The use of the tau in new particle searches at DELPHI

Several new particle searches have been performed in the DELPHI experiment involving tau leptons in the resulting final state. The topology and special characteristics of the tau leptons have been used to discriminate the signal from the Standard Model background. Limits on new particles have been set, playing an important role the channels with tau leptons.Comment: Invited talk at the Seventh International Workshop on Tau Lepton Physics (TAU02), Santa Cruz, Ca, USA, Sept 2002, 10 pages, LaTeX, 9 eps figure

The diameter of type D associahedra and the non-leaving-face property

Generalized associahedra were introduced by S. Fomin and A. Zelevinsky in connection to finite type cluster algebras. Following recent work of L. Pournin in types $A$ and $B$, this paper focuses on geodesic properties of generalized associahedra. We prove that the graph diameter of the $n$-dimensional associahedron of type $D$ is precisely $2n-2$ for all $n$ greater than $1$. Furthermore, we show that all type $BCD$ associahedra have the non-leaving-face property, that is, any geodesic connecting two vertices in the graph of the polytope stays in the minimal face containing both. This property was already proven by D. Sleator, R. Tarjan and W. Thurston for associahedra of type $A$. In contrast, we present relevant examples related to the associahedron that do not always satisfy this property.Comment: 18 pages, 14 figures. Version 3: improved presentation, simplification of Section 4.1. Final versio

Cluster algebras of type D: pseudotriangulations approach

We present a combinatorial model for cluster algebras of type $D_n$ in terms of centrally symmetric pseudotriangulations of a regular $2n$-gon with a small disk in the centre. This model provides convenient and uniform interpretations for clusters, cluster variables and their exchange relations, as well as for quivers and their mutations. We also present a new combinatorial interpretation of cluster variables in terms of perfect matchings of a graph after deleting two of its vertices. This interpretation differs from known interpretations in the literature. Its main feature, in contrast with other interpretations, is that for a fixed initial cluster seed, one or two graphs serve for the computation of all cluster variables. Finally, we discuss applications of our model to polytopal realizations of type $D$ associahedra and connections to subword complexes and $c$-cluster complexes.Comment: 21 pages, 21 figure

On the Influence of X-Ray Galaxy Clusters in the Fluctuations of the Cosmic Microwave Background

The negative evolution found in X--ray clusters of galaxies limits the amount of available hot gas for the inverse Compton scattering of the Cosmic Microwave Background (the Sunyaev--Zel'dovich effect). Using a parametrisation of the X-ray luminosity function and its evolution in terms of a coalescence model (as presented in the analysis of a flux limited X-ray cluster sample by Edge et al. 1990), as well as a simple virialised structure for the clusters (which requires a gas to total mass fraction \approxgt 0.1 in order to reproduce observed properties of nearby clusters) we show that the Compton distortion $y$ parameter is about two orders of magnitude below the current FIRAS upper limits. Concerning the anisotropies imprinted on arcmin scales they are dominated by the hottest undetected objects. We show that they are negligible ({\Delta T\over T}\approxlt 10^{-7}) at wavelengths \lambda\approxgt 1~mm. At shorter wavelengths they become more important (${\Delta T\over T}\sim 10^{-6}$ at $\lambda\sim 0.3$~mm), but in fact most clusters will produce an isolated and detectable feature in sky maps. After removal of these signals, the fluctuations imprinted by the remaining clusters on the residual radiation are still much smaller. The conclusion is that X-ray clusters can be ignored as sources of Cosmic Microwave Background fluctuations.Comment: 20 pages Plain Tex, 7 figures available upon request,UCAST-94-0

B Mixing and Lifetimes at the Tevatron

The Tevatron collider at Fermilab provides a very rich environment for the study of b-hadrons. Both the D0 and CDF experiments have collected a sample of about 1 fb^{-1}. We report results on three topics: b-hadron lifetimes, polarization amplitudes and the decay width difference in Bs to Jpsi Phi, and Bs mixing.Comment: Flavor Physics & CP Violation Conference, Vancouver, 200

Soft versus Hard X-ray emission in AGN: partial covering and warm plus cold absorber models

We analyse the ROSAT PSPC hardness ratio and the 0.5-2 keV to 2-10 keV flux ratio of 65 Active Galactic Nuclei (AGN) for which there are both ROSAT archival observations available and 2-10 keV fluxes, mostly from the HEAO-1 MC-LASS survey. We conclude that the simplest spectral model for the AGN that can accommodate the variety of X-ray colours obtained is a standard power law (with energy spectral index $\alpha\sim 0.9$) plus a $\sim 0.1$ keV black body both partially absorbed. In our sample, type 1 AGN require an absorbing column around $10^{22}\, {\rm cm}^{-2}$ with covering fractions between 20 and 100\%, while type 2 AGN display larger columns and $\sim 100\%$ coverage. This simple model also provides a good link between soft and hard AGN X-ray luminosity functions and source counts. We also consider a warm absorber as an alternative model to partial covering and find that the the presence of gas in two phases (ionized and neutral) is required.Comment: 10 pages, Latex (mn.sty), 1 table, 5 figures included (epsf), postscript version also available via anonymous ftp at ftp://astsun1.unican.es/pub/ceballos/ . Accepted for publication in MNRA