Relation between Tcc,bbT_{cc,bb} and Xc,bX_{c,b} from QCD

We have studied, using double ratio of QCD (spectral) sum rules, the ratio between the masses of $T_{cc}$ and X(3872) assuming that they are respectively described by the $D-{D}^*$ and $D-\bar{D}^*$ molecular currents. We found (within our approximation) that the masses of these two states are almost degenerate. Since the pion exchange interaction between these mesons is exactly the same, we conclude that if the observed X(3872) meson is a $D\bar{D}^*+c.c.$ molecule, then the $DD^*$ molecule should also exist with approximately the same mass. An extension of the analysis to the $b$-quark case leads to the same conclusion. We also study the SU(3) breakings for the $T^s_{QQ}/T_{QQ}$ mass ratios. Motivated by the recent Belle observation of two $Z_b$ states, we revise our determination of $X_b$ by combining results from exponential and FESR sum rules.Comment: revised version to appear on Phys. Lett.

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for $C^2$ mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the $t$-regularity and its bridge toward the $\rho$-regularity which implies topological triviality at infinity

Highly dynamically evolved intermediate-age open clusters

We present a comprehensive UBVRI and Washington CT1T2 photometric analysis of seven catalogued open clusters, namely: Ruprecht 3, 9, 37, 74, 150, ESO 324-15 and 436-2. The multiband photometric data sets in combination with 2MASS photometry and Gaia astrometry for the brighter stars were used to estimate their structural parameters and fundamental astrophysical properties.We found that Ruprecht 3 and ESO 436-2 do not show self-consistent evidence of being physical systems. The remained studied objects are open clusters of intermediate age (9.0 ≤ log(t yr-1) ≤ 9.6), of relatively small size (rcls ~ 0.4-1.3 pc) and placed between 0.6 and 2.9 kpc from the Sun.We analysed the relationships between core, half-mass, tidal and Jacoby radii as well as half-mass relaxation times to conclude that the studied clusters are in an evolved dynamical stage. The total cluster masses obtained by summing those of the observed cluster stars resulted to be ~10-15 per cent of the masses of open clusters of similar age located closer than 2 kpc from the Sun. We found that cluster stars occupy volumes as large as those for tidally filled clusters.Fil: Piatti, Andres Eduardo. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Dias, Wilton S.. Universidade Federal de Itajuba; BrasilFil: Sampedro, Laura M.. Instituto de Astrofísica de Andalucía; España. Universidade de Sao Paulo; Brasi