Pade-Improved Estimate of Perturbative Contributions to Inclusive Semileptonic b→ub\to u Decays

Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic $b \to u$ decay rate. These improved estimates of the decay rate reduce the theoretical uncertainty in the extraction of the CKM matrix element $|V_{ub}|$ from the measured inclusive semileptonic branching ratio.Comment: 3 pages, latex, write-up of talk presented at DPF 200

Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

We survey our recently proposed method for constructing biholomorphic invariants of quasihomogeneous isolated hypersurface singularities and, more generally, invariants of graded Artinian Gorenstein algebras. The method utilizes certain polynomials associated to such algebras, called nil-polynomials, and we compare them with two other classes of polynomials that have also been used to produce invariants.Comment: 13 page

The Star Formation Law in Nearby Galaxies on Sub-Kpc Scales

(Abridged) We present a comprehensive analysis of the relationship between star formation rate surface density (SFR SD) and gas surface density (gas SD) at sub-kpc resolution in a sample of 18 nearby galaxies. We use high resolution HI data from THINGS, CO data from HERACLES and BIMA SONG, 24 micron data from the Spitzer Space Telescope, and UV data from GALEX. We target 7 spiral galaxies and 11 late-type/dwarf galaxies and investigate how the star formation law differs between the H2-dominated centers of spiral galaxies, their HI-dominated outskirts and the HI-rich late-type/dwarf galaxies. We find that a Schmidt-type power law with index N=1.0+-0.2 relates the SFR SD and the H2 SD across our sample of spiral galaxies, i.e., that H2 forms stars at a constant efficiency in spirals. The average molecular gas depletion time is ~2*10^9 yrs. We interpret the linear relation and constant depletion time as evidence that stars are forming in GMCs with approximately uniform properties and that the H2 SD may be more a measure of the filling fraction of giant molecular clouds than changing conditions in the molecular gas. The relationship between total gas SD and SFR SD varies dramatically among and within spiral galaxies. Most galaxies show little or no correlation between the HI SD and the SFR SD. As a result, the star formation efficiency (SFE = SFR SD / gas SD) varies strongly across our sample and within individual galaxies. We show that in spirals the SFE is a clear function of radius, while the dwarf galaxies in our sample display SFEs similar to those found in the outer optical disks of the spirals. Another general feature of our sample is a sharp saturation of the HI SD at ~9 M_sol/pc^2 in both the spiral and dwarf galaxies.Comment: Accepted for publication in the AJ special THINGS issue. For a high-resolution version visit: http://www.mpia.de/THINGS/Publications.htm

Liquid-vapor interface of a polydisperse fluid

We report a Grand Canonical Monte Carlo simulation study of the liquid-vapor interface of a model fluid exhibiting polydispersity in terms of the particle size $\sigma$. The bulk density distribution, $\rho^0(\sigma)$, of the system is controlled by the imposed chemical potential distribution $\mu(\sigma)$. We choose the latter such that $\rho^0(\sigma)$ assumes a Schulz form with associated degree of polydispersity $\approx 14$. By introducing a smooth attractive wall, a planar liquid-vapor interface is formed for bulk state points within the region of liquid-vapor coexistence. Owing to fractionation, the pure liquid phase is enriched in large particles, with respect to the coexisting vapor. We investigate how the spatial non-uniformity of the density near the liquid-vapor interface affects the evolution of the local distribution of particle sizes between the limiting pure phase forms. We find (as previously predicted by density functional theory, Bellier-Castella {\em et al}, Phys. Rev. {\bf E65}, 021503 (2002)) a segregation of smaller particles to the interface. The magnitude of this effect is quantified for various $\sigma$ via measurements of the relative adsorption. Additionally, we consider the utility of various estimators for the interfacial width and highlight the difficulties of isolating the intrinsic contribution of polydispersity to this width.Comment: 9 pages, 10 Fig

Renormalization-Scale Invariance, Minimal Sensitivity, and the Inclusive Hadronic Decays of a 115 GeV Higgs Particle

Known perturbative expressions for the decay rates of 115 GeV Higgs particle into either two gluons or a $b\bar{b}$ pair are shown to exhibit renormalization-scale-($\mu$)-dependence that is largely removed via renormalization-group/Pade-approximant estimates of these rates' next order contributions. The extrema in $\mu$ characterizing both rates, as determined from fully-known orders of perturbation theory, are very nearly equal to corresponding $\mu$-insensitive rates obtained via estimation of their next order contributions, consistent with "minimal-sensitivity" expectations.Comment: 12 pages, 3 figures, LaTe

A study on the discrimination of human skeletons using X-ray fluorescence and chemometric tools in chemical anthropology

Forensic anthropological investigations are often restricted in their outcomes by the resources allocated to them, especially in terms of positively identifying the victims exhumed from commingled mass graves. Commingled mass graves can be defined as those graves that contain a number of disarticulated human remains from different individuals that have been mixed by either natural processes or human interventions. The research developed aimed to apply the technique of non-destructive XRF analysis to test whether there is substantial differentiation within the trace elemental composition and their ratios of individuals to separate them using chemometric analysis. The results of the different atomic spectroscopic analyses combined with the use of multivariate analysis on a set of 5 skeletons produced a series of plots using Principal Component Analysis that helped to separate them with a high percentage of accuracy when two, three or four skeletons needed to be separated. Also, two new elemental ratios, Zn/Fe related to metabolic activities and K/Fe related to blood flow into the bone, have been defined for their use in forensic anthropology for the first time to aid in the separation. © 2013 Elsevier Ireland Ltd