A Gauge-fixed Hamiltonian for Lattice QCD

We study the gauge fixing of lattice QCD in 2+1 dimensions, in the Hamiltonian formulation. The technique easily generalizes to other theories and dimensions. The Hamiltonian is rewritten in terms of variables which are gauge invariant except under a single global transformation. This paper extends previous work, involving only pure gauge theories, to include matter fields.Comment: 7 pages of LaTeX, RU-92-45 and BUHEP-92-3

Regge Trajectories with Square-Root Branch Points and Their Regge Cuts

We discuss branch points in the complex angular momentum plane formed by two Regge poles on trajectories with square-root branch points at t=0. We find several new cuts which collide with the expected Mandelstam cuts at t=0. In the bootstrap of the Pomeranchon pole, the collection of cuts has the same effect as in the case of linear trajectories: The Pomeranchon can have α(0)=1 only if certain couplings vanish at t=0

Obtaining real parts of scattering amplitudes directly from cross section data using derivative analyticity relations

We show that one can obtain real parts of scattering amplitudes by knowing the imaginary parts at only nearby energies. This is accomplished by re-casting the dispersion integral into an equivalent form which we will calla "derivative analyticity relation". Predictions are given for forward amplitudes where [sigma]T is measured: pp, . We deduce the real part of the elastic pp amplitude away from the forward direction at ISR energies.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22369/1/0000816.pd

Statistical Matrix for Electroweak Baryogenesis

In electroweak baryogenesis, a domain wall between the spontaneously broken and unbroken phases acts as a separator of baryon (or lepton) number, generating a baryon asymmetry in the universe. If the wall is thin relative to plasma mean free paths, one computes baryon current into the broken phase by determining the quantum mechanical transmission of plasma components in the potential of the spatially changing Higgs VEV. We show that baryon current can also be obtained using a statistical density operator. This new formulation of the problem provides a consistent framework for studying the influence of quasiparticle lifetimes on baryon current. We show that when the plasma has no self-interactions, familiar results are reproduced. When plasma self-interactions are included, the baryon current into the broken phase is related to an imaginary time temperature Green's function.Comment: 20 pages, no figures, Late

QCD near the Light Cone

Starting from the QCD Lagrangian, we present the QCD Hamiltonian for near light cone coordinates. We study the dynamics of the gluonic zero modes of this Hamiltonian. The strong coupling solutions serve as a basis for the complete problem. We discuss the importance of zero modes for the confinement mechanism.Comment: 32 pages, ReVTeX, 2 Encapsulated PostScript figure

THE GLUON DISTRIBUTION AT SMALL x OBTAINED FROM A UNIFIED EVOLUTION EQUATION.

We solve a unified integral equation to obtain the $x, Q_T$ and $Q$ dependence of the gluon distribution of a proton in the small $x$ regime; where $x$ and $Q_T$ are the longitudinal momentum fraction and the transverse momentum of the gluon probed at a scale $Q$. The equation generates a gluon with a steep $x^{- \lambda}$ behaviour, with $\lambda \sim 0.5$, and a $Q_T$ distribution which broadens as $x$ decreases. We compare our solutions with, on the one hand, those that we obtain using the double-leading-logarithm approximation to Altarelli-Parisi evolution and, on the other hand, to those that we determine from the BFKL equation.Comment: LaTeX file with 10 postscript figures (uuencoded

On the rise of proton-proton cross-sections at high energies

The rise of the total, elastic and inelastic hadronic cross sections at high energies is investigated by means of an analytical parametrization, with the exponent of the leading logarithm contribution as a free fit parameter. Using derivative dispersion relations with one subtraction, two different fits to proton-proton and antiproton-proton total cross section and rho parameter data are developed, reproducing well the experimental information in the energy region 5 GeV - 7 TeV. The parametrization for the total cross sections is then extended to fit the elastic (integrated) cross section data in the same energy region, with satisfactory results. From these empirical results we extract the energy dependence of several physical quantities: inelastic cross section, ratios elastic/total, inelastic/total cross sections, ratio total-cross-section/elastic-slope, elastic slope and optical point. All data, fitted and predicted, are quite well described. We find a statistically consistent solution indicating: (1) an increase of the hadronic cross sections with the energy faster than the log-squared bound by Froissart and Martin; (2) asymptotic limits 1/3 and 2/3 for the ratios elastic/total and inelastic/total cross sections, respectively, a result in agreement with unitarity. These indications corroborate recent theoretical arguments by Ya. I. Azimov on the rise of the total cross section.Comment: 35 pages, 12 figures, discussions improved with further clarifications, references added and updated, one note added, results and conclusions unchanged. Version to be published in J. Phys. G: Nucl. Part. Phy

Solving integral equations in η→3π\eta\to 3\pi

A dispersive analysis of $\eta\to 3\pi$ decays has been performed in the past by many authors. The numerical analysis of the pertinent integral equations is hampered by two technical difficulties: i) The angular averages of the amplitudes need to be performed along a complicated path in the complex plane. ii) The averaged amplitudes develop singularities along the path of integration in the dispersive representation of the full amplitudes. It is a delicate affair to handle these singularities properly, and independent checks of the obtained solutions are demanding and time consuming. In the present article, we propose a solution method that avoids these difficulties. It is based on a simple deformation of the path of integration in the dispersive representation (not in the angular average). Numerical solutions are then obtained rather straightforwardly. We expect that the method also works for $\omega\to 3\pi$.Comment: 11 pages, 10 Figures. Version accepted for publication in EPJC. The ancillary files contain an updated set of fundamental solutions. The numerical differences to the former set are tiny, see the READMEv2 file for detail