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

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

Shock waves in capillary collapse of colloids: a model system for two--dimensional screened Newtonian gravity

Using Brownian dynamics simulations, density functional theory, and analytical perturbation theory we study the collapse of a patch of interfacially trapped, micrometer-sized colloidal particles, driven by long-ranged capillary attraction. This attraction {is formally analogous} to two--dimensional (2D) screened Newtonian gravity with the capillary length \hat{\lambda} as the screening length. Whereas the limit \hat{\lambda} \to \infty corresponds to the global collapse of a self--gravitating fluid, for finite \hat{\lambda} we predict theoretically and observe in simulations a ringlike density peak at the outer rim of a disclike patch, moving as an inbound shock wave. Possible experimental realizations are discussed.Comment: 5 pages, 3 figures, revised version with new Refs. added, matches version accepted for publication in PR

A Correlation Between Hard Gamma-ray Sources and Cosmic Voids Along the Line of Sight

We estimate the galaxy density along lines of sight to hard extragalactic gamma-ray sources by correlating source positions on the sky with a void catalog based on the Sloan Digital Sky Survey (SDSS). Extragalactic gamma-ray sources that are detected at very high energy (VHE; E>100 GeV) or have been highlighted as VHE-emitting candidates in the Fermi Large Area Telescope hard source catalog (together referred to as "VHE-like" sources) are distributed along underdense lines of sight at the 2.4 sigma level. There is also a less suggestive correlation for the Fermi hard source population (1.7 sigma). A correlation between 10-500 GeV flux and underdense fraction along the line of sight for VHE-like and Fermi hard sources is found at 2.4 sigma and 2.6 sigma, respectively. The preference for underdense sight lines is not displayed by gamma-ray emitting galaxies within the second Fermi catalog, containing sources detected above 100 MeV, or the SDSS DR7 quasar catalog. We investigate whether this marginal correlation might be a result of lower extragalactic background light (EBL) photon density within the underdense regions and find that, even in the most extreme case of a entirely underdense sight line, the EBL photon density is only 2% less than the nominal EBL density. Translating this into gamma-ray attenuation along the line of sight for a highly attenuated source with opacity tau(E,z) ~5, we estimate that the attentuation of gamma-rays decreases no more than 10%. This decrease, although non-neglible, is unable to account for the apparent hard source correlation with underdense lines of sight.Comment: Accepted by MNRA

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

Differentially Private Distributed Optimization

In distributed optimization and iterative consensus literature, a standard problem is for $N$ agents to minimize a function $f$ over a subset of Euclidean space, where the cost function is expressed as a sum $\sum f_i$. In this paper, we study the private distributed optimization (PDOP) problem with the additional requirement that the cost function of the individual agents should remain differentially private. The adversary attempts to infer information about the private cost functions from the messages that the agents exchange. Achieving differential privacy requires that any change of an individual's cost function only results in unsubstantial changes in the statistics of the messages. We propose a class of iterative algorithms for solving PDOP, which achieves differential privacy and convergence to the optimal value. Our analysis reveals the dependence of the achieved accuracy and the privacy levels on the the parameters of the algorithm. We observe that to achieve $\epsilon$-differential privacy the accuracy of the algorithm has the order of $O(\frac{1}{\epsilon^2})$