Instanton-Induced Processes - An Overview

A first part of this review is devoted to a summary of our extensive studies of the discovery potential for instanton(I)-induced, deep-inelastic processes at HERA. Included are some key issues about I-perturbation theory, an exploitation of crucial lattice constraints and a status report about the recent I-search results by the HERA collaborations H1 and ZEUS in relation to our predictions. Next follows a brief outline of an ongoing project concerning a broad exploration of the discovery potential for hard instanton processes at the LHC. I then turn to an overview of our work on high-energy processes, involving larger-sized instantons. I shall mainly focus on the phenomenon of saturation at small Bjorken-x from an instanton perspective. In such a framework, the saturation scale is associated with the conspicuous average instanton size (~0.5 fm), as known from lattice simulations. Another central and intriguing result is the identification of the "Colour Glass Condensate" with the QCD sphaleron state.Comment: 14 pages,14 figures, Invited plenary talk presented at the CERN - DESY Workshop 2004/2005, "HERA and the LHC

Limit laws for the diameter of a set of random points from a distribution supported by a smoothly bounded set

We study the asymptotic behavior of the maximum interpoint distance of random points in a $d$-dimensional set with a unique diameter and a smooth boundary at the poles. Instead of investigating only a fixed number of $n$ points as $n$ tends to infinity, we consider the much more general setting in which the random points are the supports of appropriately defined Poisson processes. The main result covers the case of uniformly distributed points within a $d$-dimensional ellipsoid with a unique major axis. Moreover, several generalizations of the main result are established, for example a limit law for the maximum interpoint distance of random points from a Pearson type II distribution

QCD-Instantons and Saturation at Small x

We briefly report on the contribution of QCD-instantons to the phenomenon of saturation in deep-inelastic scattering (DIS) at small Bjorken-x. The explicitly known instanton gauge field serves as a concrete realization of an underlying non-perturbative saturation mechanism associated with strong classical fields. Two independent strategies were pursued, with consistent results: On the one hand, an approach starting from instanton-perturbation theory was considered and on the other hand, the scattering of a Wilson loop in an instanton gauge field background. In both cases, the conspicuous, intrinsic instanton size scale ~ 0.5 fm, as known from the lattice, turns out to determine the saturation scale.Comment: 6 pages, 2 figures, presented at the Workshop on Strong and Electroweak Matter (SEWM 2002), October 2-5, 2002, Heidelberg, German

Instanton-Induced Cross-Sections in Deep-Inelastic Scattering

We present our results for inclusive instanton-induced cross-sections in deep-inelastic scattering, paying in particular attention to the residual renormalization-scale dependencies. A ``fiducial'' kinematical region in the relevant Bjorken variables is extracted from recent lattice simulations of QCD. The integrated instanton-contribution to the cross-section at HERA corresponding to this fiducial region is surprisingly large: It is in the O(100) pb range, and thus remarkably close to the recently published experimental upper bounds.Comment: 13 pages, 10 figure

Instanton-Driven Saturation at Small x

We report on the interesting possibility of instanton-driven gluon saturation in lepton-nucleon scattering at small Bjorken-x. Our results crucially involve non-perturbative information from high-quality lattice simulations. The conspicuous, intrinsic instanton size scale ~ 0.5 fm, as known from the lattice, turns out to determine the saturation scale. A central result is the identification of the ``colour glass condensate'' with the QCD-sphaleron state.Comment: 14 pages, 9 figure

QCDINS 2.0 - A Monte Carlo generator for instanton-induced processes in deep-inelastic scattering

We describe a Monte Carlo event generator for the simulation of QCD-instanton induced processes in deep-inelastic scattering (HERA). The QCDINS package is designed as an ``add-on'' hard process generator interfaced to the general hadronic event simulation package HERWIG. It incorporates the theoretically predicted production rate for instanton-induced events as well as the essential characteristics that have been derived theoretically for the partonic final state of instanton-induced processes: notably, the flavour democratic and isotropic production of the partonic final state, energy weight factors different for gluons and quarks, and a high average multiplicity O(10) of produced partons with a Poisson distribution of the gluon multiplicity. While the subsequent perturbative evolution of the generated partons is always handled by the HERWIG package, the final hadronization step may optionally be performed also by means of the general hadronic event simulation package JETSET.Comment: 51 pages, 3 figure