalization group, analiticity of the polarization operators and QCD parameters
The ALEPH data on hadronic tau-decay is throughly analysed in the framework
of QCD. The perturbative calculations are performed in 1-4-loop approximation.
The analytical properties of the polarization operators are used in the whole
complex q^2 plane. It is shown that the QCD prediction for R_{tau} agrees with
the measured value R_{tau} not only for conventional Lambda^{conv}_3 =
(618+-29) MeV but as well as for Lambda^{new}_3 = (1666+-7) MeV. The
polarization operator calculated using the renormgroup has nonphysical cut
[-Lambda^2_3, 0]. If Lambda_3 = Lambda^{conv}_3, the contribution of only
physical cut is deficient in the explanation of the ALEPH experiment. If
Lambda_3 = Lambda^{new}_3 the contribution of nonphysical cut is very small and
only the physical cut explains the ALEPH experiment. The new sum rules which
follow only from analytical properties of polarization operators are obtained.
Basing on the sum rules obtained, it is shown that there is an essential
disagreement between QCD perturbation theory and the tau-lepton hadronic decay
experiment at conventional value Lambda_3. In the evolution upwards to larger
energies the matching of r(q^2) (Eq.(12)) at the masses J/psi, Upsilon and 2m_t
was performed. The obtained value alpha_s(-m^2_z) = 0.141+-0.004 (at Lambda_3 =
Lambda^{new}_3) differs essentially from conventional value, but the
calculation of the values R(s) = sigma(e+e- -> hadrons)/sigma(e+e- -> mu+mu-),
R_l = Gamma(Z -> hadrons)/Gamma(Z -> leptons), alpha_s(-3 GeV^2), alpha_s(-2.5
GeV^2) does not contradict the experiments.Comment: 20 page
Resummation of the hadronic tau decay width with the modified Borel transform method
A modified Borel transform of the Adler function is used to resum the
hadronic tau decay width ratio. In contrast to the ordinary Borel transform,
the integrand of the Borel integral is renormalization--scale invariant. We use
an ansatz which explicitly accounts for the structure of the leading infrared
renormalon. Further, we use judiciously chosen conformal transformations for
the Borel variable, in order to map sufficiently away from the origin the other
ultraviolet and infrared renormalon singularities. In addition, we apply Pade
approximants for the corresponding truncated perturbation series of the
modified Borel transform, in order to further accelerate the convergence.
Comparing the results with the presently available experimental data on the tau
hadronic decay width ratio, we obtain . These predictions
virtually agree with those of our previous resummations where we used ordinary
Borel transforms instead.Comment: 32 pages, 2 eps-figures, revtex; minor changes in the formulations; a
typo in Eq.(47) corrected; version as appearing in Phys. Rev.
Chiral phase boundary of QCD at finite temperature
We analyze the approach to chiral symmetry breaking in QCD at finite
temperature, using the functional renormalization group. We compute the running
gauge coupling in QCD for all temperatures and scales within a simple truncated
renormalization flow. At finite temperature, the coupling is governed by a
fixed point of the 3-dimensional theory for scales smaller than the
corresponding temperature. Chiral symmetry breaking is approached if the
running coupling drives the quark sector to criticality. We quantitatively
determine the phase boundary in the plane of temperature and number of flavors
and find good agreement with lattice results. As a generic and testable
prediction, we observe that our underlying IR fixed-point scenario leaves its
imprint in the shape of the phase boundary near the critical flavor number:
here, the scaling of the critical temperature is determined by the
zero-temperature IR critical exponent of the running coupling.Comment: 39 pages, 8 figure
The check of QCD based on the tau-decay data analysis in the complex q^2-plane
The thorough analysis of the ALEPH data on hadronic tau-decay is performed in
the framework of QCD. The perturbative calculations are performed in 3 and
4-loop approximations. The terms of the operator product expansion (OPE) are
accounted up to dimension D=8. The value of the QCD coupling constant
alpha_s(m_tau^2)=0.355 pm 0.025 was found from hadronic branching ratio R_tau.
The V+A and V spectral function are analyzed using analytical properties of
polarization operators in the whole complex q^2-plane. Borel sum rules in the
complex q^2 plane along the rays, starting from the origin, are used. It was
demonstrated that QCD with OPE terms is in agreement with the data for the
coupling constant close to the lower error edge alpha_s(m_tau^2)=0.330. The
restriction on the value of the gluonic condensate was found
=0.006 pm 0.012 GeV^2. The analytical perturbative QCD was
compared with the data. It is demonstrated to be in strong contradiction with
experiment. The restrictions on the renormalon contribution were found. The
instanton contributions to the polarization operator are analyzed in various
sum rules. In Borel transformation they appear to be small, but not in spectral
moments sum rules.Comment: 24 pages; 1 latex + 13 figure files. V2: misprints are corrected,
uncertainty in alpha_s is explained in more transparent way, acknowledgement
is adde
Mass spectra of doubly heavy Omega_QQ' baryons
We evaluate the masses of baryons composed of two heavy quarks and a strange
quark with account for spin-dependent splittings in the framework of potential
model with the KKO potential motivated by QCD with a three-loop beta-function
for the effective charge consistent with both the perturbative limit at short
distances and linear confinement term at long distances between the quarks. The
factorization of dynamics is supposed and explored in the nonrelativistic
Schroedinger equation for the motion in the system of two heavy quarks
constituting the doubly heavy diquark and the strange quark interaction with
the diquark. The limits of approach, its justification and uncertainties are
discussed. Excited quasistable states are classified by the quantum numbers of
heavy diquark composed by the heavy quarks of the same flavor.Comment: 14 pages, revtex4-file, 3 eps-figures, 5 tables, typos correcte
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