Dispersion Relation Bounds for pi pi Scattering

Axiomatic principles such as analyticity, unitarity and crossing symmetry constrain the second derivative of the pi pi scattering amplitudes in some channels to be positive in a region of the Mandelstam plane. Since this region lies in the domain of validity of chiral perturbation theory, we can use these positivity conditions to bound linear combinations of \bar{l}_1 and \bar{l}_2. We compare our predictions with those derived previously in the literature using similar methods. We compute the one-loop pi pi scattering amplitude in the linear sigma model (LSM) using the MS-bar scheme, a result hitherto absent in the literature. The LSM values for \bar{l}_1 and \bar{l}_2 violate the bounds for small values of m_sigma/m_pi. We show how this can occur, while still being consistent with the axiomatic principles.Comment: 12 pages, 8 figures. Two references added, a few minor changes. Published versio

Calibrating the Na\"ive Cornell Model with NRQCD

Along the years, the Cornell Model has been extraordinarily successful in describing hadronic phenomenology, in particular in physical situations for which an effective theory of the strong interactions such as NRQCD cannot be applied. As a consequence of its achievements, a relevant question is whether its model parameters can somehow be related to fundamental constants of QCD. We shall give a first answer in this article by comparing the predictions of both approaches. Building on results from a previous study on heavy meson spectroscopy, we calibrate the Cornell model employing NRQCD predictions for the lowest-lying bottomonium states up to N$^3$LO, in which the bottom mass is varied within a wide range. We find that the Cornell model mass parameter can be identified, within perturbative uncertainties, with the MSR mass at the scale $R = 1\,$GeV. This identification holds for any value of $\alpha_s$ or the bottom mass, and for all perturbative orders investigated. Furthermore, we show that: a) the "string tension" parameter is independent of the bottom mass, and b) the Coulomb strength $\kappa$ of the Cornell model can be related to the QCD strong coupling constant $\alpha_s$ at a characteristic non-relativistic scale. We also show how to remove the $u=1/2$ renormalon of the static QCD potential and sum-up large logs related to the renormalon subtraction by switching to the low-scale, short-distance MSR mass, and using R-evolution. Our R-improved expression for the static potential remains independent of the heavy quark mass value and agrees with lattice QCD results for values of the radius as large as $0.8\,$fm, and with the Cornell model potential at long distances. Finally we show that for moderate values of $r$, the R-improved NRQCD and Cornell static potentials are in head-on agreement.Comment: 22 pages, 13 figures, 3 table

Distance-Based Methods: Ripley’s K function vs. K density function

In this paper, we propose an analytical and methodological comparison between two of the most known distance-based methods in the evaluation of the geographic concentration of economic activity. These two methods are Ripley’s K function, a cumulative function popularised by Marcon and Puech (2003) that counts the average number of neighbours of each point within a circle of a given radius, and K density function, a probability density function of point-pair distances introduced by Duranton and Overman (2005), which considers the distribution of distances between pairs of points. To carry out this comparison, we first apply both methodologies to an exhaustive database containing Spanish manufacturing establishments and we evaluate the spatial location patterns obtained from both analysis. After an initial analysis, we realise that although these functions have always been treated as substitutes they should be considered as complementary, as both cumulative function and probability density function provide relevant and necessary information about the distribution of activity in space. Therefore, our next step will be to assess what are the advantages and disadvantages of each methodology from a descriptive and analytical way.

Searching for tidal tails around ω\omega Centauri using RR Lyrae Stars

We present a survey for RR Lyrae stars in an area of 50 deg$^2$ around the globular cluster $\omega$ Centauri, aimed to detect debris material from the alleged progenitor galaxy of the cluster. We detected 48 RR Lyrae stars of which only 11 have been previously reported. Ten among the eleven previously known stars were found inside the tidal radius of the cluster. The rest were located outside the tidal radius up to distances of $\sim 6$ degrees from the center of the cluster. Several of those stars are located at distances similar to that of $\omega$ Centauri. We investigated the probability that those stars may have been stripped off the cluster by studying their properties (mean periods), calculating the expected halo/thick disk population of RR Lyrae stars in this part of the sky, analyzing the radial velocity of a sub-sample of the RR Lyrae stars, and finally, studying the probable orbits of this sub-sample around the Galaxy. None of these investigations support the scenario that there is significant tidal debris around $\omega$ Centauri, confirming previous studies in the region. It is puzzling that tidal debris have been found elsewhere but not near the cluster itself.Comment: 11 pages, 11 figures, Accepte

No Excess of RR Lyrae Stars in the Canis Major Overdensity

Our multi-epoch survey of ~20 sq. deg. of the Canis Major overdensity has detected only 10 RR Lyrae stars (RRLS). We show that this number is consistent with the number expected from the Galactic halo and thick disk populations alone, leaving no excess that can be attributed to the dwarf spheroidal (dSph) galaxy that some authors have proposed as the origin of the CMa overdensity. If this galaxy resembles the dSph satellites of the Milky Way and of M31 and has the putative Mv~-14.5, our survey should have detected several tens of RRLS. Even if Mv10, which is not observed. Either the old stellar population of this galaxy has unique properties or, as others have argued before, the CMa overdensity is produced by the thin and thick disk and spiral arm populations of the Milky Way and not by a collision with a dSph satellite galaxy.Comment: 35 pages, 9 figures, 5 tables. Accepted for publication at the Astronomical Journa

Searching for RR Lyrae stars in the Canis Major Overdensity

The Canis Major overdensity (CMa) was initially proposed to be the remnant of a tidally disrupting dSph galaxy. Since its nature is still subject of debate, the goal of the present work was to conduct a large-scale RR Lyrae survey in CMa, in order to see if there is an overdensity of these stars. The survey spans a total area of ~34 sq. deg. with observations in V and R filters, made with the 1.0m Jurgen Stock Schmidt telescope at the National Astronomical Observatory of Venezuela. Current results in a subregion, including spectroscopic observations, show that the small number of RR Lyrae stars found can be accounted for by the halo and thick disk components of our Galaxy.Comment: 2 pages, 1 figure, to appear in the proceedings of IAU Symposium No241 "Stellar Populations as Building Blocks of Galaxies

Hierarchical spatial modeling of the presence of Chagas disease insect vectors in Argentina. A comparative approach

We modeled the spatial distribution of the most important Chagas disease vectors in Argentina, in order to obtain a predictive mapping method for the probability of presence of the vector species. We analyzed both the binary variable of presence-absence of Chagas disease and the vector species richness in Argentina, in combination with climatic and topographical covariates associated to the region of interest. We used several statistical techniques to produce distribution maps of presence–absence for the different insect species as well as species richness, using a hierarchical Bayesian framework within the context of multivariate geostatistical modeling. Our results show that the inclusion of covariates improves the quality of the fitted models, and that there is spatial interaction between neighboring cells/pixels, so mapping methods used in the past, which assumed spatial independence, are not adequate as they provide unreliable results.We thank J. E. Rabinovich from Centro de Estudios Parasitologicos y de Vectores of Buenos Aires, Argentina for drawing our attention to this particular application problem and for providing access to the Chagas data base used. Work partially funded by grant MTM2013-43917-P from the Spanish Ministry of Science and Education, grant PAPIIT IN114814 of the Direccio ́ n General de Asuntos del Personal Acade ́ mico of the Universidad Nacional Auto ́ noma de Me ́ xico and Grant CONACYT number 241195

Ultra deep sub-kpc view of nearby massive compact galaxies

Using Gemini North telescope ultra deep and high resolution (sub-kpc) K-band adaptive optics imaging of a sample of 4 nearby (z~0.15) massive (~10^{11}M_sun) compact (R<1.5 kpc) galaxies, we have explored the structural properties of these rare objects with an unprecedented detail. Our surface brightness profiles expand over 12 magnitudes in range allowing us to explore the presence of any faint extended envelope on these objects down to stellar mass densities ~10^{6} M_sun/kpc^{2} at radial distances of ~15 kpc. We find no evidence for any extended faint tail altering the compactness of these galaxies. Our objects are elongated, resembling visually S0 galaxies, and have a central stellar mass density well above the stellar mass densities of objects with similar stellar mass but normal size in the present universe. If these massive compact objects will eventually transform into normal size galaxies, the processes driving this size growth will have to migrate around 2-3x10^{10}M_sun stellar mass from their inner (R<1.7 kpc) region towards their outskirts. Nearby massive compact galaxies share with high-z compact massive galaxies not only their stellar mass, size and velocity dispersion but also the shape of their profiles and the mean age of their stellar populations. This makes these singular galaxies unique laboratories to explore the early stages of the formation of massive galaxies.Comment: Accepted for publication in ApJ Letter. Version revised to match the accepted versio

Boundary regularity of rotating vortex patches

We show that the boundary of a rotating vortex patch (or V-state, in the terminology of Deem and Zabusky) is of class C^infinity provided the patch is close enough to the bifurcation circle in the Lipschitz norm. The rotating patch is convex if it is close enough to the bifurcation circle in the C^2 norm. Our proof is based on Burbea's approach to V-states. Thus conformal mapping plays a relevant role as well as estimating, on H\"older spaces, certain non-convolution singular integral operators of Calder\'on-Zygmund type.Comment: Various proofs have been shortened. One added referenc