Bounds on Gromov Hyperbolicity Constant

If $X$ is a geodesic metric space and $x_{1},x_{2},x_{3} \in X$, a geodesic triangle $T=\{x_{1},x_{2},x_{3}\}$ is the union of the three geodesics $[x_{1}x_{2}]$, $[x_{2}x_{3}]$ and $[x_{3}x_{1}]$ in $X$. The space $X$ is $\delta$-hyperbolic in the Gromov sense if any side of $T$ is contained in a $\delta$-neighborhood of the union of the two other sides, for every geodesic triangle $T$ in $X$. If $X$ is hyperbolic, we denote by $\delta(X)$ the sharp hyperbolicity constant of $X$, i.e. $\delta(X) =\inf \{ \delta\geq 0:{0.3cm}$ X ${0.2cm}$ $\text{is} {0.2cm} \delta \text{-hyperbolic} \}.$ To compute the hyperbolicity constant is a very hard problem. Then it is natural to try to bound the hyperbolycity constant in terms of some parameters of the graph. Denote by $\mathcal{G}(n,m)$ the set of graphs $G$ with $n$ vertices and $m$ edges, and such that every edge has length $1$. In this work we estimate $A(n,m):=\min\{\delta(G)\mid G \in \mathcal{G}(n,m) \}$ and $B(n,m):=\max\{\delta(G)\mid G \in \mathcal{G}(n,m) \}$. In particular, we obtain good bounds for $B(n,m)$, and we compute the precise value of $A(n,m)$ for all values of $n$ and $m$. Besides, we apply these results to random graphs

Limit and end functors of dynamical systems via exterior spaces

In this paper we analyze some applications of the category of exterior spaces to the study of dynamical systems (flows). We study the notion of an absorbing open subset of a dynamical system; i.e., an open subset that contains the "future part" of all the trajectories. The family of all absorbing open subsets is a quasi-filter which gives the structure of an exterior space to the flow. The limit space and end space of an exterior space is used to construct the limit spaces and end spaces of a dynamical system. On the one hand, for a dynamical system two limits spaces L^{\r}(X) and \bar L^{\r}(X) are constructed and their relations with the subflows of periodic, Poisson stable points and \Omega^{\r}-limits of $X$ are analyzed. On the other hand, different end spaces are also associated to a dynamical system having the property that any positive semi-trajectory has an end point in these end spaces. This type of construction permits us to consider the subflow containing all trajectories finishing at an end point $a$. When $a$ runs over the set of all end points, we have an induced decomposition of a dynamical system as a disjoint union of stable (at infinity) subflows.Comment: 20 pages, 2 figures. arXiv admin note: text overlap with arXiv:1202.666

Neutral Higgs Boson Pair-Production and Trilinear Self-Couplings in the MSSM at ILC and CLIC Energies

We study pair-production as well as the triple self-couplings of the neutral Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) at the Future International Linear $e^{+}e^{-}$ Collider (ILC) and Compact Linear Collider (CLIC). The analysis is based on the reactions $e^{+}e^{-}\to b \bar b h_ih_i, t \bar t h_ih_i$ with $h_i=h, H, A$. We evaluate the total cross-section for both $b\bar bh_ih_i$, $t\bar th_ih_i$ and calculate the total number of events considering the complete set of Feynman diagrams at tree-level. We vary the triple couplings $\kappa\lambda_{hhh}$, $\kappa\lambda_{Hhh}$, $\kappa\lambda_{hAA}$, $\kappa\lambda_{HAA}$, $\kappa\lambda_{hHH}$ and $\kappa\lambda_{HHH}$ within the range $\kappa=-1$ and +2. The numerical computation is done for the energies expected at the ILC with a center-of-mass energy 500, 1000, 1600 $GeV$ and a luminosity 1000 $fb^{-1}$. The channels $e^{+}e^{-}\to b \bar b h_ih_i$ and $e^{+}e^{-}\to t \bar t h_ih_i$ are also discussed to a center-of-mass energy of 3 $TeV$ and luminosities of 1000 $fb^{-1}$ and 5000 $fb^{-1}$.Comment: 26 pages, 11 figure

Studying the Triple Higgs Self-Coupling Via e+e- --> b bar b HH, t bar t HH at Future Linear e+e- Colliders

We study the triple Higgs self-coupling at future $e^{+}e^{-}$ colliders energies, with the reactions $e^{+}e^{-}\to b \bar b HH$ and $e^{+}e^{-}\to t \bar t HH$. We evaluate the total cross section of $b\bar bHH$, $t\bar tHH$ and calculate the total number of events considering the complete set of Feynman diagrams at tree-level. The sensitivity of the triple Higgs coupling is considered in the Higgs mass range 110-190 $GeV$, for the energy which is expected to be available at a possible Next Linear $e^{+}e^{-}$ Collider with a center-of-mass energy $800, 1000, 1500$ $GeV$ and luminosity 1000 $fb^{-1}$.Comment: 15 pages, 10 figure

Comparison between two scalar field models using rotation curves of spiral galaxies

Scalar fields have been used as candidates for dark matter in the universe, from axions with masses $\sim10^{-5}$eV until ultra-light scalar fields with masses $\sim10^{-22}$eV. Axions behave as cold dark matter while the ultra-light scalar fields galaxies are Bose-Einstein condensate drops. The ultra-light scalar fields are also called scalar field dark matter model. In this work we study rotation curves for low surface brightness spiral galaxies using two scalar field models: the Gross-Pitaevskii Bose-Einstein condensate in the Thomas-Fermi approximation and a scalar field solution of the Klein-Gordon equation. We also used the zero disk approximation galaxy model where photometric data is not considered, only the scalar field dark matter model contribution to rotation curve is taken into account. From the best-fitting analysis of the galaxy catalog we use, we found the range of values of the fitting parameters: the length scale and the central density. The worst fitting results (values of $\chi^2_{red}$ much greater than 1, on the average) were for the Thomas-Fermi models, i.e., the scalar field dark matter is better than the Thomas-Fermi approximation model to fit the rotation curves of the analysed galaxies. To complete our analysis we compute from the fitting parameters the mass of the scalar field models and two astrophysical quantities of interest, the dynamical dark matter mass within 300 pc and the characteristic central surface density of the dark matter models. We found that the value of the central mass within 300 pc is in agreement with previous reported results, that this mass is $\approx 10^{7}$ $M_\odot/$pc$^2$, independent of the dark matter model. And, on the contrary, the value of the characteristic central surface density do depend on the dark matter model.Comment: 7 pages, 1 figure, three table

Higgs bosons production and decay at future e+e−e^+e^- linear colliders as a probe of the B-L model

We study the phenomenology of the light and heavy Higgs boson production and decay in the context of a $U(1)_{B-L}$ extension of the Standard Model with an additional $Z'$ boson at future $e^+e^-$ linear colliders with center-of-mass energies of $\sqrt{s}=500-3000\hspace{0.8mm}GeV$ and integrated luminosities of ${\cal L}=500-2000\hspace{0.8mm}fb^{-1}$. The study includes the processes $e^{+}e^{-}\rightarrow (Z, Z') \to Zh$ and $e^{+}e^{-}\rightarrow (Z, Z') \to ZH$, considering both the resonant and non-resonant effects. We find that the total number of expected $Zh$ and $ZH$ events can reach 909,124 and 97,487, respectively, which is a very optimistic scenario and thus it would be possible to perform precision measurements for both Higgs bosons $h$ and $H$, as well as for the $Z'$ boson in future high-energy and high-luminosity $e^+e^-$ colliders experiments. Our study complements other studies on the B-L model and on the Higgs-strahlung processes $e^{+}e^{-}\rightarrow (Z, Z') \to Zh$ and $e^{+}e^{-}\rightarrow (Z, Z') \to ZH$.Comment: 39 pages, 15 figures; To be published in The Journal of Physics G: Nuclear and Particle Physics. arXiv admin note: substantial text overlap with arXiv:1506.07575; text overlap with arXiv:1106.4462 by other author

A completion construction for continuous dynamical systems

In this work we construct the \Co^{\r}-completion and \Co^{\l}-completion of a dynamical system. If $X$ is a flow, we construct canonical maps X\to \Co^{\r}(X) and X\to \Co^{\l}(X) and when these maps are homeomorphism we have the class of \Co^{\r}-complete and \Co^{\l}-complete flows, respectively. In this study we find out many relations between the topological properties of the completions and the dynamical properties of a given flow. In the case of a complete flow this gives interesting relations between the topological properties (separability properties, compactness, convergence of nets, etc.) and dynamical properties (periodic points, omega limits, attractors, repulsors, etc.).Comment: 30 page

Model-independent sensibility studies for the anomalous dipole moments of the ντ\nu_\tau at the CLIC based γe−\gamma e^- colliders

To improve the theoretical prediction of the anomalous dipole moments of the $\tau$-neutrino, we have carried out a study through the process $\gamma e^- \to \tau \bar\nu_\tau \nu_e$, which represents an excellent and useful option in determination of these anomalous parameters. To study the potential of the process $\gamma e^- \to \tau \bar\nu_\tau \nu_e$, we apply a future high-energy and high-luminosity linear electron-positron collider, such as the CLIC, with $\sqrt{s}=380, 1500, 3000\hspace{0.8mm}GeV$ and ${\cal L}=10, 50, 100, 200, 500, 1000, 1500, 2000, 3000\hspace{0.8mm}fb^{-1}$, and we consider systematic uncertainties of $\delta_{sys}=0, 5, 10\%$. With these elements, we present a comprehensive and detailed sensitivity study on the total cross-section of the process $\gamma e^- \to \tau \bar\nu_\tau \nu_e$, as well as on the dipole moments $\mu_{\nu_\tau}$ and $d_{\nu_\tau}$ at the $95\%$ C.L., showing the feasibility of such process at the CLIC at the $\gamma e^-$ mode with unpolarized and polarized electron beams.Comment: 28 pages, 15 figure

Bounding the Number of Light Neutrinos Species in a Left-Right Symmetric Model

Using the experimental values for the rates $R^{LEP} _{exp}=\Gamma_{inv}/\Gamma_{l\bar l}=5.942\pm 0.016$, $R^{Giga-Z_1}=\Gamma_{inv}/\Gamma_{l\bar l}=5.942\pm 0.012$ (most conservative) and $R^{Giga-Z_1}=\Gamma_{inv}/\Gamma_{l\bar l}=5.942\pm 0.006$ (most optimistic) we derive constraints on the number of neutrinos light species $(N_\nu)_{LRSM}$ with the invisible width method in the framework of a left-right symmetric model (LRSM) as a function of the LR mixing angle $\phi$. Using the LEP result for $N_\nu$ we may place a bound on this angle, $-1.6\times 10^{-3}\leq\phi \leq 1.1\times 10^{-3}$, which is stronger than those obtained in previous studies of the LRSM.Comment: 8 pages, 3 figure

Central galaxies in different environments: Do they have similar properties?

We perform an exhaustive comparison among central galaxies from SDSS catalogs in different local environments at 0.01<=z<=0.08. The central galaxies are separated into two categories: group centrals (host halos containing satellites) and field centrals (host halos without satellites). From the latter, we select other two subsamples: isolated centrals and bright field centrals, both with the same magnitude limit. The stellar mass (Ms) distributions of the field and group central galaxies are different, which explains why in general the field central galaxies are mainly located in the blue cloud/star forming regions, whereas the group central galaxies are strongly biased to the red sequence/passive regions. The isolated centrals occupy the same regions as the bright field centrals since both populations have similar Ms distributions. At parity of Ms, the color and specific star formation rate (sSFR) distributions of the samples are similar, specially between field and group centrals. Furthermore, we find that the stellar-to-halo mass (Ms-Mh) relation of isolated galaxies does not depend on the color, sSFR and morphological type. For systems without satellites, the Ms-Mh relation steepens at high halo masses compared to group centrals, which is a consequence of assuming a one-to-one relation between group total stellar mass and halo mass. Under the same assumption, the scatter around the Ms-Mh relation of centrals with satellites increases with halo mass. Our results suggest that the mass growth of central galaxies is mostly driven by the halo mass, with environment and mergers playing a secondary role.Comment: 17 pages, 11 figures after last Referee's report. Accepted for publication in Ap