Multi-Regge cluster model versus multiparticle experimental data

Zeitschrift für Physik C Particles and Fields - We perform an analysis of predictions of the multi-Regge cluster model and compare them with available longitudinal and transverse data. We show...     

Multi-Regge limit of the Shapiro-Virasoro model; A sister for the pomeron

The structure of the four-, five-and six-point functions in the Shapiro-Virasoro model in multi-Regge and double-helicity pole limits is studied in detail. A pomeron propagator is derived along with the pomeron-particle-pomeron vertex function. The structure of both is investigated and evidence provided for the existence of a pomeron sister trajectory, related to the usual trajectory, αp, by $\text{β}\text{p}\text{=}\text{1}\text{2}\text{α}\text{p}\text{? 1}$; this is demonstrated to exist and its contribution to the full amplitude derived. Throughout, a correspondence between regions of angular integration in the Shapiro-Virasoro model and twisted configurations in the conventional dual model is emphasised.     

Correlations in the XY model and screw dislocations in the solid-on-solid model

An exact relation is proven between the two-point correlation function of the classical XY model and the free energy of a step associated with two screw dislocations on a crystal surface described by a solid-on-solid model. This result suggests a way to obtain the XY critical exponent η_c from Monte Carlo studies of the solid-on-solid model.     

Review of the Present Evidence for Multi-Regge Pole Processes

The present understanding of particle production processes in terms of the multi-Regge pole exchange model is reviewed from the theoretical and phenomenological point of view. It is concluded that the model discussed up to the present represents many different features of the data. Further tests of the model are discussed.     

Correlations and static energies in the standard Higgs model

Correlations in the W-boson and Higgs boson channels and the static energy of an external SU(2) doublet charge pair are investigated by Monte Carlo calculations in the SU(2) lattice gauge theory with a scalar Higgs doublet field. The mass ratio m_W/m_H and the shape of the static potential are used to obtain information on the renormalization group trajectories in the three-dimensional coupling constant space. As a function of an appropriately chosen varibale, the measured quantities are, within errors, independent from the scalar self-coupling (λ) in a wide range 0.1 ⩽ λ ⩽ ∝. In the Higgs phase, a lower bound m_W/m_H ⩾ (1.0 ± 0.3) is obtained for the ratio of the Higgs boson mass to the W-boson mass.     

Multi-Regge form of gluon-exchange amplitudes in supersymmetric Yang-Mills theories

Within supersymmetric Yang-Mills theories, all effective vertices for the interaction of Reggeized gluons with particles were found both in the leading-logarithm approximation and in the next-to-leading-order approximation. The contributions of scalars to the eigenfunction of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel for the adjoint representation of the gauge group and to impact factors similar to those in QCD were calculated. The impact factors that arise in supersymmetric Yang-Mills theories, but which are not present in QCD, are also found. Fulfillment of all bootstrap conditions, which guarantees the multi-Regge form of multiparticle amplitudes in supersymmetric Yang-Mills theories in the next-to-leading-order approximation, was proven. A method for testing bootstrap relations without calculating explicit expressions for vertices and impact factors was developed. This method was used to prove fulfillment of bootstrap conditions in theories featuring any number of fermions and scalar particles transformed according to any representations of the color group and involved in interactions with one another via Yukawa coupling.     

Correlations in the ground state of the one-dimensional Hubbard model

With eigenfunctional theory and a rigorous expression of exchange-correlation energy of a general interacting electron system, we study the ground state properties of the one-dimensional Hubbard model, and calculate the ground-state energy as well as the charge gap at half-filling for arbitrary coupling strength u=U/(4t) and electron density nc. We find that the simple linear approximation of the phase field works well in weak coupling case, but it becomes inappropriate as the on-site Coulomb interaction becomes strong where the fluctuations of the bosonic auxiliary field are strong. Then we propose a new scheme by adding Gutzwiller projection which suppresses the density fluctuations and the new results are quite close to the exact ones up to considerably strong coupling strength u=3.0 and for arbitrary electron density nc. Our calculation scheme is proved to be effective for strongly correlated electron systems in one dimension, and its extension to higher dimensions is straightforward.     

Correlations in the SU(2) fundamental higgs model

Correlations in SU(2) lattice gauge theory with a Higgs doublet are studied by Monte Carlo calculation. Some qualitative consequences for the particle spectrum in isoscalar and isovector channels are discussed.     

Correlations between charged particles in a diffractive dissociation model

An analytically solvable model of the single excitation diffractive type is investigated. It is assumed that a factorizable Pomeron (α _P (0)=1) excites a cluster, which subsequently decays through a multiperipheral mechanism with pure meson exchanges. Thus various charge structures can be incorporated. For the charged particle multiplicity distribution in inelasticp-p scattering Wroblewski's law, i. e. the experimentally found linear dependence of the dispersion on the mean multiplicity, is derived.     

Correlations in the sand pile model: From the log-normal distribution to self-organized criticality

We have studied the approach of the Abelian sand pile model towards the stationary, self-organized criticality state. The uncorrelated limit is shown both numerically and by a simple analysis to follow the log-normal distribution. We introduce and evaluate several correlation fuctions to study the correlated region.     

Correlations for the circular Dyson brownian motion model with Poisson initial conditions

The circular Dyson brownian motion model refers to the stochastic dynamics of the log-gas on a circle. It also specifies the eigenvalues of certain parameter-dependent ensembles of unitary random matrices. This model is considered with the initial condition that the particles are non-interacting (Poisson statistics). Jack polynomial theory is used to derive a simple exact expression for the density-density correlation with the position of one particle specified in the initial state, and the position of one particle specified at time τ, valid for all β > 0. The same correlation with two particles specified in the initial state is also derived exactly, and some special cases of the theoretical correlations are illustrated by comparison with the empirical correlations calculated from the eigenvalues of certain parameter-dependent Gaussian random matrices. Application to fluctuation formulas for time-displaced linear statistics in made.     

Correlations in the hadronization process

Pions cannot be fully described as simple $q\bar q$ systems. They have a very small mass and may appear as a kind of Goldstone particles. It is demonstrated how this is expected to give correlations in flavour andp _⊥ in the string model hadronization process. Improved agreement with experimental data is obtained, in particular for η′, η production and π⁺π^? mass correlations.     

Correlations in the bond-future market

We analyse the time series of overnight returns for the BUND and BTP futures exchanged at LIFFE (London). The overnight returns of both assets are mapped onto a one-dimensional symbolic-dynamics random walk: The “bond walk”. During the considered period (October 1991–January 1994) the BUND-future market opened earlier than the BTP-future one. The crosscorrelations between the two bond walks, as well as estimates of the conditional probability, show that they are not independent; however each walk can be modelled by means of a trinomial probability distribution. Monte Carlo simulations confirm that it is necessary to take into account the bivariate dependence in order to properly reproduce the statistical properties of the real-world data. Various investment strategies have been devised to exploit the “prior” information obtained by the aforementioned analysis.     

Correlations beyond the horizon

It is a fundamental feature of quantum field theory that correlations between observable quantities occur over all spacetime regions. In particular, in cosmological models with horizons, such correlations will be present in regions which lie outside of each other's horizon. Such correlations may play an important role in processes occurring in the early universe.This essay received the first award from the Gravity Research Foundation, 1992—Ed.