184 research outputs found
Towards Order alpha_s^4 Accuracy in tau-decays
Recently computed terms of orders O(\alpha_s^4 n_f^2) in the perturbative
series for the tau decay rate, and similar (new) strange quark mass
corrections, are used to discuss the validity of various optimization schemes.
The results are then employed to arrive at improved predictions for the
complete terms order O(\alpha_s^4) and O(\alpha_s^5) in the massless limit as
well as for terms due to the strange quark mass. Phenomenological implications
are presented.Comment: 14 pages, REVTeX4. The complete paper is also available via the www
at http://www-ttp.physik.uni-karlsruhe.de/Preprints
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
alpha_s from tau decays revisited
Being a determination at low energies, the analysis of hadronic tau decay
data provides a rather precise determination of the strong coupling alpha_s
after evolving the result to M_Z. At such a level of precision, even small
non-perturbative effects become relevant for the central value and error. While
those effects had been taken into account in the framework of the operator
product expansion, contributions going beyond it, so-called duality violations,
have previously been neglected. The following investigation fills this gap
through a finite-energy sum rule analysis of tau decay spectra from the OPAL
experiment, including duality violations and performing a consistent fit of all
appearing QCD parameters. The resulting values for alpha_s(M_tau) are 0.307(19)
in fixed-order perturbation theory and 0.322(26) in contour-improved
perturbation theory, which translates to the n_f=5 values 0.1169(25) and
0.1187(32) at M_Z, respectively.Comment: 4 pages, 3 figures. Prepared for the Proceedings of the International
Workshop on e+e- collisions from Phi to Psi (PHIPSI11), Sep. 19-22, 2011,
BINP, Novosibirsk, Russi
Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants
The different natures of approximate symmetries and their corresponding first
integrals/invariants are delineated in the contexts of both Lie symmetries of
ordinary differential equations and Noether symmetries of the Action Integral.
Particular note is taken of the effect of taking higher orders of the
perturbation parameter. Approximate symmetries of approximate first
integrals/invariants and the problems of calculating them using the Lie method
are considered
Issues in determining alpha_s from hadronic tau decay and electroproduction data
We discuss some key issues associated with duality-violating and
non-perturbative OPE contributions to the theoretical representations of light
quark current-current two-point functions and relevant to precision
determinations of alpha_s from hadronic tau decay and electroproduction
cross-section data. We demonstrate that analyses with an explicit
representation of duality-violating effects are required to bring theoretical
errors in such extractions under control, motivating the accompanying paper in
these proceedings, which presents the results of such an analysis.Comment: 5 pages, 4 figures. Prepared for the Proceedings of the International
Workshop on e+e- collisions from Phi to Psi (PHIPSI11), Sep. 19-22, 2011,
BINP, Novosibirsk, Russi
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
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
Chiral corrections to the Gell-Mann-Oakes-Renner relation
The next to leading order chiral corrections to the
Gell-Mann-Oakes-Renner (GMOR) relation are obtained using the pseudoscalar
correlator to five-loop order in perturbative QCD, together with new finite
energy sum rules (FESR) incorporating polynomial, Legendre type, integration
kernels. The purpose of these kernels is to suppress hadronic contributions in
the region where they are least known. This reduces considerably the systematic
uncertainties arising from the lack of direct experimental information on the
hadronic resonance spectral function. Three different methods are used to
compute the FESR contour integral in the complex energy (squared) s-plane, i.e.
Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a
fixed renormalization scale scheme. We obtain for the corrections to the GMOR
relation, , the value . This result
is substantially more accurate than previous determinations based on QCD sum
rules; it is also more reliable as it is basically free of systematic
uncertainties. It implies a light quark condensate . As a byproduct, the chiral perturbation theory (unphysical) low energy
constant is predicted to be , or .Comment: A comment about the value of the strong coupling has been added at
the end of Section 4. No change in results or conslusion
Accuracy of Calculations Involving Vacuum-Polarization Diagrams: Muonic Hydrogen Lamb Shift and Muon
The contribution of the single electron-loop vacuum-polarization
diagrams to the Lamb shift of the muonic hydrogen has been evaluated recently
by two independent methods. One uses the exact parametric representation of the
vacuum-polarization function while the other relies on the Pad\'{e}
approximation method. High precision of these values offers an opportunity to
examine the reliability of the Monte-Carlo integration as well as that of the
Pad\'{e} method. Our examination covers both muonic hydrogen atom and muon
. We tested them further for the cases involving two-loop vacuum
polarization, where an exact analytic result is known. Our analysis justifies
the result for the Lamb shift of the muonic hydrogen and also resolves the
long-standing discrepancy between two previous evaluations of the muon
value.Comment: 12 pages, 1 figure, title and abstract change
GRACE/SUSY Automatic Generation of Tree Amplitudes in the Minimal Supersymmetric Standard Model
GRACE/SUSY is a program package for generating the tree-level amplitude and
evaluating the corresponding cross section of processes of the minimal
supersymmetric extension of the standard model (MSSM). The Higgs potential
adopted in the system, however, is assumed to have a more general form
indicated by the two-Higgs-doublet model. This system is an extension of GRACE
for the standard model(SM) of the electroweak and strong interactions. For a
given MSSM process the Feynman graphs and amplitudes at tree-level are
automatically created. The Monte-Carlo phase space integration by means of
BASES gives the total and differential cross sections. When combined with
SPRING, an event generator, the program package provides us with the simulation
of the SUSY particle productions.Comment: 39 page, 1 figur
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