Abstracts for the CSSM Workshop on Light-Cone QCD and Nonperturbative Hadron Physics

Abstracts for the CSSM Workshop on Light-Cone QCD and Nonperturbative Hadron Physics
December 13 to 22, 1999

Brent H. Allen (Columbus, Ohio)

Glueballs in a Hamiltonian Light-Front Approach to Pure-Glue QCD

We calculate a renormalized Hamiltonian for pure-glue QCD and diagonalize it. The renormalization procedure is designed to produce a Hamiltonian that will yield glueball states that have rapidly convergent expansions in gluon number. To make this approach possible, we work in light-front field theory to isolate vacuum effects, and we place a smooth cutoff on the Hamiltonian to suppress free-state matrix elements with large changes in free mass. We derive recursion relations that in principle define the Hamiltonian to all orders in perturbation theory in the running coupling. Using these recursion relations, we calculate the part of the Hamiltonian that is relevant to our bound-state calculation to second order in the running coupling. We proceed to approximate the glueball states as two-gluon states, and diagonalize the Hamiltonian using basis-state expansions for the gluons' color, spin, and momentum degrees of freedom. We examine the sensitivity of our bound-state results to the cutoff and use the results to analyze the nonperturbative scale dependence of the coupling. We investigate the effect of the dynamical rotational symmetry of light-front field theory on the rotational degeneracies of the glueball spectrum and compare the spectrum to recent lattice results. Finally, we analyze our glueball wave functions.

Chris Allton (Swansea, UK)

Recent results from (full) Lattice QCD

Recent results from the UKQCD lattice collaboration are presented. These will concentrate on spectral quantities calculated using full (i.e. unquenched) QCD. A comparison with quenched results, and with those from other methods will be presented.

Pierre van Baal (Leiden, The Netherlands)

Monopoles in disguise

I present the recent results that demonstrate that instantons are in fact build from BPS monopoles and discuss the relevance for QCD.

Vincenzo Barone (Torino, Italy)

A new global analysis of DIS data and the strange sea distribution

I present a new QCD analysis of DIS measurements which includes all available neutrino and antineutrino cross section data. The strange distribution is determined with a higher accuracy with respect to the other global fits. The issue of a possible charge asymmetry of the strange sea is addressed.

Perturbation Theory Constraints on the 3-point vertex in massless QED3

We evaluate analytic expression for one-loop vertex in perturbation theory for massless fermions. Making use of the Ward-Takahashi Identity, we decompose the vertex into its longitudinal and transverse parts. Following Ball and Chiu and Kizilersü et. al., the transverse part is written in its most general form as a function of 4 independent vectors. We calculate the coefficients of each of these vectors. The perturbative knowledge of the coefficients of the transverse vectors provides a reference for the non-perturbative construction of the vertex as every Ansatz should reduce to this perturbative result in the weak coupling regime, leading to a more reliable non-perturbative truncation of Schwinger-Dyson equations.

Exact and perturbative results for Yang-Mills theories in two dimensions: A duality transformation

We discuss several interesting features of U(N) Yang-Mills theory in two dimensions, obtained both with perturbative and with non perturbative techniques. Gauge invariant quantities (Wilson loops), when perturbatively computed, depend on the way the infrared singularities are handled. Typically, light-front quantization and equal-time quantization lead to different results. These results are compared with exact solutions obtained by geometrical methods and the above discrepancy is solved by means of a duality transformation showing that genuine non perturbative contributions (instantons) are needed in equal-time quantization in order to obtain the correct $q\bar q$ potential. When the loop winds n times, it displays an intriguing property with respect to the exchange n <-> N, and, in the limit of small area {\cal A}, keeping n2 {\cal A} fixed, it becomes blind to instantons.

Zvi Bern (UCLA, California)

Perturbative Gravity and Gauge Theory

Perturbative 'squaring' relations between gravity and gauge theories such as QCD are discussed. These relations allow us to extract non-trivial information about quantum gravity theories using known results for QCD.

Csaba Boros (CSSM)

Structure and Production of Lambda Baryons in a Diquark Model

I discuss the quark parton structure of the $\Lambda$ and the fragmentation of quarks into $\Lambda$ baryons and show that the hyperfine interaction, responsible for the $\Delta$-$N$ and $\Sigma^0$-$\Lambda$ mass splittings, leads not only to sizeable SU(3) and SU(6) symmetry breaking in the shape of the quark distributions of the $\Lambda$, but also to significant polarized non-strange quark distributions. The same arguments suggest flavor symmetric quark fragmentation functions and non-zero polarized non-strange quark fragmentation functions. The calculated fragmentation functions give a good description of all measured observables. The model predicts significant positive $\Lambda$ polarization in semi-inclusive DIS experiments while models based on SU(3) flavor symmetry predict zero or negative $\Lambda$ polarization.

Stan Brodsky (SLAC, California)

Light Cone Wavefunctions and The Intrinsic Structure of Hadrons

Abstract not available

Matthias Burkardt (Las Cruces, New Mexico)

Fermions on the light-front

I am giving an overview of issues that are specific to the formulation of fermions in the light-front framework. In particular, I will focus on renormalization, parity invariance and the formulation of fermions on a transverse lattice.

Fu-Guang Cao (Palmerston North, New Zealand)

Electromagnetic transition form factors in the medium energy region (Poster)

Meson-photon transition form factors, FP gamma(Q2) (P=pi0, etac, etab) are analyzed in the light-cone perturbative QCD. We emphasize corrections from parton's transverse momentum, higher helicity components in the light cone wave function, and heavy quark mass etc. in the medium energy region.

Steve Cotanch (Raleigh, North Carolina)

A renormalized Hamiltonian containing only one predetermined parameter, the slope of the linear confining interaction specified by lattice, is approximately diagonalized using standard many body approaches: BCS for the ground state (vacuum) and TDA and RPA for the excited states hadrons (mesons and glueballs in this talk). The gluon and quark condensates and constituent masses are reproduced along with the pseudoscalar, and vector meson spectrum. The glueball lattice quenched spectrum is also reproduced. Most significantly, the chiral symmetry governance of the pion is detailed but only in the RPA as the pion mass and decay constant is reproduced (but not TDA). This is also explained and the generalized Gell-Mann- Oakes-Renner relation is numerically verified.

Simon Dalley (Cambridge, UK)

Transverse Lattice QCD

Recent progress in the solution of light-front gauge theories formulated with colour-dielectric variables on a transverse lattice.

Yitzhak Frishman (Rehovot, Israel)

The String Tension in Two Dimensional Gauge Theories

We review and elaborate on properties of the string tension in two-dimensional gauge theories. The first model we consider is massive (QED) in the m << e limit. We evaluate the leading string tension both in the Fermionic and Bosonized descriptions. We discuss the next to leading corrections in m/e. The next-to-leading terms in the long distance behavior of the quark-antiquark potential, are evaluated in a certain region of external versus dynamical charges. The finite temperature behavior is also determined. In QCD(2) we review the results for the string tension of quarks in cases with dynamical quarks in the fundamental, adjoint, symmetric and antisymmetric representations. The screening nature of SYM(2) is rederived.

Stan Glazek (Warsaw, Poland)

Running coupling constants in effective Hamiltonians

We apply a boost-invariant similarity renormalization group procedure to a light-front Hamiltonian of a scalar field phi of bare mass mu and interaction term g phi3 in 6 dimensions using 3rd order perturbation theory in the coupling constant g. Two counterterms are obtained: a change in mu and a change of g. The renormalization group flow of effective Hamiltonians is integrated analytically. The resulting running coupling constant exhibits asymptotic freedom. The evolution of the coupling with the width of effective Hamiltonians agrees with results obtained using Feynman diagrams and dimensional regularization when one identifies the renormalization scale with the effective Hamiltonian width. The effective light-front Schroedinger equation is equally valid in a whole class of moving frames of reference including the infinite momentum frame. Therefore, the calculation described here provides an interesting pattern to follow in the case of Hamiltonians applicable in particle physics.

Luca Griguolo (INFN, Italy)

The instanton contributions to Yang-Mills theory on the torus: localization, Wilson loops and the perturbative expansion

The instanton contributions to the partition function and to homologically trivial Wilson loops for a U(N) Yang-Mills theory on a torus T2 are analyzed. An exact expression for the partition function is obtained as a sum of contributions localized around the classical solutions of YM equations, that appear according to the general classification of Atiyah and Bott. Exact Wilson loop averages are obtained for small N while the zero instanton contribution are carefully derived, in general, in the decompactification limit. It reproduces the sum of the perturbative series on the plane, in which the light-cone propagator is prescribed according to Wu-Mandelstam-Liebbrandt (WML): agreement with analogous result coming from the sphere S2 is therefore obtained, confirming the truly perturbative nature of the WML computations.

Elena Gubankova (Raleigh, North Carolina)

Flow equations for solving QCD bound state problem

The systematic approach to study bound states in quantum chromodynamics is presented. The method utilizes nonperturbative flow equations in the confining background, that makes possible to perform perturbative renormalization and to bring the QCD Hamiltonian to a block-diagonal form with the number of quasiparticles (constituent quarks and gluons) conserving in each block. The effective block-diagonal Hamiltonian provides a kind of constituent model for hadronic observables (mesons, hybrids, glueballs). The renormalized to the second order effective Hamiltonian of gluodynamics in the Coulomb gauge is obtained at low energies. The masses for scalar and pseudoscalar glueballs are predicted.

John Hiller (Duluth, Minnesota)

Pauli-Villars regularization and discrete light-cone quantization in Yukawa theory

The techniques of Pauli-Villars regularization and discrete light-cone quantization are combined to analyze Yukawa theory in a single-fermion truncation. The Lanczos algorithm, in a special form adapted for indefinite metrics, is used to extract the lowest massive eigenstate and eigenvalue of the light-cone Hamiltonian.

Chueng Ji (Raleigh, North Carolina)

Light-Front Degrees of Freedom in QCD Exclusive Processes

We discuss the utility of light-front degrees of freedom in QCD exclusive processes. The electroweak form factors and semileptonic decay rates of pseudoscalar and vector mesons are investigated using the constituent quark model based on the light-front quark model. Our results indicate the broader applicability of light-front approach including the time-like region of exclusive processes.

Changhao Jin (Melbourne, Australia)

Inclusive Heavy Hadron Decays and Light-Cone Dynamics

I demonstrate the governing role of light-cone dynamics in inclusive heavy hadron decay processes. Nonperturbative QCD effects on the processes can be incorporated in a systematic way. The applications to studying strong and electroweak interactions and hadron structure with semileptonic and radiative decays of b hadrons are reviewed.

Marek Karliner (Tel-Aviv, Israel)

OZI violation, Deep Inelastic and Polarized Strangeness in the Nucleon

The large apparent violations of the OZI rule found in many channels in $\bar{p}p$ annihilation at LEAR is interpreted as evidence for an intrinsic polarized component of the nucleon wave function. The physical picture is tightly coupled with results from polarized deep inelastic scattering. The model, originally proposed several years ago, is further supported by new data from LEAR and elsewhere. I will discuss in more detail the possible form of the $\bar{s} s$ component of the nucleon wave function, interpret the new data and clarify the relative roles of strangeness {\sl shake-out} and {\sl rearrangement}, discuss whether alternative interpretations are still allowed by the new data, and propose more tests of the model.

Susumu Koretune (Izumo, Japan)

Soft pions at high energy and its phenomenological implications

The soft pion theorem in the inclusive reaction at high energy was formulated by Sakai and Yamada many years ago(Phys.Lett.37B(1971)505). Compared with the soft pion theorem in the exclusive reactions, the soft pion limit in the inclusive reaction can not in general be directly related to the physical processes without further assumption except in the neutral pion case. This points was studied and developed using light-cone formalism(see for example Prog.Theor.Phys.59(1978)1989 and Phys.Lett.115B(1982)261). At present the fixed-mass sum rule approach and the perturbative QCD approach are known. The former approach included a new theoretical ingredient called as current anticommutation relation on the null plane and has been developed to the modified Gottfried sum rule and its relatives(Phys.Rev.D47(1993)2690; Nucl.Phys.B526(1998)445). The latter approach is as follows. We use the results of the light-cone current algebra at some particular Q2=Q02. Then for example in the vector bilocal currents case we classify the terms into non-singlet ones and singlet ones, and further classify each terms into symmetric and antisymmetric bilocal currents. By taking these facts we identify each components to the physical structure functions in the total inclusive reactions. Then the Q2 dependence in the perturbative QCD can be incorporated through the Q2 dependence of these functions. Of course the SU(n) * SU(n) algebraic structure together with the free field singurality structure of the light-cone current algebra is violated through the different Q2 dependence of the 4 different componets classified above (The one exception is the moment at n=1 in the non-singlet component of the structure function F2. In this case the SU(n) * SU(n) algebraic structure becomes important in all Q2. It is this algebraic structure at n=1 which we used in the former approach though the theoretical base is different greatly). In this way we can relate the soft pion limit of the semi-inclusive current induced reactions in the deep inelastic region to the total inclusive reactions in the deep inelastic region. The charge asymmetry in the central region in the target-virtual-photon center of the mass frame of the inclusive electroproduction and the contribution to the Gottfried sum are caluculated. We show that charge asymmetry is fairly well explained. Further we show that the contribution of the soft pion to the Gottfried sum is about -0.04 to -0.02. This is small but sizable contribution to the sum which should be taken into account. The main contribution comes from the small x region.

Dean Lee (Amherst, Massachusetts)

Introduction to modal field theory

Modal field theory is a generalization of the spherical field method, which treats d-dimensional field theory as a set of coupled quantum mechanical systems. This non-perturbative method allows for computations in Euclidean field theory via Monte Carlo techniques. Fermion doubling does not occur in this scheme and fermion sign problems are treated with specially adapted Runge-Kutta methods. This talk will introduce the general formalism, demonstrate several results for various field theories, and discuss recent progress in variational and spectral methods as applied to field theory with Minkowskian metric.

Derek Leinweber (CSSM)

Visualizations of the QCD Vacuum

The QCD vacuum is not empty, rather typical field configurations display vacuum fluctuations at all scales. To reveal the nonperturbative aspects of these vacuum fluctuations, a cooling algorithm designed to minimize the local action is iteratively applied. However, a well known problem with standard cooling methods is that the properties of the filtered configurations are dependent on the number of cooling sweeps and discretization errors in the lattice action. This seminar will feature visualizations and animations of typical vacuum field configurations which illustrate the nature of advances in cooling algorithms. In particular, we evaluate claims that instantons become stable over many hundreds of iterations, thus revealing the physical aspects of these field configurations. We also examine smearing methods which may be viewed an improvement of the topological charge density operator via the introduction of irrelevant operators. Highlights will include animations of instanton anti-instanton annihilations.

Lev Lipatov (St. Petersburg, Russia)

High energy asymptotics in QCD

Abstract not available

Lubomir Martinovic (Bratislava, Slovakia)

Symmetry and vacuum structure in light-front field theory

We show that light-front quantization in a finite volume represents a convenient framework for studying symmetries of a given Hamiltonian at the quantum level. For simple gauge theories, large gauge transformations implemented by unitary operators lead to a coherent-state structure of the vacuum and to vacuum degeneracy. This is demonstrated within the massive Schwinger model in the light cone gauge as well as in the Weyl gauge, where a more general formulation is discussed. For a fermion non-gauge theory, an approach to chiral symmetry breaking on the light front based on fermionic zero mode is suggested.

Garry McCartor (Dallas, Texas)

Regulating the P+ = 0 Singularity

The problem of regulating the P+ = 0 singularity will be discussed with emphasis on the operator mixing induced by the regulation procedure. Problems with using DLCQ as a regulator will be illustrated with examples and fixes will be given where they are known.

Jerry Miller (Seattle, Washington)

Nuclear Physics on the Light Front--Applications to Deep Inelastic Scattering

High energy scattering experiments involving nuclei are typically analyzed in terms of light front variables. The desire to provide realistic, relativistic wave functions expressed in terms of these variables led me to try to use light front dynamics to compute nuclear wave functions. We have done so for inifinite nuclear matter using the mean-field approach and also includng the correlations between nucleons. Wave functions for finite nuclei, which respect rotational invariance, have also been obtained. The talk will concentrate on new results related to understanding lepton-nucleus deep inelastic scattering.

Wally Melnitchouk (TJNAF, Virginia/CSSM)

Non-forward parton distributions on the light-cone

Non-forward parton distributions formally interpolate between elastic form factors and inelastic structure functions, and can therefore be used to correlate a wide variety of observables. With a light-cone formulation of the chiral cloud model one can consistently describe various flavour asymmetries observed in sea quark distributions in inclusive deep inelastic scattering and Drell-Yan production, as well as in elastic electron-nucleon scattering.

Giuseppe Nardelli (Trento, Italy)

Zero modes and conformal anomaly in Liouville vortices

The partition function of a two dimensional Abelian gauge model reproducing magnetic vortices is discussed in the harmonic approximation. Classical solutions exhibit conformal invariance, that is broken by quantum fluctuations, apart from an exceptional case. The corresponding anomaly has been evaluated. Zero modes of the thermal fluctuation operator have been carefully discussed.

Hans-Christian Pauli (Heidelberg, Germany)

On the renormalized effective interaction in a QED or QCD Light-Cone Hamitonian

I prepare for a programmatic talk on how to solve the bound state problem for gauge theory in physical space-time on the light cone. I derive an effective interaction from the full canonical QCD Hamiltonian using both the methods of Discretized Light-Cone Quantization and the Method of Iterated Resolvents. I present two levels of approximations. I discuss explicitly how to solve the equations on the lower level, for which I present a simple analytical form. I carry out explicitly the programme of non-perturbative renormalization in the context of a Hamiltonian, which is a thus far unresolved problem. I present explicit calculations for the renormalized `running coupling constant'. I determine explicitly all parameters of the theory by experiment and calculate the eigenfunctions and the spectrum with the very same model for all physical scalar mesons, including the lightest (the pion) and the heaviest (toponium). I present explicit numerical results. The agreement with experiment more than satisfactory.-- I thank Susanne Bielefeld for letting me use part of her results prior to publication.

Robert Perry (Columbus, Ohio)

Light-Front QCD

Initial optimism that light-front field theory woud lead to a simple constituent approximation for QCD in which it is not necessary to build a complicated vacuum was overly optimistic. Serious renormalization problems slowed progress; however, steady progress first led to a precise understanding of light-front QED and reasonable descriptions of heavy quark bound states. Work has now turned to the study of glueballs and the initial goal of understanding light quark bound states is coming into sight.

Steve Pinsky (Columbus, Ohio)

Supersymmetry and DLCQ

In this talk we describe the application of discrete light cone quantization (DLCQ) to supersymmetric field theories. We find that it is possible to formulate DLCQ so that supersymmetry is exactly preserved in the discrete approximation and call this formulation of DLCQ, SDLCQ. It combines the power of DLCQ with all of the beauty of supersymmetry. We have applied SDLCQ to several interesting supersymmetric theories and discussed zero modes, vacuum degeneracy, massless states, mass gaps, and theories in higher dimensions. Most recently we have used it to discuss the Maldacena conjecture.

Craig Roberts (ANL, Illinois)

A perspective on the contemporary application of Dyson-Schwinger equations in hadron physics, ranging over exact results and phenomenological applications, and highlighting current challenges.

Christophe Royon (Saclay, France)

Low x physics and hard diffraction at Tevatron versus HERA

I will focus on the relationship between what is observed at HERA and Tevatron: the measurement of the proton structure function at low x (HERA), inclusive diffraction at HERA and Tevatron and the relationship between them, and comparison with models.

Maria Samaras (Sydney, Australia)

Green's Function Monte Carlo for SU(3) Hamiltonian Lattice Gauge Theory

The 'forward walking' Green's Function Monte Carlo method is applied to the SU(3) Yang-Mills lattice Hamiltonian. The accuracy of the ground state energy and Wilson loops when compared with previous results show that this algorithm is a good approach to studying lattice gauge theories.

Andreas Schreiber (CSSM)

Variational worldline QED

We have generalized Feynman's variational approach for the polaron problem to quenched QED expressed in the worldline formalism. I will present an overview of recent results, concentrating on the nonperturbative electron propagator.

Amedeo Staiano (Torino, Italy)

QCD in diffraction, low-x physics and the hadronic final state at HERA

Diffractive phenomena at HERA are reviewed. Results on measurements of diffractive structure functions, vector meson production and the hadronic final states (event shapes, jets and charm production) are presented.

Eric Thomas (Rome)

First Regge description of polarised photon-nucleon absorption cross section.

A description of the virtual photon absorption polarised cross section for the proton and neutron is obtained with a parameterisation based on a Regge type approach. The parametrisation is obtained from global fits to the cross section data derived from the spin asymmetries measured in deep inelastic scattering of longitudinally polarised leptons from polarised 1H, 3He and 2H targets in the range 0.3 GeV2 < Q2 < 70 GeV2 and 4 GeV2 < W2 < 300 GeV2. The fits give a reliable description of the data and provide predictions for the photo-production through a smooth Q2-transition. The contribution above the resonance region to the Gerasimov-Drell-Hearn sum rule for real and virtual photons has been evaluated. For the real photon this contribution accounts for a large fraction of the discrepancy between the sum rule expectations and the single pion photo-production analysis estimates.
Ref: N. Bianchi and E. Thomas, Phys. Lett. B450 (1999) 439-447.

Eric Thomas (Rome)

Recent Spin Physics results from HERMES

Recent results from the HERMES experiment on the nucleon spin structure will be presented. Flavour decomposition of the nucleon spin from Semi-inclusive analysis of HERMES data was obtained, showing a positive (negative) polarization for the up (down) quark. The sea polarization was found to be compatible with zero. Spin asymmetries measured in the production of high pT hadron pairs indicate a positive gluon contribution to the nucleon spin. Observation of single spin asymmetries in semi-inclusive pion production can be interpreted as the combination of chiral odd distribution functions and a time odd fragmentation function. This result indicate the possibility to access transverse spin distribution function h1 by the HERMES experiment running with a transversely polarized target.

Tony Thomas (CSSM)

Lattice QCD Beyond Chiral Perturbation Theory

While we think we have a complete field theory for the strong interaction, namely QCD, it can only be solved exactly in some situations where perturbative methods are applicable. The structure of protons, neutrons and other hadrons and nuclei is a non-perturbative problem for which numerical calculations on a space-time lattice are currently the only rigorous approach. Computer limitations presently restrict such calculations to quark masses a factor of 10 or more larger than they are in nature. Thus in order to compare these calculations with experimental data one must extrapolate a very long way. We will report on recent progress in understanding how to do this in a much more reliable way.

Uwe Trittmann (Columbus, Ohio)

The Mass Spectrum of N=1 SYM(2+1) at Strong Coupling

In the talk I will consider supersymmetric Yang-Mills theory on R x S1 x S1. In particular, we choose one of the compact directions to be light-like and another to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound state wave functions and masses numerically without renormalizing. We present the masses as functions of the longitudinal and transverse resolutions and show that the masses converge rapidly in both resolutions. We also study the behavior of the spectrum as a function of the coupling and find that at strong coupling there is a stable, well defined spectrum which we present. We also find several unphysical states that decouple at large transverse resolution. There are two sets of massless states; one set is massless only at zero coupling and the other is massless at all couplings. Together these sets of massless states are in one-to-one correspondence with the full spectrum of the dimensionally reduced theory.

Tony Williams (CSSM)

Gluon and quark propagators in Landau gauge from the lattice

We study the Landau gauge gluon and quark propagators using lattice gauge theory. We consider both their infrared and ultraviolet behaviors and consider a variety of lattice volumes, lattice spacings, and actions in order to establish the reliability of the results. The ultraviolet behaviour is compared with perturbation theory. The infrared behavior is discussed in terms of confinement models and the presence of Gribov copies.

Cosmology at QCD scale and RHIC

The development of the early Universe is a remarkable laboratory for the study of most nontrivial properties of the particle physics. What is more amazing is the fact that these phenomena at the QCD scale can be, in principle, experimentally tested at RHIC, Brookhaven. We expect that, in general, an arbitrary $|\theta\ra$-state would be created in the heavy ion collisions, similarly to the creation of the disoriented chiral condensate (DCC) with an arbitrary isospin direction. It should be a large domain with a wrong $\theta\neq 0$ orientation. If a reasonably stable $|\theta\neq 0\ra$ state is created, it could be observed by analyzing some unusual decays of this $\theta$ state. We have done some numerical simulations which support the idea that the \theta vacuum condensate, indeed, will be created if the cooling process is very rapid and, therefore, the system is out of equilibrium (quench approximation). Therefore, the heavy ion collisions give us a unique chance for a study QCD .

Monopoles and Coulomb Gas Representation of the QCD Effective Lagrangian

A novel Coulomb gas (CG) description of low energy QCD4(Nc) is constructed. The construction is based on the dual transformation of the QCD effective Lagrangian. By considering a large gauge transformation, the charges of this statistical system are identified with magnetic monopoles which carry fractional charges of strength 1/Nc. The relation of the CG picture with the instanton-quarks is discussed.

Fabian Zomer (Orsay, France)

Structure Functions and Short Distance Physics

Recent measurements of the inclusive structure functions of the proton are presented. The results are contrasted with complementary measurements of charm- and jet production cross sections. A detailed QCD analysis reveals details of the partonic nature of the proton.