15,434 research outputs found
Quark masses in QCD: a progress report
Recent progress on QCD sum rule determinations of the light and heavy quark
masses is reported. In the light quark sector a major breakthrough has been
made recently in connection with the historical systematic uncertainties due to
a lack of experimental information on the pseudoscalar resonance spectral
functions. It is now possible to suppress this contribution to the 1% level by
using suitable integration kernels in Finite Energy QCD sum rules. This allows
to determine the up-, down-, and strange-quark masses with an unprecedented
precision of some 8-10%. Further reduction of this uncertainty will be possible
with improved accuracy in the strong coupling, now the main source of error. In
the heavy quark sector, the availability of experimental data in the vector
channel, and the use of suitable multipurpose integration kernels allows to
increase the accuracy of the charm- and bottom-quarks masses to the 1% level.Comment: Invited review paper to be published in Modern Physics Letters
Comment on current correlators in QCD at finite temperature
We address some criticisms by Eletsky and Ioffe on the extension of QCD sum
rules to finite temperature. We argue that this extension is possible, provided
the Operator Product Expansion and QCD-hadron duality remain valid at non-zero
temperature. We discuss evidence in support of this from QCD, and from the
exactly solvable two- dimensional sigma model O(N) in the large N limit, and
the Schwinger model.Comment: 10 pages, LATEX file, UCT-TP-208/94, April 199
Convolutional Goppa Codes
We define Convolutional Goppa Codes over algebraic curves and construct their
corresponding dual codes. Examples over the projective line and over elliptic
curves are described, obtaining in particular some Maximum-Distance Separable
(MDS) convolutional codes.Comment: 8 pages, submitted to IEEE Trans. Inform. Theor
Corrections to the Gell-Mann-Oakes-Renner relation and chiral couplings and
Next to leading order corrections to the
Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite
Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two
types of integration kernels in the FESR are used to suppress the contribution
of the kaon radial excitations to the hadronic spectral function, one with
local and the other with global constraints. The result for the pseudoscalar
current correlator at zero momentum is , leading to the chiral corrections to GMOR: . The resulting uncertainties are mostly due to variations in the upper
limit of integration in the FESR, within the stability regions, and to a much
lesser extent due to the uncertainties in the strong coupling and the strange
quark mass. Higher order quark mass corrections, vacuum condensates, and the
hadronic resonance sector play a negligible role in this determination. These
results confirm an independent determination from chiral perturbation theory
giving also very large corrections, i.e. roughly an order of magnitude larger
than the corresponding corrections in chiral . Combining
these results with our previous determination of the corrections to GMOR in
chiral , , we are able to determine two low
energy constants of chiral perturbation theory, i.e. , and , both at the
scale of the -meson mass.Comment: Revised version with minor correction
Is there evidence for dimension-two corrections in QCD two-point functions?
The ALEPH data on the (non-strange) vector and axial-vector spectral
functions, extracted from tau-lepton decays, is used in order to search for
evidence for a dimension-two contribution, , to the Operator Product
Expansion (other than quark mass terms). This is done by means of a
dimension-two Finite Energy Sum Rule, which relates QCD to the experimental
hadronic information. The average is
remarkably stable against variations in the continuum threshold, but depends
rather strongly on . Given the current wide spread in the values
of , as extracted from different experiments, we would
conservatively conclude from our analysis that is consistent with zero.Comment: A misprint in Eq. (14) has been corrected. No other changes. Paper to
appear in Phys. Rev.
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
Dynamical Critical Phenomena and Large Scale Structure of the Universe: the Power Spectrum for Density Fluctuations
As is well known, structure formation in the Universe at times after
decoupling can be described by hydrodynamic equations. These are shown here to
be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang
equation with time-- dependent viscosity in epochs of dissipation. As a
consequence of the Dynamical Critical Scaling induced by noise and
fluctuations, these equations describe the fractal behavior (with a scale
dependent fractal dimension) observed at the smaller scales for the
galaxy--to--galaxy correlation function and the Harrison--Zel'dovich
spectrum at decoupling. By a Renormalization Group calculation of the
two--point correlation function between galaxies in the presence of (i) the
expansion of the Universe and (ii) non--equilibrium, we can account, from first
principles, for the main features of the observed shape of the power spectrum.Comment: 13 pages with 2 encapsulated PostScript figures included, gzipped tar
forma
- …