Large multiplicity fluctuations and saturation effects in onium collisions

This paper studies two related questions in high energy onium-onium scattering: the probability of producing an unusually large number of particles in a collision, where it is found that the cross section for producing a central multiplicity proportional to $k$ should decrease exponentially in $\sqrt{k}$. Secondly, the nature of gluon (dipole) evolution when dipole densities become so high that saturation effects due to dipole-dipole interactions become important: measures of saturation are developed to help understand when saturation becomes important, and further information is obtained by exploiting changes of frame, which interchange unitarity and saturation corrections.Comment: 30 pages LaTeX2e, 11 figures included using epsfig. Compressed postscript of whole paper also available at http://www.hep.phy.cam.ac.uk/theory/papers

Parton Saturation-An Overview

The idea of partons and the utility of using light-cone gauge in QCD are introduced. Saturation of quark and gluon distributions are discussed using simple models and in a more general context. The Golec-Biernat W\usthoff model and some simple phenomenology are described. A simple, but realistic, equation for unitary, the Kovchegov equation, is discussed, and an elementary derivation of the JIMWLK equation is given.Comment: Cargese Lectures, 34 pages, 19 figure

Single and Double BFKL Pomeron Exchange and a Dipole Picture of High Energy Hard Processes

Onium-onium scattering at high energy is used to illustrate a dipole picture of high energy hard scattering in the large $N_c$ limit. Single and double BFKL pomeron exchanges are calculated in the leading logarithmic approximation. An expression is given for the triple pomeron coupling when one of the pomeron's momentum is zero while the other two have momentum transfer, t. This expression is explicit and could be evaluated numerically. It has a $(-t)^{-{1\over 2}}$ singularity at t=0.Comment: CU-TP-625, minor TeX problems of previous version have been fixe

Large Scale Rapidity Correlations in Heavy Ion Collisions

We discuss particle production mechanisms for heavy ion collisions. We present an argument demonstrating how the fluctuations of the number of produced particles in a series of classical emissions can account for KNO scaling. We predict rapidity correlations in the particle production in the event by event analysis of heavy ion collisions on the rapidity scales of the order of one over the strong coupling constant.Comment: REVTeX, 13 pages, 3 figure

BFKL Dynamics in Jet Evolution

We calculate $e^+e^- \to Q\bar{Q}(k) + anything in a certain momentum, k, region for heavy quark-antiquark (Q\bar{Q})production. In our chosen region we find that the number of heavy quark pairs produced is determined by BFKL dynamics and the energy dependence of the number of pairs is given by$\alpha p-1$ the hard pomeron intercept.Comment: 14 pages, Latex, 4 figure

A Simple Derivation of the JIMWLK Equation

A simple derivation of the Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and Kovner (JIMWLK) equation for the evolution of small-x QCD wavefunctions is given. The derivation makes use of the equivalence between the evolution of a (in general complicated) small-x wavefunction with that of the evolution of the (simple) dipole probing the wavefunction in a high energy scattering.Comment: 11 pages, 3 figures, corrected typo in abstract titl

Parton Saturation at Small x and in Large Nuclei

Quark and gluon distributions in the light-cone wavefunction of a high energy hadron or nucleus are calculated in the saturation regime. One loop calculations are performed explicitly using the equivalence between the parton distribution in the light-cone wavefunction and the production distribution of that parton in a current-nucleon (nucleus) scattering. We argue that, except for some overall numerical factors, the Weizsacker- Williams wavefunction correctly gives the physics of the gluon distribution in a light-cone wavefunction.Comment: 24 pages, 4 figure

Toward Equilibration in the Early Stages After a High Energy Heavy Ion Collision

The early stages in the evolution of the gluons produced in the central region of a head-on high-energy heavy ion collision is studied. An equation is given for the rate of change of transverse momentum into longitudinal momentum where the longitudinal direction is along the collision axis. We are able to follow the system up to the time where equilibration seems to be setting in, but we are unable to actually follow the system as it reaches equilibrium.Comment: 18 pages, Late

The triple pomeron interaction in the perturbative QCD

The triple pomeron interaction is studied in the perturbative approach of BFKL-Bartels. At finite momentum transfers $\sqrt{-t}$ the contribution factorizes in the standard manner with a triple-pomeron vertex proportional to $1/\sqrt{-t}$. At $t=0$ the contribution is finite, although it grows faster with energy than for finite $t$ and does not factorize.Comment: 17 pages, 4 figures, LATE

Gluon Distributions and Color Charge Correlations in a Saturated Light-cone Wavefunction

We describe the light-cone wavefunction in the saturation regime in terms of the density of gluons per unit of transverse phase space, the occupation number, and in terms of the color charge correlator. The simple McLerran- Venugopalan model gives what are claimed to be general results for the phase space gluon density, but it does not well describe the general case for the charge correlator. We derive the general momentum dependence and rapidity dependence of the color charge correlator which exhibits strong color shielding. A simplel physical picture which leads to these general results is described.Comment: 17 pages, Latex, 7 figure