Spectrum of lattice gauge theories with fermions from a 1/d expansion at strong coupling

We study the strong coupling limit of U(N) or SU(N) gauge theories with fermions on a lattice. The integration over the gauge and fermion degrees of freedom is performed by analytic methods, leading to a partition function in terms of localized meson and baryon fields. A method for deriving a systematic expansion in the inverse of the space-time dimension of the corresponding Green functions is developed. It is applied to the study of spontaneous breakdown of chiral symmetry, which occurs for any U(N) or SU(N) theory with fermions in the fundamental representation. Meson and baryon spectra are then computed, and found to be in close agreement with those obtained by numerical methods at finite coupling. The pion decay constant is estimated.     

Gluon jet in deep inelastic muon scattering

We study the quark and gluon final state in deep inelastic μ-scattering. For a hadron observed at sufficiently large angleθ _h with respect to the virtual photon direction, and sufficiently large energy fractionz _h , this final state dominates the cross-section. Moreover, at the same time, most events in this regime are due to the fragmentation of the quark. In such cases the position of the gluon in phase space is determined, the quark acting as a trigger for gluon jet detection. We demonstrate that in the rest frame of the final quark and gluon, the gluon is energetic and well separated from quark and target fragments. We study the boost from the lab to this frame, and give expressions for the most probable boost in terms ofθ _h andz _h . This study should lead to a convenient visualization of the gluon jet.     

CO2 sorption and transport in miscible poly(phenylene oxide)/polystyrene blends

The sorption and permeation of carbon dioxide gas in miscible blends of poly(phenylene oxide) and polystyrene was measured as a function of pressure at 35°C over the entire range of blend compositions. The results are well described quantitatively by the dual sorption and dual mobility models developed for glassy polymers. The Henry's law sorption parameter was analyzed by the Flory—Huggins theory of ternary mixtures to obtain an interaction parameter which quantifies the exothermic heat of mixing for this blend system. The Langmuir capacity term was successfully related to the unrelaxed volume of the glassy blends. Transport properties of the blends were found to lie well below predictions based on simple additivity which is consistent with the strong interaction between the two polymers.     

Finite-size effects due to Goldstone particles in lattice gauge theory

We study the finite-size effects associated with the appearance of a light, i.e. Goldstone, particle in the Kogut-Susskind lattice gauge theory. We analytically study the order parameter $\text{(}\text{X}\text{X)}$ and the two-meson propagator in the strong coupling limit on a finite lattice. We give their explicit interpolations between the broken phase of the infinite-volume limit and the symmetric one of the finite system. We argue that the results obtained in the strong coupling limit are more general.     

An Extension of Generalized Linear Models to Finite Mixture Outcome Distributions

Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the analysis of categorical and count outcomes when standard generalized linear models (GLMs) cannot adequately express variability observed in the data. We propose an extension of GLMs where the response follows a finite mixture distribution and the regression of interest is linked to the mixture’s mean. This approach may be preferred over a finite mixture of regressions when the population mean is of interest; here, only one regression must be specified and interpreted in the analysis. A technical challenge is that the mixture’s mean is a composite parameter that does not appear explicitly in the density. The proposed model maintains its link to the regression through a certain random effects structure and is completely likelihood-based. We consider typical GLM cases where means are either real-valued, constrained to be positive, or constrained to be on the unit interval. The resulting model is applied to two example datasets through Bayesian analysis. Supporting the extra variation is seen to improve residual plots and produce widened prediction intervals reflecting the uncertainty. Supplementary materials for this article are available online.