A multiperipheral model with continued cross channel unitarity

We derive, by using a spectral representation in momentum transfer, t, an integral equation, similar in structure to a multipheral equation, with continued cross channel unitarity, for the absorptive part for a composite particle scattering amplitude from a Bethe-Salpeter equation describing composite particle scattering in the s channel. At high energy in the t channel, the equation becomes homogeneous and has a Reggeized solution. We indicate how this equation may be solved using determinental techniques. We also show how the composite particle amplitude resulting from the original equation may be used to construct production and three body amplitudes. We also infer the possibility of studying, using the amplitude from the cross channel problem, the effect of extra unitarity on Reggeon-Reggeon-particle vertices.     

Fragmentation models and unitarity

We use the diffractive excitation model to evaluate the inelastic part of the proton-proton unitarity equation. Conventional assumptions about the phase of the vacuum singularity, and an experimentally motivated choice of mass dependence for the diffractive slope, lead to an upper bound for the proportion of diffractively excited inelastic processes. We also discuss the apparent breakdown of factorization.     

Semi-group approach to multiperipheral dynamics

We consider the multiperipheral integral equation at vanishing four-momentum transfer in the form given by Chew and de Tar and we remark that the angular integrations can be interpreted as a convolution of measures defined in a semi-group S contained in the Lorentz group. We study the geometrical properties and a class Banach-space representations of this semi-group. By projection on these representations, we perform a partial wave analysis of the multiperipheral equation. Under some physically very natural conditions, we prove that the projection integrals converge, the partial wave amplitudes are analytic in a half-plane of the complex angular momentum and the kernel of the partial wave equation represents a bounded operator. We give a preliminary discussion of the inversion problem, i.e., of the construction of the amplitude from its partial wave projections.     

The shrinkage of the elastic differential cross section from the multiperipheral model using unitarity

The overlap function has been calculated analytically from a simplified Chan-?oskiewicz-Allison (C?A) model with Regge phase. Hamer and Peierls have shown using the impact parameter variables that in the C?A model with Regge phase the slope of the overlap function increases too rapidly with total energy when compared to experiments. According to Jadach and Turnau this was due to inadequate approximations made for the norm of the C?A amplitude and they showed that in the C?A model with no momentum-dependent phase the shrinkage agrees with experiments but the magnitude of the slope is too small. We show without making the inadequate approximations mentioned by Jadach and Turnau that when the Regge phase is used in the C?A model; it makes the overlap function shrink too rapidly and have a too large slope above 20 GeV/c. Clustering will improve the agreement with experiments, especially when one further assumes that the clusters do not form resonances. Then the trajectories which are exchanged between two clusters are exchange degenerate and have a real contribution to the amplitude. The analytic calculations make it possible to discuss contributions to the overlap function from various properties of the production amplitude.     

Compton scattering from chiral dynamics with unitarity and causality

Proton Compton scattering is analyzed with the chiral Lagrangian. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagnetic-gauge invariance, causality and unitarity are used to stabilize the extrapolation. We present and discuss predictions for various spin observables and polarizabilities of the proton. While for the transition polarizabilities γE1M2, γM1E2 we recover the results of strict chiral perturbation theory, for the diagonal γE1E1, γM1M1 elements we find significant effects from rescattering.     

A field theoretic cluster model of multiperipheral production

A field theoretic cluster model of multiproduction process in hadron-hadron collisions at high energy is considered. The multiproduction here is a two-step process. In the first step clusters are produced. We use a field theoretic formalism to describe cluster creation. A validity of the standard approximations, that are usually made in multiperipheral models is discussed. A modified strong ordering hypothesis is proposed. This leads to the Feynman scaling violation. Then cluster decay is considered. Expressions for semi-inclusive pion distributions in rapidity are given and a comparison with experimental data is made.     

Geometrodynamics vs. connection dynamics

The purpose of this review is to describe in some detail the mathematical relationship between geometrodynamics and connection dynamics in the context of the classical theories of 2+1 and 3+1 gravity. We analyze the standard Einstein-Hilbert theory (in any spacetime dimension), the Palatini and Chern-Simons theories in 2+1 dimensions, and the Palatini and self-dual theories in 3+1 dimensions. We also couple varions matter fields to these theories and briefly describe a pure spin-connection formulation of 3+1 gravity. We derive the Euler-Lagrange equations of motion from an action principle and perform a Legendre transform to obtain a Hamiltonian formulation of each theory. Since constraints are present in all these theories, we construct constraint functions and analyze their Poisson bracket algebra. We demonstrate, whenever possible, equivalences between the theories.     

Generalized eikonalization and unitarity

In the literature, the notion of eikonalization is often used as synonymous of unitarization or, at least, as implying that unitarity is not violated. This, to the very least, appears to be wishful thinking. We discuss the properties of various types of eikonalization within a unified treatment. Linear trajectories with intercept larger than unity (so popular nowadays) lead to small asymptotic violations of unitarity even after eikonalization. Classes of eikonalizations in which the Odderon could dominate over the Pomeron are given; even so the maximal Odderon is still excluded by eikonalization.     

Pion-nucleon scattering: Chiral symmetry and unitarity

The chiral quark models which have been constructed over the past five years generally preserve chiral symmetry in the tree approximation. However, unitarity is then violated. We examine the problem of going beyond the tree approximation for s-wave pion-nucleon scattering within the context of the cloudy bag model.     

Eikonalization and unitarity constraints

An extensive generalization of the ordinary and quasi-eikonal methods is presented for the pp and elastic scattering amplitudes, which takes into account in a phenomenological way all intermediate multiparticle states involving the crossing even and crossing odd combinations of Reggeons. The formalism in this version involves a maximum of three parameters corresponding to the intermediate states which are possible in this configuration. The unitarity restriction is investigated and particular cases are discussed. An interesting result that emerges concerns the Odderon trajectory intercept: we find that unitarity dictates that this quantity must be below or equal unity unless a very peculiar equality exists between the coupling of the particles to the Pomeron and the Odderon. Received: 3 September 1999 / Revised version: 21 February 2000 / Published online: 8 May 2000 2000     

Multiparticle unitarity and diffractive amplitudes

Generalizing the results of previous work, an explicit construction of elastic and inelastic diffractive amplitudes through multiparticle unitarity is given starting from a simple parametrization of non-diffractive production amplitudes. The energy dependent interference mechanism which has been previously shown to be essential to produce the diffraction peak in the elastic process is now seen to be also responsible, in a natural way, for the leading particle effect which dominates production yields.     

A comparative study of model ingredients: Fragmentation in heavy-ion collisions using quantum molecular dynamics model

We aim to understand the role of NN cross-sections, equation of state as well as different model ingredients such as width of Gaussian, clusterization range and different clusterization algorithms in multifragmentation using quantum molecular dynamics model. We notice that all model ingredients have sizable effect on the fragment pattern.     

A model of baryons based on duality and unitarity

A model of “planar” baryons with (10 + 8) ? (1 + 8) exchange degeneracy is proposed, based on duality and unitarity. Dynamical mechanisms for deviation from the “planar” baryons are considered and the consequent pattern of broken exchange degenerate trajectories is compared with observed baryon spectra. Our model suggests a string picture of linear molecule type for baryons.     

Gluon shadowing and unitarity effects

New data from HERA experiment on deep inelastic scattering have been used to parametrize nucleon and Pomeron structure functions. Within the Gribov theory, the parameterizations were employed to calculate gluon shadowing for various heavy ions. The latter was compared with predictions from other models. Calculations of multiplicity reduction due to gluon shadowing for d+Au collisions at forward rapidities at √s _NN =200 GeV are in good agreement with BRAHMS data on the nuclear modification factor.     

Neural field dynamics with heterogeneous connection topology

Neural fields receive inputs from local and nonlocal sources. Notably in a biologically realistic architecture the latter vary under spatial translations (heterogeneous), the former do not (homogeneous). To understand the mutual effects of homogeneous and heterogeneous connectivity, we study the stability of the steady state activity of a neural field as a function of its connectivity and transmission speed. We show that myelination, a developmentally relevant change of the heterogeneous connectivity, always results in the stabilization of the steady state via oscillatory instabilities, independent of the local connectivity. Nonoscillatory instabilities are shown to be independent of any influences of time delay.