Hamiltonian lattice gauge theory: wavefunctions on large lattices

We discuss an algorithm for the approximate solution of Schrodinger's equation for lattice gauge theory, using lattice SU(3) as an example. A basis is generated by repeatedly applying an effective Hamiltonian to a ``starting state.'' The resulting basis has a cluster decomposition and long-range correlations. One such basis has about 10^4 states on a 10X10X10 lattice. The Hamiltonian matrix on the basis is sparse, and the elements can be calculated rapidly. The lowest eigenstates of the system are readily calculable.Comment: 4 pages, (contribution to Lattice'92 conference); requires espcrc2.st

Modified WKB approximation

In the WKB approximation the \nabla^2S term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the \nabla^2 S term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to \phi^4 field theory.In the WKB approximation the $\nabla~2S$ term in Schrodinger's equation is subordinate to the |\nabla S|~2 term. Here we study an anti-WKB approximation in which the $\nabla~2 S$ term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to $\phi~4$ field theory.In the WKB approximation the $\nabla^2S$ term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the $\nabla^2 S$ term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to $\phi^4$ field theory

Multifractal current distribution in random diode networks

Recently it has been shown analytically that electric currents in a random diode network are distributed in a multifractal manner [O. Stenull and H. K. Janssen, Europhys. Lett. 55, 691 (2001)]. In the present work we investigate the multifractal properties of a random diode network at the critical point by numerical simulations. We analyze the currents running on a directed percolation cluster and confirm the field-theoretic predictions for the scaling behavior of moments of the current distribution. It is pointed out that a random diode network is a particularly good candidate for a possible experimental realization of directed percolation.Comment: RevTeX, 4 pages, 5 eps figure

Properties of the BFKL equation and structure function predictions for HERA

The general properties of the Lipatov or BFKL equation are reviewed. Modifications to the infrared region are proposed. Numerical predictions for the deep-inelastic electron-proton structure functions at small $x$ are presented and confronted with recent HERA measurements.Comment: 21 pages, 11 figures, Latex file, Durham preprint DTP 92/2

Generalized parton distributions and Deeply Virtual Compton Scattering in Color Glass Condensate model

Within the framework of the Color Glass Condensate model, we evaluate quark and gluon Generalized Parton Distributions (GPDs) and the cross section of Deeply Virtual Compton Scattering (DVCS) in the small-$x_{B}$ region. We demonstrate that the DVCS cross section becomes independent of energy in the limit of very small $x_{B}$, which clearly indicates saturation of the DVCS cross section. Our predictions for the GPDs and the DVCS cross section at high-energies can be tested at the future Electron-Ion Collider and in ultra-peripheral nucleus-nucleus collisions at the LHC.Comment: 20 pages, 8 Figure

Chirality Violation in QCD Reggeon Interactions

The appearance of the triangle graph infra-red axial anomaly in reduced quark loops contributing to QCD triple-regge interactions is studied. In a dispersion relation formalism, the anomaly can only be present in the contributions of unphysical triple discontinuities. In this paper an asymptotic discontinuity analysis is applied to high-order feynman diagrams to show that the anomaly does indeed occur in sufficiently high-order reggeized gluon interactions. The reggeon states involved must contain reggeized gluon combinations with the quantum numbers of the anomaly (winding-number) current. A direct connection with the well-known U(1) problem is thus established. Closely related diagrams that contribute to the pion/pomeron and triple pomeron couplings in color superconducting QCD are also discussed.Comment: 52 pages, 29 PS figures in the tex

Color Transparency versus Quantum Coherence in Electroproduction of Vector Mesons off Nuclei

So far no theoretical tool for the comprehensive description of exclusive electroproduction of vector mesons off nuclei at medium energies has been developed. We suggest a light-cone QCD formalism which is valid at any energy and incorporates formation effects (color transparency), the coherence length and the gluon shadowing. At medium energies color transparency (CT) and the onset of coherence length (CL) effects are not easily separated. Indeed, although nuclear transparency measured by the HERMES experiment rises with Q^2, it agrees with predictions of the vector dominance model (VDM) without any CT effects. Our new results and observations are: (i) the good agreement with the VDM found earlier is accidental and related to the specific correlation between Q^2 and CL for HERMES kinematics; (ii) CT effects are much larger than have been estimated earlier within the two channel approximation. They are even stronger at low than at high energies and can be easily identified by HERMES or at JLab; (iii) gluon shadowing which is important at high energies is calculated and included; (iv) our parameter-free calculations explain well available data for variation of nuclear transparency with virtuality and energy of the photon; (v) predictions for electroproduction of \rho and \phi are provided for future measurements at HERMES and JLab.Comment: Latex 57 pages and 17 figure

Coherent QCD phenomena in the Coherent Pion-Nucleon and Pion-Nucleus Production of Two Jets at High Relative Momenta

We use QCD to compute the cross section for coherent production of a di-jet (treated as a $q\bar q$ moving at high relative transverse momentum,$\kappa_t$). In the target rest frame,the space-time evolution of this reaction is dominated by the process in which the high $\kappa_t$ $q\bar q$ component of the pion wave function is formed before reaching the target. It then interacts through two gluon exchange. In the approximation of keeping the leading order in powers of $\alpha_s$ and all orders in $\alpha_{s}\ln(\kappa_{t}^2/k_{0}^2),$ the amplitudes for other processes are shown to be smaller at least by a power of $\alpha_{s}$. The resulting dominant amplitude is proportional to $z(1-z) \kappa_t^{-4}$ ($z$ is the fraction light-cone(+)momentum carried by the quark in the final state) times the skewed gluon distribution of the target. For the pion scattering by a nuclear target, this means that at fixed $x_{N}= 2\kappa_{t}^2/s$ (but $\kappa_{t}^2\to \infty$) the nuclear process in which there is only a single interaction is the most important one to contribute to the reaction. Thus in this limit color transparency phenomena should occur.These findings are in accord with E971 experiment at FNAL. We also re-examine a potentially important nuclear multiple scattering correction which is positive and $\propto A^{1/3}/\kappa_t^4$. The meaning of the signal obtained from the experimental measurement of pion diffraction into two jets is also critically examined and significant corrections are identified.We show also that for values of $\kappa_t$ achieved at fixed target energies, di-jet production by the e.m. field of the nucleus leads to an insignificant correction which gets more important as $\kappa_t$ increases.Comment: 23 pages, 9 figure

Cut Diagrams for High Energy Scatterings

A new approach is introduced to study QCD amplitudes at high energy and comparatively small momentum transfer. Novel cut diagrams, representing resummation of Feynman diagrams, are used to simplify calculation and to avoid delicate cancellations encountered in the usual approach. Explicit calculation to the 6th order is carried out to demonstrate the advantage of cut diagrams over Feynman diagrams.Comment: uu-encoded file containing a latex manuscript with 14 postscript figure