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 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 axial-vector coupling of the nucleon at finite temperature

A thermal QCD Finite Energy Sum Rule (FESR) is used to obtain the temperature dependence of the axial-vector coupling of the nucleon, $g_{A}(T)$. We find that $g_{A}(T)$ is essentially independent of $T$, in the very wide range $0 \leq T \leq 0.9 T_{c}$, where $T_{c}$ is the critical temperature. While $g_{A}$ at T=0 is $q^{2}$-independent, it develops a $q^{2}$ dependence at finite temperature. We then obtain the mean square radius associated with $g_{A}$ and find that it diverges at $T=T_{c}$, thus signalling quark deconfinement. As a byproduct, we study the temperature dependence of the Goldberger-Treiman relation.Comment: 8 pages and 3 figure

Introduction to QCD sum rules

A general, and very basic introduction to QCD sum rules is presented, with emphasis on recent issues to be described at length in other papers in this volume of Modern Physics Letters A. Collectively, these papers constitute the proceedings of the {\it{International Workshop on Determination of the Fundamental Parameters of QCD}}, Singapore, March 2013.Comment: Plenary talk at the International Workshop on Determination of the Fundamental Parameters of QCD. To be published in Mod. Phys. Lett.

Deconfinement and Chiral-Symmetry Restoration in Finite Temperature QCD

QCD sum rules are based on the Operator Product Expansion of current correlators, and on QCD-hadron duality. An extension of this program to finite temperature is discussed. This allows for a study of deconfinement and chiral-symmetry restoration. In addition, it is possible to relate certain hadronic matrix elements to expectation values of quark and gluon field operators by using thermal Finite Energy Sum Rules. In this way one can determine the temperature behaviour of hadron masses and couplings, as well as form factors. An attempt is made to clarify some misconceptions in the existing literature on QCD sum rules at finite temperature.Comment: Invited talk at CAM-94, Cancun, Mexico, September 1994. 21 pages and 8 figures (not included). LATEX file. UCT-TP-218/9

Electromagnetic Form Factors of Hadrons in Dual-Large NcN_c QCD

In this talk, results are presented of determinations of electromagnetic form factors of hadrons (pion, proton, and $\Delta(1236)$) in the framework of Dual-Large $N_c$ QCD (Dual-$QCD_\infty$). This framework improves considerably tree-level VMD results by incorporating an infinite number of zero-width resonances, with masses and couplings fixed by the dual-resonance (Veneziano-type) model.Comment: Invited talk at the XII Mexican Workshop on Particles & Fields, Mazatlan, November 2009. To be published in American Institute of Physics Conference Proceedings Serie