17,082 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
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
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
(Pseudo)Scalar Charmonium in Finite Temperature QCD
The hadronic parameters of pseudoscalar () and scalar ()
charmonium are determined at finite temperature from Hilbert moment QCD sum
rules. These parameters are the hadron mass, leptonic decay constant, total
width, and continuum threshold (). Results for in both channels
indicate that starts approximately constant, and then it decreases
monotonically with increasing until it reaches the QCD threshold, , at a critical temperature T = T_c \simeq 180 \; \mbox{MeV}
interpreted as the deconfinement temperature. The other hadronic parameters
behave qualitatively similarly to those of the , as determined in this
same framework. The hadron mass is essentially constant, the total width is
initially independent of T, and after it begins to increase
with increasing up to for
(), and subsequently it decreases sharply up to , for (), beyond which the sum rules are no
longer valid. The decay constant of at first remains basically flat up
to , then it starts to decrease up to , and finally it increases sharply with increasing . In the case of
the decay constant does not change up to where
it begins a gentle increase up to beyond which it
increases dramatically with increasing . This behaviour contrasts with that
of light-light and heavy-light quark systems, and it suggests the survival of
the and the states beyond the critical temperature, as
already found for the from similar QCD sum rules. These conclusions
are very stable against changes in the critical temperature in the wide range
T_c = 180 - 260 \; \mbox{MeV}.Comment: 12 pages, 5 figures. A wide range of critical temperatures has been
considered. No qualitative changes to the conclusion
Numerical simulation of a binary communication channel: Comparison between a replica calculation and an exact solution
The mutual information of a single-layer perceptron with Gaussian inputs
and deterministic binary outputs is studied by numerical simulations. The
relevant parameters of the problem are the ratio between the number of output
and input units, , and those describing the two-point
correlations between inputs. The main motivation of this work refers to the
comparison between the replica computation of the mutual information and an
analytical solution valid up to . The most relevant results
are: (1) the simulation supports the validity of the analytical prediction, and
(2) it also verifies a previously proposed conjecture that the replica solution
interpolates well between large and small values of .Comment: 6 pages, 8 figures, LaTeX fil
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