The exact renormalization group in Astrophysics

The coarse-graining operation in hydrodynamics is equivalent to a change of scale which can be formalized as a renormalization group transformation. In particular, its application to the probability distribution of a self-gravitating fluid yields an "exact renormalization group equation" of Fokker-Planck type. Since the time evolution of that distribution can also be described by a Fokker-Planck equation, we propose a connection between both equations, that is, a connection between scale and time evolution. We finally remark on the essentially non-perturbative nature of astrophysical problems, which suggests that the exact renormalization group is the adequate tool for them.Comment: World Scientific style, 6 pages, presented at the 2nd Conference on the Exact RG, Rome 200

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

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

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.

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