24 research outputs found
Twist-3 Distribute Amplitude of the Pion in QCD Sum Rules
We apply the background field method to calculate the moments of the pion
two-particles twist-3 distribution amplitude (DA) in QCD sum
rules. In this paper,we do not use the equation of motion for the quarks inside
the pion since they are not on shell and introduce a new parameter to
be determined. We get the parameter in this approach. If
assuming the expansion of in the series in Gegenbauer polynomials
, one can obtain its approximate expression which can be
determined by its first few moments.Comment: 12 pages, 3 figure
Nonperturbative Effects from the Resummation of Perturbation Theory
Using the general argument in Borel resummation of perturbation theory that
links the divergent perturbation theory to the nonperturbative effect we argue
that the nonperturbative effect associated with the perturbation theory should
have a branch cut only along the positive real axis in the complex coupling
plane. The component in the weak coupling expansion of the nonperturbative
amplitude, which usually includes the leading term in the weak coupling
expansion, that gives rise to the branch cut can be calculated in principle
from the perturbation theory combined with some exactly calculable properties
of the nonperturbative effect. The realization of this mechanism is
demonstrated in the double well potential and the two-dimensional O(N)
nonlinear sigma model. In these models the leading term in weak coupling of the
nonperturbative effect can be obtained with good accuracy from the first terms
of the perturbation theory. Applying this mechanism to the infrared renormalon
induced nonperturbative effect in QCD, we suggest some of the QCD condensate
effects can be calculated in principle from the perturbation theory.Comment: 21 Pages, 1 Figure; To appear 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
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
On the Behavior of the Effective QCD Coupling alpha_tau(s) at Low Scales
The hadronic decays of the tau lepton can be used to determine the effective
charge alpha_tau(m^2_tau') for a hypothetical tau-lepton with mass in the range
0 < m_tau' < m_tau. This definition provides a fundamental definition of the
QCD coupling at low mass scales. We study the behavior of alpha_tau at low mass
scales directly from first principles and without any renormalization-scheme
dependence by looking at the experimental data from the OPAL Collaboration. The
results are consistent with the freezing of the physical coupling at mass
scales s = m^2_tau' of order 1 GeV^2 with a magnitude alpha_tau ~ 0.9 +/- 0.1.Comment: 15 pages, 4 figures, submitted to Physical Review D, added
references, some text added, no results nor figures change
Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation
We use various methods of Borel integration to calculate the binding ground
energies and masses of b-bbar and t-tbar quarkonia. The methods take into
account the leading infrared renormalon structure of the hard+soft part of the
binding energies E(s), and of the corresponding quark pole masses m_q, where
the contributions of these singularities in M(s) = 2 m_q + E(s) cancel.
Beforehand, we carry out the separation of the binding energy into its
hard+soft and ultrasoft parts. The resummation formalisms are applied to
expansions of m_q and E(s) in terms of quantities which do not involve
renormalon ambiguity, such as MSbar quark mass, and alpha_s. The
renormalization scales are different in calculations of m_q, E(s) and E(us).
The MSbar mass of b quark is extracted, and the binding energies of t-tbar and
the peak (resonance) energies for (t+tbar) production are obtained.Comment: 23 pages, 8 double figures, revtex4; the version to appear in
Phys.Rev.D; extended discussion between Eqs.(25) and (26); the paragraph
between Eqs.(32) and (33) is new and explains the numerical dependence of the
residue parameter on the factorization scale; several new references were
added; acknowledgments were modified; the numerical results are unchange