Rho and Sigma Mesons in Unitarized Thermal ChPT

We present our recent results for the rho and sigma mesons considered as resonances in pion-pion scattering in a thermal bath. We use chiral perturbation theory to fourth order in p for the low energy behaviour, then extend the analysis via the unitarization method of the Inverse Amplitude into the resonance region. The width of the rho broadens about twice the amount required by phase space considerations alone, its mass staying practically constant up to temperatures of order 150 MeV. The sigma meson behaves in accordance to chiral symmetry restoration expectations.Comment: Proc. Workshop Strong and Electroweak Matter 02, Heidelberg, German

Tetraquark spectroscopy

A complete classification of tetraquark states in terms of the spin-flavor, color and spatial degrees of freedom was constructed. The permutational symmetry properties of both the spin-flavor and orbital parts of the quark-quark and antiquark-antiquark subsystems are discussed. This complete classification is general and model-independent, and is useful both for model-builders and experimentalists. The total wave functions are also explicitly constructed in the hypothesis of ideal mixing; this basis for tetraquark states will enable the eigenvalue problem to be solved for a definite dynamical model. This is also valid for diquark-antidiquark models, for which the basis is a subset of the one we have constructed. An evaluation of the tetraquark spectrum is obtained from the Iachello mass formula for normal mesons, here generalized to tetraquark systems. This mass formula is a generalizazion of the Gell-Mann Okubo mass formula, whose coefficients have been upgraded by means of the latest PDG data. The ground state tetraquark nonet was identified with $f_{0}(600)$, $\kappa(800)$, $f_{0}(980)$, $a_{0}(980)$. The mass splittings predicted by this mass formula are compared to the KLOE, Fermilab E791 and BES experimental data. The diquark-antidiquark limit was also studied.Comment: Invited talk at 11th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2007), Julich, Germany, 10-14 Sep 2007. In the Proceedings of 11th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2007), Julich, Germany, 10-14 Sep 2007, eConf C070910, 163 (2007

On the order of summability of the Fourier inversion formula

In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesàro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesàro summable of order k, then the distribution is the (k+1)-th derivative of a locally integrable function, and the distribution has a distributional point value of order k+2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems

On the determination of Θ+\Theta^+ quantum numbers and other topics of exotic baryons

In this talk I look into three different topics, addressing first a method to determine the quantum numbers of the $\Theta^+$, then exploiting the possibility that the $\Theta^+$ is a bound state of $K \pi N$ and in the third place I present results on a new resonant exotic baryonic state which appears as dynamically generated by the Weinberg Tomozawa $\Delta K$ interaction.Comment: 9 pags. Talk in the NSTAR04 Workshop, Grenoble, march 200

Hadronic aspects of exotic baryons

In this talk I look into three different topics, addressing first the possibility that the $\Theta^+$ is a bound state of $K \pi N$, exploiting the results of this study to find out the contribution of two meson and one baryon components in the baryon antidecuplet and in the third place I present results on a new resonant exotic baryonic state which appears as dynamically generated by the Weinberg Tomozawa $\Delta K$ interaction.Comment: Talk at the International Workshop PENTAQUARK0

Complémentarités et convergences de méthodes de régionalisation des précipitations : application à une région endoréique du Nord-Mexique

La connaissance des champs pluviométriques annuels est importante dans les zones arides et semi-arides où la gestion de l'eau est un exercice permanent d'aménagement de la pénurie, comme cela est le cas au Nord du Mexique.On se propose de montrer ici qu'une meilleure connaissance des disponibilités en eau peut s'appuyer sur la détermination de régions pluviométriquement homogènes à partir de diverses méthodes complémentaires ou convergentes.Pour définir des régions homogènes, on part de la répartition des stations par rapport à la régression pluviométrie/altitude. Des analyses factorielles en composantes principales et des correspondances permettent également de proposer des régions homogènes suivant des variables définies et disponibles pour toutes les stations. On s'appuie aussi sur les régimes pluviométriques pour déterminer d'autres régionalisations. Parallèlement on a pu utiliser la répartition des stations par rapport au gradient altitudinal pour créer des régions dont l'homogénéité vis-à-vis des précipitations a pu être vérifiée par la Méthode du Vecteur Régional (MVR), basée sur le principe de la pseudo-proportionnalité des données de postes proches.La comparaison des résultats obtenus par chacune des méthodes permet de constater que dans la région traitée, les limites entre régions " homogènes " sont souvent les mêmes, bien que les modes de détermination soient différents. Enfin, les différences apportent une information supplémentaire pour la compréhension des mécanismes locaux ou régionaux de la répartition des champs de pluie.Knowledge of annual rainfall is of great importance in arid and semi-arid areas, because water management is dominated by scarcity. The Nazas-Aguanaval river basin constitutes one of the main endoreic basins in Mexico (92 000 km2). It extends from the crests of the Western SierraMadre to as far as the Chihuahuan desert, in the states of Durango, Coahuila and Zacatecas. Spatial variability of rainfall is significant with annual rainfall amounts ranging from 900 mm in the higher areas of the Sierra Madre to 180 mm at the centre of the Laguna de Mayran. However, temporal variability of the precipitation amount is also appreciable, and it increases from the sub-humid areas of the mountains to the desert. The coefficient of variation for annual precipitation ranges from 0.2 in the mountains to 0.4 in Chihuahuan desert. Furthermore, in 1992, 1994, 1995, and from 1997 to 2000 severe rainfall deficits forced farmers to reduce strongly irrigated areas, thus leading to socio-economic development problems in this region. It is shown in this paper that an improvement in water availability knowledge is attainable by the determination of homogeneous rainfall regions, based on complementary or convergent methods.Rainfall distribution is a result of many factors, including the atmospheric circulation, the continental pattern, the coastal design, the location of major mountainous massifs, the distance from the ocean, and other site factors. The regionalisation of precipitation has been the subject of much research for almost all types of climates. The influence of zonal and regional factors is also determined in regional monographs where the role of local variables (relief, vegetation, general roughness of landscape, etc.) is described in relation to the large-scale circulation scheme. In most of the cases, the interpolation of values between two observations is necessary and quite difficult. Kriging is widely used for this purpose, as is co-kriging, which takes into account the topography or some other local factors and frequently gives better reconstitution of rainfall data. In order to determine the first set of homogeneous regions in northwestern Mexico, the elevation gradient of the rainfall amount was defined by a simple regression. All the stations were located with respect to the regression line and they can form apparent groups. The following relation was obtained :P=0.31 H - 133r2=0.73; n=84)(where P is annual rainfall in mm and H the altitude in m).In the same way, various statistical analysis were performed using all data available from the rainfall measurement stations, such as elevation, distance from the Pacific Ocean, exposure, annual rainfall amount, and the type of topography and vegetation cover surrounding the station. An Empirical Orthogonal Function Analysis (EOF) and a Factorial Analysis of Correspondences (FAC) revealed other kinds of regionalisation. The precipitation regime is tropical-like in spite of the latitude (25° N), but the percentage of annual precipitation in winter appeared as a segregating factor and thus was used to define the climatic geography. This was determined by a stepwise discriminant analysis, which allowed the segregation of the north-eastern area of the Nazas-Aguanaval basin. This is the dryer region of the basin because it is less exposed to monsoon fluxes and the proportion of winter rain is higher there than in the remaining basin.The main variables explaining the spatial distribution of precipitation are altitude and distance from the Pacific Ocean, as determined by both the EOF analysis and the analysis of correspondences. The grouping of stations segregated by the elevation gradient regression led to regions where the homogeneity in relation to the annual rainfall amount was tested and verified by the Regional Vector Method (RVM). This method is based on the principle of pseudo-proportionality between annual rainfall amounts at close stations.The Nazas-Aguanaval basin is divided into three climatic regions defined by precipitation: the Western Sierra Madre, the Chihuahuan desert, and a semi-arid area that is divided into two sub-regions (Middle Nazas basin and Aguanaval plateau) by the analysis of correspondences. As a result of the regional rainfall analysis, some variograms were performed to determine the length of the validity of the rainfall data. However, it appeared that a multidirectional variogram did not explain these data. The role that relief (mainly the Western Sierra Madre) plays in the spatial distribution of precipitation does not explain the length of rainfall data. Introducing the direction of mountain range into the variogram demonstrated that the relief played a significant role, and in this case the length of the rainfall variogram data was 180 km.A comparison of results obtained using each method led to the conclusion that the boundaries between homogeneous regions are often the same while the determination processes are different. Finally, all the proposed methods are complementary and the differences between all characterisations give additional information regarding the local and regional processes that explain the annual rainfall spatial distribution. Simple tools have been used to acquire a better knowledge of rainfall spatial distribution.In the case of Northern Mexico, the low density of a measurement network (rain gauges), particularly in mountainous or arid zones, is partially attenuated by the possibility of evaluating the main climatic characteristics for the different regions defined in terms of rainfall