Y. Leroyer

Adsorption of line segments on a square lattice.

We study the deposition of line segments on a two-dimensional square lattice. The estimates for the coverage at jamming obtained by Monte Carlo simulations and by seventh-order time-series expansion are successfully compared. The nontrivial limit of adsorption of infinitely long segments is studied, and the lattice coverage is consistently obtained using these two approaches.

REAL PARTS OF SCATTERING AMPLITUDES AND REGGE PHENOMENOLOGY.

Abstract High energy scattering amplitudes are computed using the Harari model for the imaginary parts and fixed t dispersion relations for the real parts. This procedure induces a corrective term to the real part of the Regge amplitudes whose effects are investigated in π -nucleon and K-nucleon charge exchange reactions.

Model-independent amplitude analysis for the reaction πN → ρΔ

A method is proposed for determining the amplitudes for the reaction πN → ϱΔ using only those moments of the joint decay angular distribution 〈YL1M1YL2M2〉 with both L1 and L2 even. The solution is not unique; both continuous and discrete ambiguities exist. The conditions under which an analysis is possible are studied in detail; in addition to certain positivity conditions on the joint density matrix, a complicated inequality involving the experimental moments must be satisfied. This condition defines a non-convex domain in the space of the moments. We apply our methods to the high-statistics experimental data at 3.7 GeV/c.

Tests of positivity conditions in joint vector-meson Δ production

Abstract The moments of the joint-decay angular distribution in the reactions π + p → ρ 0 Δ ++ , π + p → ωΔ ++ and KN → K ∗ Δ should satisfy certain inequalities implied by the positivity of the joint-density matrix. Using published data on these reactions, at various values of energy and momentum transfer, we find that, of fifty-eight data points, in only one case are the conditions satisfied by the central experimental values. In addition, in some experiments the reconstructed joint-decay angular distribution is found to be not strictly positive. A quantitative measure of the positivity violation is presented, which suggests that modest changes in the experimental results, of the size of the error estimates, would yield moments consistent with positivity.

Model-independent analysis of the reaction π+p → π+π−Δ++

Abstract The high-statistics data on π + p → π + π − Δ ++ at 7.1 GeV/ c are used in a detailed analysis using model-independent means. Positivity conditions are found to be violated, although there is overlap between the positivity domain and the error ellipsoid. Using points modified to satisfy positivity, we confirm certain aspects of a previous model-dependent analysis. In particular, the percentage S-wave is found to be close to the lower limit consistent with the ππ moments alone. A number of quark-model predictions are confronted with the data and also with our modified points, and reasonable but not total agreement is observed.

Langevin simulation of the ising model with application to field theory in two and three dimensions

A Langevin method is developed for computing the spin correlations of the Ising model. It is applied in two and three dimensions in order to evaluate critical quantities, including the renormalized coupling constant of the corresponding field theory. A simple minimization of finite size effects is shown to give a realistic determination of these numbers from quite small lattices.

Horizontal symmetry and pseudo-goldstone bosons

Abstract We investigate the minimization problem of Higgs potentials invariant under a semisimple gauge group of the form G V × G H . G V is taken to be the SU(2) × U(1) electroweak group and G H , a horizontal symmetry group, is either SU(2) or SU(3). The different possibilities of G H representation for the Higgs fields are considered in turn, and in most cases we find that the minimum of the corresponding potential is such that pseudo-Goldstone bosons occur.