Lifshitz tails for alloy type models in a constant magnetic field

In this note, we study Lifshitz tails for a 2D Landau Hamiltonian perturbed by a random alloy-type potential constructed with single site potentials decaying at least at a Gaussian speed. We prove that, if the Landau level stays preserved as a band edge for the perturbed Hamiltonian, at the Landau levels, the integrated density of states has a Lifshitz behavior of the type $e^{-\log^2|E-2bq|}$

Galaxy Clusters Associated with Short GRBs. II. Predictions for the Rate of Short GRBs in Field and Cluster Early-Type Galaxies

We determine the relative rates of short GRBs in cluster and field early-type galaxies as a function of the age probability distribution of their progenitors, P(\tau) \propto \tau^n. This analysis takes advantage of the difference in the growth of stellar mass in clusters and in the field, which arises from the combined effects of the galaxy stellar mass function, the early-type fraction, and the dependence of star formation history on mass and environment. This approach complements the use of the early- to late-type host galaxy ratio, with the added benefit that the star formation histories of early-type galaxies are simpler than those of late-type galaxies, and any systematic differences between progenitors in early- and late-type galaxies are removed. We find that the ratio varies from R(cluster)/R(field) ~ 0.5 for n = -2 to ~ 3 for n = 2. Current observations indicate a ratio of about 2, corresponding to n ~ 0 - 1. This is similar to the value inferred from the ratio of short GRBs in early- and late-type hosts, but it differs from the value of n ~ -1 for NS binaries in the Milky Way. We stress that this general approach can be easily modified with improved knowledge of the effects of environment and mass on the build-up of stellar mass, as well as the effect of globular clusters on the short GRB rate. It can also be used to assess the age distribution of Type Ia supernova progenitors.Comment: ApJ accepted versio

Measurement of cross sections and leptonic forward-backward asymmetries at the Z pole and determination of electroweak parameters

We report on the measurement of the leptonic and hadronic cross sections and leptonic forward-backward asymmetries at the Z peak with the L3 detector at LEP. The total luminosity of 40.8 pb −1 collected in the years 1990, 1991 and 1992 corresponds to 1.09·10 6 hadronic and 0.98·10 5 leptonic Z decays observed. These data allow us to determine the electroweak parameters. From the cross sections we derive the properties of the Z boson: assuming lepton universality. We obtain an invisible width of Γ inv =496.5±7.9 MeV which, in the Standard Model, corresponds to a number of light neutrino species of N v =2.981±0.050.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47894/1/10052_2005_Article_BF01574160.pd

Search for non-minimal Higgs bosons in Z 0 decays

We report on a search for the neutral and charged Higgs bosons predicted by models of spontaneous symmetry breaking with more than one Higgs doublet field. No signals are observed. We set model-independent limits on masses or branching ratios of singly and pair-produced neutral and charged Higgs bosons. In addition, we interpret our results in the framework of a general two-doublet Higgs model and the Minimal Supersymmetric extension of the Standard Model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47892/1/10052_2005_Article_BF01474331.pd