M. Hontebeyrie

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.

Construction of π± photoproduction amplitudes at high energy from dispersion relations and local duality

We investigate the charged-pion photoproduction amplitudes at all energies. We first show that low-energy s-channel helicity amplitudes exhibit, in most cases, a Bessel-function structure of zeroes. At high energy we therefore parametrize the imaginary parts of helicity amplitudes according to the Harari model, and compute the real parts using fixed-t dispersion relations as proposed recently. Such an evaluation of scattering amplitudes presents some very nice properties. In particular, it allows one to understand from duality arguments how the Born contribution may survive with full strength in the forward direction but not at large t-values. Furthermore FESR are identically satisfied by the model.

On the random filling of Rd by non-overlapping d-dimensional cubes

Abstract We compute the time-dependent coverage in the random sequential adsorption of aligned d-dimensional cubes in R d using time-series expansions. The seventh-order series in 2,3 and 4 dimensions is resummed in order to predict the coverage at jamming. The result is in agreement with Monte Carlo simulations. A simple argument, based on a property of the pertubative expansion valid at arbitrary orders, allows us to analytically derive some generalizations of the Palasti approximation.

IS s-channel helicity really conserved in ϱ0 photoproduction?

Abstract We discuss problems related to helicity conservation and show that it is difficult to conclude that s -channel helicity is conserved from our present knowledge of ϱ meson photoproduction.

On the strong coupling expansion of the Φd2k theory

Abstract The strong coupling expansion of the Φ2k field theory with either usual or gaussian propagators is investigated in a d-dimensional euclidean space. Some simple diagrams which occur at all orders of the vacuum energy density expansion are summed. This resummation is shown to give, in the zero lattice spacing limit, good results for all anharmonic oscillators, even for k = ∞, and in all dimensions in the case of a gaussian propagator.

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.

Magnetic susceptibility of the O(N) σ-model from high temperature expansions and scaling

Abstract High temperature expansions at 14th order and asymptotic scaling are used to reconstruct at any coupling the magnetic susceptibility of the non-linear O( N ) σ -model. The method we use, a Pade resummation in a mapped variable, is shown to be exact in the N = ∞ case. The results, which are in agreement with Monte Carlo data, show how the onset of scaling changes between O(4) and O(3), in a way compatible with the renormalization group asymptotic value.

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.

Harmonic oscillator on a lattice

Abstract The continuum limit of the ground state energy for the harmonic oscillator with discrete time is derived for all possible choices of the lattice derivative. The occurence of unphysical values is shown to arise whenever the lattice laplacian is not strictly positive on its Brillouin zone. These undesirable limits can either be finite and arbitrary (multiple spectrum) or infinite (overlapping sublattices with multiple spectrum).

On the critical behaviour of Φd2k from the massive continuum limit of the Ising model

Abstract The continuum limit of the first four renormalized vertices of the Ising model are derived from a large order strong coupling expansion in the regime in which the bare coupling is infinite and the renormalized mass held fixed. This method of computing the critical superpotential of Φ d 2 k is discussed for the euclidean dimension d . In one dimension, exact results can be obtained analytically, and the method remains perfectly reliable up to d = 2. Its validity is, however, unclear at higher dimension, for which we present some conjectures.