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

Gas expulsion in highly substructured embedded star clusters

We investigate the response of initially substructured, young, embedded star clusters to instantaneous gas expulsion of their natal gas. We introduce primordial substructure to the stars and the gas by simplistically modelling the star formation process so as to obtain a variety of substructure distributed within our modelled star forming regions. We show that, by measuring the virial ratio of the stars alone (disregarding the gas completely), we can estimate how much mass a star cluster will retain after gas expulsion to within 10% accuracy, no matter how complex the background structure of the gas is, and we present a simple analytical recipe describing this behaviour. We show that the evolution of the star cluster while still embedded in the natal gas, and the behavior of the gas before being expelled, are crucial processes that affect the timescale on which the cluster can evolve into a virialized spherical system. Embedded star clusters that have high levels of substructure are subvirial for longer times, enabling them to survive gas expulsion better than a virialized and spherical system. By using a more realistic treatment for the background gas than our previous studies, we find it very difficult to destroy the young clusters with instantaneous gas expulsion. We conclude that gas removal may not be the main culprit for the dissolution of young star clusters.Comment: 19 pages, 8 figures, 2 tables. Accepted for publication in MNRA

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

Mesoscopic Theory of Critical Fluctuations in Isolated Granular Gases

Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed by vorticity fluctuations only, that also lead to a renormalization of the average total energy. The theory predicts a power-law divergent behavior of the scaled second moment of the fluctuations, and a scaling property of their probability distribution, both in agreement with simulations results. A more quantitative comparison between theory and simulation for the critical amplitudes and the form of the scaling function is also carried out

Hadronic contribution to the muon g-2: a theoretical determination

The leading order hadronic contribution to the muon g-2, $a_{\mu}^{HAD}$, is determined entirely from theory using an approach based on Cauchy's theorem in the complex squared energy s-plane. This is possible after fitting the integration kernel in $a_{\mu}^{HAD}$ with a simpler function of $s$. The integral determining $a_{\mu}^{HAD}$ in the light-quark region is then split into a low energy and a high energy part, the latter given by perturbative QCD (PQCD). The low energy integral involving the fit function to the integration kernel is determined by derivatives of the vector correlator at the origin, plus a contour integral around a circle calculable in PQCD. These derivatives are calculated using hadronic models in the light-quark sector. A similar procedure is used in the heavy-quark sector, except that now everything is calculable in PQCD, thus becoming the first entirely theoretical calculation of this contribution. Using the dual resonance model realization of Large $N_{c}$ QCD to compute the derivatives of the correlator leads to agreement with the experimental value of $a_\mu$. Accuracy, though, is currently limited by the model dependent calculation of derivatives of the vector correlator at the origin. Future improvements should come from more accurate chiral perturbation theory and/or lattice QCD information on these derivatives, allowing for this method to be used to determine $a_{\mu}^{HAD}$ accurately entirely from theory, independently of any hadronic model.Comment: Several additional clarifying paragraphs have been added. 1/N_c corrections have been estimated. No change in result