Determination of the strange-quark mass from QCD pseudoscalar sum rules

A new determination of the strange-quark mass is discussed, based on the two-point function involving the axial-vector current divergences. This Green function is known in perturbative QCD up to order O(alpha_s^3), and up to dimension-six in the non-perturbative domain. The hadronic spectral function is parametrized in terms of the kaon pole, followed by its two radial excitations, and normalized at threshold according to conventional chiral-symmetry. The result of a Laplace transform QCD sum rule analysis of this two-point function is: m_s(1 GeV^2) = 155 pm 25 MeV.Comment: Invited talk given by CAD at QCD98, Montpellier, July 1998. To appear in Nucl.Phys.B Proc.Suppl. Latex File. Four (double column) page

Finite energy chiral sum rules in QCD

A set of well known chiral sum rules, expected to be valid in QCD, is confronted with experimental data on the vector and axial-vector hadronic spectral functions, obtained from tau-lepton decay by the ALEPH collaboration. The Das-Mathur-Okubo sum rule, the first and second Weinberg sum rules, and the electromagnetic pion mass difference sum rule are not well saturated by the data. Instead, a modified set of sum rules having additional weight factors that vanish at the end of the integration range on the real axis, is found to be precociously saturated by the data to a remarkable extent.Comment: 6 pages, 6 figures. Invited talk at WIN99, 17th International Workshop on Weak Interactions and Neutrinos, Cape Town, South Africa, January 1999. To be published in the proceedings (World Scientific

Ratio of strange to non-strange quark condensates in QCD

Laplace transform QCD sum rules for two-point functions related to the strangeness-changing scalar and pseudoscalar Green's functions $\psi(Q^2)$ and $\psi_5(Q^2)$, are used to determine the subtraction constants $\psi(0)$ and $\psi_5(0)$, which fix the ratio $R_{su}\equiv \frac{}{}$. Our results are $\psi(0)= - (1.06 \pm 0.21) \times 10^{-3} {GeV}^4$, $\psi_5(0)= (3.35 \pm 0.25) \times 10^{-3} {GeV}^4$, and $R_{su}\equiv \frac{}{} = 0.5 \pm 0.1$. This implies corrections to kaon-PCAC at the level of 50%, which although large, are not inconsistent with the size of the corrections to Goldberger-Treiman relations in $SU(3)\otimes SU(3)$.Comment: Latex file, 14 pages including 3 figure

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

QCD determination of the leading order hadronic contribution to the muon g-2

The leading order hadronic contribution to the muon magnetic moment anomaly, $a^{HAD}_\mu$, is determined entirely in the framework of QCD. The result in the light-quark sector, in units of $10^{-10}$, is $a^{HAD}_\mu|_{uds} =686 \pm 26$, and in the heavy-quark sector $a^{HAD}_\mu|_{c} =14.4 \pm 0.1$, and $a^{HAD}_\mu|_{b} =0.29 \pm 0.01$, resulting in $a^{HAD}_\mu = 701 \pm 26$. The main uncertainty is due to the current lattice QCD value of the first and second derivative of the electromagnetic current correlator at the origin. Expected improvement in the precision of these derivatives may render this approach the most accurate and trustworthy determination of the leading order $a^{HAD}_\mu$.Comment: Invited talk at "Les Rencontres de Physique de la Vallee d'Aosta", March 2017. Speaker: C. A. Dominguez. To be published in Nuovo Cimento

Up- and down-quark masses from QCD sum rules

The QCD up- and down-quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector current divergences. In the QCD sector this correlator is known to five loop order in perturbative QCD (PQCD), together with non-perturbative corrections from the quark and gluon condensates. This FESR is designed to reduce considerably the systematic uncertainties arising from the hadronic spectral function. The determination is done in the framework of both fixed order and contour improved perturbation theory. Results from the latter, involving far less systematic uncertainties, are: \bar{m}_u (2\, \mbox{GeV}) = (2.6 \, \pm \, 0.4) \, {\mbox{MeV}}, \bar{m}_d (2\, \mbox{GeV}) = (5.3 \, \pm \, 0.4) \, {\mbox{MeV}}, and the sum $\bar{m}_{ud} \equiv (\bar{m}_u \, + \, \bar{m}_d)/2$, is \bar{m}_{ud}({ 2 \,\mbox{GeV}}) =( 3.9 \, \pm \, 0.3 \,) {\mbox{MeV}}.Comment: A Mathematica^(C) file pertaining to numerical evaluations is attached as Ancillar