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

Chiral corrections to the SU(2)×SU(2)SU(2)\times SU(2) Gell-Mann-Oakes-Renner relation

The next to leading order chiral corrections to the $SU(2)\times SU(2)$ Gell-Mann-Oakes-Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, $\delta_\pi$, the value $\delta_\pi = (6.2, \pm 1.6)$. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate $\simeq \equiv |_{2\,\mathrm{GeV}} = (- 267 \pm 5 MeV)^3$. As a byproduct, the chiral perturbation theory (unphysical) low energy constant $H^r_2$ is predicted to be $H^r_2 (\nu_\chi = M_\rho) = - (5.1 \pm 1.8)\times 10^{-3}$, or $H^r_2 (\nu_\chi = M_\eta) = - (5.7 \pm 2.0)\times 10^{-3}$.Comment: A comment about the value of the strong coupling has been added at the end of Section 4. No change in results or conslusion

(Pseudo)Scalar Charmonium in Finite Temperature QCD

The hadronic parameters of pseudoscalar ($\eta_c$) and scalar ($\chi_c$) charmonium are determined at finite temperature from Hilbert moment QCD sum rules. These parameters are the hadron mass, leptonic decay constant, total width, and continuum threshold ($s_0$). Results for $s_0(T)$ in both channels indicate that $s_0(T)$ starts approximately constant, and then it decreases monotonically with increasing $T$ until it reaches the QCD threshold, $s_{th} = 4 m_Q^2$, at a critical temperature T = T_c \simeq 180 \; \mbox{MeV} interpreted as the deconfinement temperature. The other hadronic parameters behave qualitatively similarly to those of the $J/\psi$, as determined in this same framework. The hadron mass is essentially constant, the total width is initially independent of T, and after $T/T_c \simeq 0.80$ it begins to increase with increasing $T$ up to $T/T_c \simeq 0.90 \; (0.95)$ for $\chi_c$ ($\eta_c$), and subsequently it decreases sharply up to $T \simeq 0.94 \; (0.99) \; T_c$, for $\chi_c$ ($\eta_c$), beyond which the sum rules are no longer valid. The decay constant of $\chi_c$ at first remains basically flat up to $T \simeq 0.80\; T_c$, then it starts to decrease up to $T \simeq 0.90 \;T_c$, and finally it increases sharply with increasing $T$. In the case of $\eta_c$ the decay constant does not change up to $T \simeq 0.80 \;T_c$ where it begins a gentle increase up to $T \simeq 0.95 \;T_c$ beyond which it increases dramatically with increasing $T$. This behaviour contrasts with that of light-light and heavy-light quark systems, and it suggests the survival of the $\eta_c$ and the $\chi_c$ states beyond the critical temperature, as already found for the $J/\psi$ from similar QCD sum rules. These conclusions are very stable against changes in the critical temperature in the wide range T_c = 180 - 260 \; \mbox{MeV}.Comment: 12 pages, 5 figures. A wide range of critical temperatures has been considered. No qualitative changes to the conclusion

Fanatismo religioso y decadencia nacional. Los escritos afrancesados de Manuel Alonso de Viado

Los escritos que Manuel Alonso de Viado publicó durante la Guerra de la Independencia son una buena muestra del papel que los partidarios de José Bonaparte desempeñaron en los orígenes ideológicos del progresismo español. En ellos se repite, con una contundencia hasta entonces impensable en España, una idea común de los ilustrados europeos: que la decadencia española era fruto del fanatismo religioso. Pero no por eso carecen de patriotismo. Con la misma claridad, se enfrentan al tópico que atribuía la decadencia nacional al carácter del pueblo español e insisten en culpar únicamente a clérigos y gobernantes. De este modo, defienden el honor patrio al mismo tiempo que justifican la intervención napoleónica en España: sólo un cambio drástico en el gobierno y en las leyes del país podía permitir que los talentos españoles contribuyesen libremente al progreso de su patria.The writings of Manuel Alonso de Viado during the Peninsular War offer evidence of the significant but largely ignored role played by the supporters of Joseph Bonaparte in the ideological development of modern Spanish liberalism. With an openness previously unthinkable in Spain, those writings repeated an idea many times expressed in other European countries since the Early Enlightenment: that the decline of Spain was caused by religious fanaticism. But however much they copied some arguments from the so-called Black Legend, these were not anti-patriotic writings. They firmly rejected the widespread attribution of Spanish decline to the national character of its people, and insisted that clerics and rulers were the only ones to blame. In this way they defended the honour of the nation while at the same time justifying the Napoleonic intervention in Spain: only a drastic change in the country’s government and legislation could free Spanish minds from the chains that until then had prevented them from contributing to national progress.Les écrits que Manuel Alonso de Viado publia pendant la Guerre d’Indépendance constituent un bel exemple du rôle joué par les partisans de Joseph Bonaparte dans les origines idéologiques du progressisme espagnol. On retrouve répété dans ces derniers, avec une force jusque là impensable en Espagne, une idée récurrente chez les penseurs des Lumières en Europe : à savoir que la décadence espagnole était le fruit du fanatisme religieux. Pour autant ces écrits ne manquent pas de patriotisme. Avec la même franchise, ils s’attaquent au lieu commun qui attribuait la décadence nationale au caractère du peuple espagnol et insistent pour faire porter la culpabilité aux clercs et aux dirigeants. Ainsi, ils défendent l’honneur national en même temps qu’ils justifient l’intervention napoléonienne en Espagne : seul un changement drastique dans le gouvernement et dans les lois du pays pourra permettre aux talents espagnols de contribuer librement au progrès de leur patrie

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

Charm-quark mass from weighted finite energy QCD sum rules

The running charm-quark mass in the $\bar{MS}$ scheme is determined from weighted finite energy QCD sum rules (FESR) involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of $s$, the squared energy. The optimal kernels are found to be a simple {\it pinched} kernel, and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s-plane, and the latter allows to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theoretical information differently from e.g. inverse moments FESR. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the FESR, together with the latest experimental data. The integration in the complex s-plane is performed using three different methods, fixed order perturbation theory (FOPT), contour improved perturbation theory (CIPT), and a fixed renormalization scale $\mu$ (FMUPT). The final result is $\bar{m}_c (3\, {GeV}) = 1008\,\pm\, 26\, {MeV}$, in a wide region of stability against changes in the integration radius $s_0$ in the complex s-plane.Comment: A short discussion on convergence issues has been added at the end of the pape