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The theoretical evaluation of the coupling constants gpiNN , gKNLambda and gKNSigma is undertaken using QCD sum rules. These quantities were previously calculated with exponential (Borel) kernels used to suppress the unknown contributions of the hadronic continua. This method however introduces arbitrariness and instability in the calculation. In order to avoid these I redo the calculation using polynomial kernels tailored to vanish at the baryonic resonance masses. The results are gpiNN = 12.5 +- 1.0, gKNSigma = 5.45 +- .4, gKNSigma= -(12.7 - 15.0) which are close to experiment and to the predictions of SU(3) and which , with the corresponding Goldberger-Treiman Discrepancy satisfy quite well the Dashen-Weinstein relation., Comment: 10 pages, 3 figures. version 3

The contribution of the hadronic continuum in the QCD sum rule calculation of the parameters entering in pseudoscalar meson mixing is evaluated by making use of simple integration kernels tailored in order to practically eliminate the contribution of the hadronic continuum. This approach avoids the arbitrariness and instability inherent to previous sum rule calculations. An independent evaluation of the mixed quark gluon condensate $\left\langle QGC\right\rangle =$$\left\langle g\bar{q}\sigma_{\mu\nu}\frac{\lambda^{a}}{2}G_{\mu\nu}^{a}q\right\rangle $ which enters in the calculation is presented as well as the calculation of the K-meson decay constant $f_{K}$ to five loops., Comment: Minor omissions added and details explicitised. 10 pages, 2 figures. arXiv admin note: text overlap with arXiv:1804.06066

A new QCD calculation of the B parameter of $K^{0}-\bar{K^{0}}$ mixing is presented. It makes use of polynomial kernels in dispersion integrals in order to practically eliminate the contributions of the unknown pseudoscalar strange continuum. This approach avoids the arbitrariness and instability inherent to the Borel exponential kernels used in previous sum rules calculations. A simultaneous calculation of the mixed quark gluon condensate $\langle g\bar{q}\sigma_{\mu\nu}\frac{\lambda^{a}}{2}\sigma_{\mu\nu}^{a}q\rangle$ which enters in the expression for B is presented. Finally the K-meson decay constant $f_{K}$ is calculated to five loop, Comment: 10 pages, 2 figures

A new QCD sum rule determination of the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a_{\mu}^{\rm hvp}$, is proposed. This approach combines data on $e^{+}e^{-}$ annihilation into hadrons, perturbative QCD and lattice QCD results for the first derivative of the electromagnetic current correlator at zero momentum transfer, $\Pi_{\rm EM}^\prime(0)$. The idea is based on the observation that, in the relevant kinematic domain, the integration kernel $K(s)$, entering the formula relating $a_{\mu}^{\rm hvp}$ to $e^{+}e^{-}$ annihilation data, behaves like $1/s$ times a very smooth function of $s$, the squared energy. We find an expression for $a_{\mu}$ in terms of $\Pi_{\rm EM}^\prime(0)$, which can be calculated in lattice QCD. Using recent lattice results we find a good approximation for $a_{\mu}^{\rm hvp}$, but the precision is not yet sufficient to resolve the discrepancy between the $R(s)$ data-based results and the experimentally measured value., Comment: 14 pages, added some clarifying text and two references, removed typos, results unchanged. Version to be published in Phys.Rev.D

The couplings of the isosinglet axial-vector currents to the Eta and Eta' mesons are evaluated in a stable, model independent way by use of polynomial kernels in dispersion integrals. The corrections to the Gell-Mann-Oakes-Renner relation in the isoscalar channel are deduced. The derivative of the topological susceptibility at the origin is calculated taking into account instantons and instanton screening., Comment: Mistakes corrected. Text after eq.3.14 changed. An evaluation of the topological susceptibility itself is presented in addition

Classic calculations of the magnetic moments mu_p and mu_n of the nucleons using the traditional exponential kernel show instability with respect to variations of the Borel mass as well as arbitrariness with respect to the choice of the onset of perturbative QCD. The use of a polynomial kernel, the coefficients of which are determined by the masses of the nucleon resonances stabilizes the calculation and provides much better damping of the unknown contribution of the nucleon continuum. The method is also applied to the evaluation of the coupling gA of proton to the axial current and to the strong part of the neutron-proton mass difference Delta M_np. All these quantities depend sensitively on the value of the 4-quark condensate < 0 | qqqq | 0 > and the value < 0 | qqqq | 0 > ~ 1.5< 0 | qq | 0 >^2 reproduces the experimental results., Comment: 8 pages, details explicit-ed, misprints corrected, version to appear in Physical Review C

A new QCD calculation of the mass of the nucleon is presented. It makes use of a polynomial kernel in the dispersion integrals tailored to practically eliminate the contribution of the unknown 1/2+ and 1/2- continuum. This approach avoids the arbitrariness and other drawbacks attached to the Borel kernel used in previous sum rules calculations. Our method yields stable results for the nucleon mass and coupling for standard values of the condensates. The prediction of the nucleon mass m_{N}=(0.945 \pm .045) GeV is in good agreement with experiment., Comment: 7 pages

The (non-strange) vector and axial-vector spectral functions extracted from $\tau $-decay by the ALEPH collaboration are confronted with QCD in the framework of a Finite Energy QCD sum rule (FESR) involving a polynomial kernel tuned to suppress the region beyond the kinematical end point where there is no longer data. This effectively allows for a QCD FESR analysis to be performed beyond the region of the existing data. Results show excellent agreement between data and perturbative QCD in the remarkably wide energy range $s = 3 - 10 {GeV}^2$, leaving room for a dimension $d$ =4 vacuum condensate consistent with values in the literature. A hypothetical dimension $d$=2 term in the Operator Product Expansion is found to be extremely small, consistent with zero. Fixed Order and Contour Improved perturbation theory are used, with both leading to similar results within errors. Full consistency is found between vector and axial-vector channel results., Comment: Additional remarks have been added. There is no change in the results, conclusions, etc

The light quark masses are determined using a new QCD Finite Energy Sum Rule (FESR) in the pseudoscalar channel. This FESR involves an integration kernel designed to reduce considerably the contribution of the (unmeasured) hadronic resonance spectral functions. The QCD sector of the FESR includes perturbative QCD (PQCD) to five loop order, and the leading non-perturbative terms. In the hadronic sector the dominant contribution is from the pseudoscalar meson pole. Using Contour Improved Perturbation Theory (CIPT) the results for the quark masses at a scale of 2 GeV are $m_u(Q= 2 {GeV}) = 2.9 \pm 0.2 {MeV}$, $m_d(Q= 2 {GeV}) = 5.3 \pm 0.4 {MeV}$, and $m_s(Q= 2 {GeV}) = 102 \pm 8 {MeV}$, for $\Lambda = 381 \pm 16 {MeV}$, corresponding to $\alpha_s(M_\tau^2) = 0.344 \pm0.009$. In this framework the systematic uncertainty in the quark masses from the unmeasured hadronic resonance spectral function amounts to less than 2 - 3 %. The remaining uncertainties above arise from those in $\Lambda$, the unknown six-loop PQCD contribution, and the gluon condensate, which are all potentially subject to improvement., Comment: In Memoriam: Giuseppe (Beppe) Nardulli, Jan Stern, and Francisco (Paco) Yndurain. Invited talk given by C.A. Dominguez at QCD-08, 14th International QCD Conference, Montpellier, France, July 2008

The up and down quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector divergences, to five loop order in Perturbative QCD (PQCD), and including leading non-perturbative QCD and higher order quark mass corrections. This FESR is designed to reduce considerably the systematic uncertainties arising from the (unmeasured) hadronic resonance sector, which in this framework contributes less than 3-4% to the quark mass. This is achieved by introducing an integration kernel in the form of a second degree polynomial, restricted to vanish at the peak of the two lowest lying resonances. The driving hadronic contribution is then the pion pole, with parameters well known from experiment. The determination is done in the framework of Contour Improved Perturbation Theory (CIPT), which exhibits a very good convergence, leading to a remarkably stable result in the unusually wide window $s_0 = 1.0 - 4.0 {GeV}^2$, where $s_0$ is the radius of the integration contour in the complex energy (squared) plane. The results are: $m_u(Q= 2 {GeV}) = 2.9 \pm 0.2 $ MeV, $m_d(Q= 2 {GeV}) = 5.3 \pm 0.4$ MeV, and $(m_u + m_d)/2 = 4.1 \pm 0.2$ Mev (at a scale Q=2 GeV)., Comment: Additional references to lattice QCD results have been added

It is argued that it is valid to use QCD sum rules to determine the scalar and pseudoscalar two-point functions at zero momentum, which in turn determine the ratio of the strange to non-strange quark condensates $R_{su} = \frac{<\bar{s} s>}{<\bar{q} q>}$ with ($q=u,d$). This is done in the framework of a new set of QCD Finite Energy Sum Rules (FESR) that involve as integration kernel a second degree polynomial, tuned to reduce considerably the systematic uncertainties in the hadronic spectral functions. As a result, the parameters limiting the precision of this determination are $\Lambda_{QCD}$, and to a major extent the strange quark mass. From the positivity of $R_{su}$ there follows an upper bound on the latter: $\bar{m_{s}} (2 {GeV}) \leq 121 (105) {MeV}$, for $\Lambda_{QCD} = 330 (420) {MeV} .$, Comment: Minor changes to Sections 2 and 6

The coupling constants G_(K N Lambda) and G_(K N Sigma) are obtained from the Goldberger-Treiman relation in the strange channel with chiral symmetry breaking taken into account. The results, G_(K N Lambda)=-12.3+-1.2 and G_(K N Sigma)=5.5+-.5 come close to the SU(3) values., Comment: 6 Pages

The couplings of the eta and eta' mesons to the nucleon are obtained from the U_A(1) Goldberger-Treiman relation. The chiral symmetry breaking corrections are very large and bring the calculated values of the coupling constants G_etaNN and G_eta'NN close to values obtained from potential models., Comment: Version 3. The old version went by mistake Version to appear in Phys. Lett. B

Masses and topological charges of the eta and eta' mesons are expressed in terms of the singlet-octet mixing angle theta. Contributions of the pseudoscalar 0- continuum are evaluated in a model independant way. Applications to the decay eta --> 3pi and to the radiative decay of vector mesons involving eta and eta' are considered. Agreement with experiment is in general good and the results quite stable for -30.5 <= theta <= -18.5

An old calculation of the s-wave pi-pi scattering lengths is updated and supplemented with experimental data on the pi-pi s-wave phase shift. The results ma0 = .215 and ma2 = -.039 are in excellent agreement with those obtained from a recent analysis of the results published by the Brookhaven E865 collaboration., Comment: 8 pages

The cross-section for a charged pion pair production by two photons is evaluated by using the low energy expression previously obtained from current algebra and PCAC which involves an integral over a vector and axial-vector spectral functions. Data on the latter obtained from tau-decay as measured by the ALEPH collaboration is then inserted in the integral which is appropriately modified in order to eliminate contributions near the cut in the duality contour integral. The experimental behavior of the cross-section for gamma-gamma into pi (+)-pi(-) is well reproduced at low energies., Comment: 4pages, 1 figure

The extrapolation of the decay amplitudes of the pseudoscalar mesons into two photons from the soft meson limit where it is obtained from the axial-anomaly to the mass shell involves the contribution of the 0^ - continuum. These chiral symmetry breaking corrections turn out to be large. The effects of these corrections on the calculated pi ^0 decay rate, on the values of the singlet-octet mixing angle and on the ratios f_8 / f_pi and f_0 / f_pi are discussed. The implications for the transition form factors gamma gamma* --> pseudoscalars are also evaluated and confronted with the available experimental data., Comment: Computational errors straightened and study of the implications on the form factors of the transitions gamma gamma* --> pseudoscalars added

A simple method is used to extrapolate the form factor for the process gamma* gamma *--->pi^0 when two virtual photons produce a pi ^0 from the region of large spacelike photon virtualities to the experimentally accessible case when one of the photons is real. The method is also applied to the study of the axial anomaly and omega -rho -pi coupling and to the pion charge and charge radius. The results compare favourably with the experimental measurements., Comment: 9 pages, 1 eps figure

In 1967 Glashow, Schnitzer and Weinberg derived a sum rule in the soft-pion and soft kaon limit relating the Delta I=1/2 non-leptonic K->2pi amplitude to integrals over strange and non-strange spectral functions. Using the recent ALEPH data from tau-decay, we show that the sum rule, slightly modified to reduce contributions near the cut, yields the correct magnitude decay amplitude corresponding to the Delta I=1/2 rule., Comment: 7 pages, including 2 ps figures

The Golberger- Treiman discrepancy is related to the asymptotic behaviour of the pionic form factor of the nucleon obtained from baryonic QCD sum rules. The result is .015<=Delta_{GT}<=.022, Comment: References updated and minor corrections

The evaluation of sum rules and vacuum condensates used in the calculation of the mixing parameters of the $\omega -\rho$ system involve dangerous cancellations of large numbers. In this note the contribution of the continuum is eliminated in order to avoid such a large source of uncertainty. It is also seen that the hypothesis of vacuum saturation used in the estimate of the dimension 6 condensate is inadequate. The value obtained for the parameter $\beta$ which governs the off-shell variation of the $\omega -\rho$ mixing is $\beta=.25$., Comment: 7 pages, no figures, minor corrections

A QCD sum rule calculation of Balistky and Ji on the spin content of the nucleon is done with a different approach to the evaluation of the bilocal contributions and to the extraction of the nucleon pole residues. The result obtained is much more numerically stable which puts their conclusion that about half of the nucleon spin is carried by gluons on firmer ground., Comment: 7 pages, two (eps) figure, minor corrections and one figure added

We present the results of a new evaluation of the running fine structure constant $\alpha$ at the scale of the $Z$ mass in which the role of the $e^+e^-$ annihilation input data needed in this evaluation is minimized. This is achieved by reducing the weight function $M_Z^2/(s(M_Z^2-s))$ in the dispersion integral over the $e^+e^-$ annihilation data by subtracting a polynomial function from the weight function which mimics its energy dependence in given energy intervals. In order to compensate for this subtraction the same polynomial weight integral is added again but is now evaluated on a circular contour in the complex plane using QCD and global duality. For the hadronic contribution to the shift in the fine structure constant we obtain $\Delta\alpha^{(5)}_{\rm had}=(277.6\pm 4.1)\cdot 10^{-4}$. Adding in the leptonic and top contributions our final result is $\alpha(M_Z)^{-1}=128.925\pm 0.056$., Comment: no changes, PostScript figures included in the text for convenience