Corrections to the SU(3)×SU(3){\bf SU(3)\times SU(3)} Gell-Mann-Oakes-Renner relation and chiral couplings L8rL^r_8 and H2rH^r_2

Next to leading order corrections to the $SU(3) \times SU(3)$ 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 $\psi_5(0) = (2.8 \pm 0.3) \times 10^{-3} GeV^{4}$, leading to the chiral corrections to GMOR: $\delta_K = (55 \pm 5)$. 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 $SU(2) \times SU(2)$. Combining these results with our previous determination of the corrections to GMOR in chiral $SU(2) \times SU(2)$, $\delta_\pi$, we are able to determine two low energy constants of chiral perturbation theory, i.e. $L^r_8 = (1.0 \pm 0.3) \times 10^{-3}$, and $H^r_2 = - (4.7 \pm 0.6) \times 10^{-3}$, both at the scale of the $\rho$-meson mass.Comment: Revised version with minor correction

Large Scale Morphological Segregation in Optically Selected Galaxy Redshift Catalogs

We present the results of an exhaustive analysis of the morphological segregation of galaxies in the CfA and SSRS catalogs through the scaling formalism. Morphological segregation between ellipticals and spirals has been detected at scales up to 15-20 h$^{-1}$ Mpc in the CfA catalog, and up to 20-30 h$^{-1}$ Mpc in the SSRS catalog. Moreover, it is present not only in the densest areas of the galaxy distribution, but also in zones of moderate density.Comment: 9 pages, (1 figure included), uuencode compressed Postscript, (accepted for publication in ApJ Letters), FTUAM-93-2

Chiral corrections to the SU(2)×SU(2)SU(2)\times SU(2) Gell-Mann-Oakes-Renner relation

The next to leading order chiral corrections to the $SU(2)\times SU(2)$ 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, $\delta_\pi$, the value $\delta_\pi = (6.2, \pm 1.6)$. 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 $\simeq \equiv |_{2\,\mathrm{GeV}} = (- 267 \pm 5 MeV)^3$. As a byproduct, the chiral perturbation theory (unphysical) low energy constant $H^r_2$ is predicted to be $H^r_2 (\nu_\chi = M_\rho) = - (5.1 \pm 1.8)\times 10^{-3}$, or $H^r_2 (\nu_\chi = M_\eta) = - (5.7 \pm 2.0)\times 10^{-3}$.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

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

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, $C_{2 V,A}$, to the Operator Product Expansion (other than $d=2$ 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 $C_{2} \equiv (C_{2V} + C_{2A})/2$ is remarkably stable against variations in the continuum threshold, but depends rather strongly on $\Lambda_{QCD}$. Given the current wide spread in the values of $\Lambda_{QCD}$, as extracted from different experiments, we would conservatively conclude from our analysis that $C_{2}$ is consistent with zero.Comment: A misprint in Eq. (14) has been corrected. No other changes. Paper to appear in Phys. Rev.

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