Equivalence between non-bilinear spin-SS Ising model and Wajnflasz model

We propose the mapping of polynomial of degree 2S constructed as a linear combination of powers of spin-$S$ (for simplicity, we called as spin-$S$ polynomial) onto spin-crossover state. The spin-$S$ polynomial in general can be projected onto non-symmetric degenerated spin up (high-spin) and spin down (low-spin) momenta. The total number of mapping for each general spin-$S$ is given by $2(2^{2S}-1)$. As an application of this mapping, we consider a general non-bilinear spin-$S$ Ising model which can be transformed onto spin-crossover described by Wajnflasz model. Using a further transformation we obtain the partition function of the effective spin-1/2 Ising model, making a suitable mapping the non-symmetric contribution leads us to a spin-1/2 Ising model with a fixed external magnetic field, which in general cannot be solved exactly. However, for a particular case of non-bilinear spin-$S$ Ising model could become equivalent to an exactly solvable Ising model. The transformed Ising model exhibits a residual entropy, then it should be understood also as a frustrated spin model, due to competing parameters coupling of the non-bilinear spin-$S$ Ising model

Measurement of the Spectroscopy of Orbitally Excited B Mesons at LEP

We measure the masses, decay widths and relative production rate of orbitally excited B mesons using 1.25 million hadronic Z decays recorded by the L3 detector. B-meson candidates are inclusively reconstructed and combined with charged pions produced at the primary event vertex. An excess of events above the expected background in the B\pi mass spectrum in the region 5.6-5.8 GeV is interpreted as resulting from the decay B_u,d^** -> B^(*)\pi, where B_u,d^** denotes a mixture of l=1 B-meson states containing a u or a d quark. A fit to the mass spectrum yields the masses and decay widths of the B_1^* and B_2^* spin states, as well as the branching fraction for the combination of l=1 states. In addition, evidence is presented for the existence of an excited B-meson state or mixture of states in the region 5.9-6.0 GeV

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 Z0 decays to hadrons, and a precise determination of the number of neutrino species

We have made a precise measurement of the cross section for e+e--->Z0-->hadrons with the L3 detector at LEP, covering the range from 88.28 to 95.04 GeV. From a fit to the Z0 mass, total width, and the hadronic cross section to be MZ0=91.160 +/- 0.024 (experiment) +/-0.030(LEP) GeV, [Gamma]Z0=2.539+/-0.054 GeV, and [sigma]h(MZ0)=29.5+/-0.7 nb. We also used the fit to the Z0 peak cross section and the width todetermine [Gamma]invisible=0.548+/-0.029 GeV, which corresponds to 3.29+/-0.17 species of light neutrinos. The possibility of four or more neutrino flavors is thus ruled out at the 4[sigma] confidence level.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28683/3/0000500.pd

A measurement of the Z0 leptonic partial widths and the vector and axial vector coupling constants

We have measured the partial widths of the Z0 into lepton pairs, and the forward-backward charge asymmetry for the process e+e--->[mu]+[mu]- using the L3 detector at LEP. We obtain an average [Gamma]ll of 83.0+/-2.1+/-1.1 MeV.From this result and the asymmetry measurement, we extract the values of the vector and axial vector couplings of the Z0 to leptons: grmv=-0.066-0.027+0.046 and grmA= -0.495-0.007+0.007.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28666/3/0000483.pd