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

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

A Physical Model for SN 2001ay, a normal, bright, extremely slowly declining Type Ia supernova

We present a study of the peculiar Type Ia supernova 2001ay (SN 2001ay). The defining features of its peculiarity are: high velocity, broad lines, and a fast rising light curve, combined with the slowest known rate of decline. It is one magnitude dimmer than would be predicted from its observed value of Delta-m15, and shows broad spectral features. We base our analysis on detailed calculations for the explosion, light curves, and spectra. We demonstrate that consistency is key for both validating the models and probing the underlying physics. We show that this SN can be understood within the physics underlying the Delta-m15 relation, and in the framework of pulsating delayed detonation models originating from a Chandrasekhar mass, white dwarf, but with a progenitor core composed of 80% carbon. We suggest a possible scenario for stellar evolution which leads to such a progenitor. We show that the unusual light curve decline can be understood with the same physics as has been used to understand the Delta-m15 relation for normal SNe Ia. The decline relation can be explained by a combination of the temperature dependence of the opacity and excess or deficit of the peak luminosity, alpha, measured relative to the instantaneous rate of radiative decay energy generation. What differentiates SN 2001ay from normal SNe Ia is a higher explosion energy which leads to a shift of the Ni56 distribution towards higher velocity and alpha < 1. This result is responsible for the fast rise and slow decline. We define a class of SN 2001ay-like SNe Ia, which will show an anti-Phillips relation.Comment: 35 pages, 14 figures, ApJ, in pres