abstract

At the end of the fixed-target deep inelastic scattering experimental programme we summarize the developments on the structure of the proton that were studied in these experiments. We survey the latest structure function data and their QCD interpretation. Special attention is paid to the measurements taken in the low \(Q^2\) region. The spin properties of the proton are discussed.

abstract

We summarize data on the proton structure function \(F_2(x, Q^2)\) from the electron–proton collider HERA. The kinematic range covered for \(F_2(x, Q^2)\) measurements now reaches momentum transfers squared \(Q^2\) between 1.5 GeV\(^2\) and 5000 GeV\(^2\) and Bjorken \(x\) between \(3 \cdot 10^{-5}\) and 0.32. The new results represent an increase in statistics by a factor of ten with respect to the analysis of the 1993 data. The structure function is found to increase significantly with decreasing \(x\), even in the lowest accessible \(Q^2\) region. For \(Q^2 \gt 5\) GeV\(^2\), the data exhibit double asymptotic scaling. The data are well described by a Next-to-Leading Order QCD fit and the gluon density is extracted. Searches for BFKL signatures in the hadronic final states are briefly presented.

abstract

The results on the structure of proton and pomeron, obtained during the years 1993–1994 by the ZEUS experiment are presented. The proton structure function \(F_2(x, Q^2)\) was measured in the deep inelastic scattering (DIS) down to \(x\) value of \(3.5 \times 10^{-5}\) and \(Q^2\) down to 1.5 GeV\(^2\) and it was found that the fast increase of this function with \(x\) decreasing persists in this region. Predictions based on DGLAP dynamics (GRV(94)) reproduce the data. The proton diffractive structure function was measured using the sample of diffractive DIS events and the comparison with QCD inspired models was made. The parton structure of pomeron is studied and the presence of the soft and hard partons is necessary to describe the data. The study of the diffractive dissociation in photoproduction revealed also the partonic nature of pomeron and allowed the rough estimation ((30–80)%) of the gluon content of the pomeron.

abstract

In this note I discuss recent results obtained by the two experiments H1 and ZEUS at the first electron proton collider — HERA. In particular, I concentrate on results which are of importance for our understanding of the nature of strong interactions. In the weak coupling limit of strong interactions i.e. in the processes involving short distances, perturbative Quantum Chromodynamics can be confronted with the HERA data in a new regime. What is however more challenging is the unique possibility of HERA to map the transition from the regime of the short distance phenomena, which are controlled by perturbative QCD, to the large distance phenomena where perturbative QCD can not be applied.

abstract

Some perturbative approaches to the QCD description of the deep-inelastic \(ep\) scattering at the small Bjorken variable \(x\) are reviewed. It is shown, that in the leading logarithmic approximation the gluon is reggeized and the pomeron is a compound state of two reggeized gluons. The relation between the Schrödinger equation for the compound state of several reggeized gluons in the multi-colour QCD and the completely integrable Heisenberg spin model is discussed. The effective action for the gluon-Reggeon interactions is constructed and applied to the problem of finding next to leading corrections to the QCD pomeron.

abstract

The dipole picture of high-energy deep inelastic collisions is described. Nucleon structure function and diffractive dissociation in the triple-pomeron limit are discussed in some detail.

abstract

In this talk we present some links of the theory of the odderon with elliptic curves. These results were obtained in an earlier work [19]. The natural degrees of freedom of the odderon turn out to coincide with conformal invariants of elliptic curves with a fixed ‘sign’. This leads to a formulation of the odderon which is modular invariant with respect to \({\mit \Gamma }^2\) — the unique normal subgroup of SL\((2,{Z})\) of index 2.

abstract

We review the latest information that is available about the parton distributions of the proton, paying particular attention to the determination of the gluon. We briefly describe the various processes that have been advocated to be a measure of the gluon. We discuss the importance of the gluon to the description of the structure function \(F_2\) at small \(x\), with emphasis on the ln \(1/x\) resummations.

abstract

The resummation of \(O(\alpha ^{l+1}\) ln\(^{2l}x)\) terms in the evolution kernels of non-singlet combinations of structure functions is investigated for both QED and QCD. Numerical results are presented for unpolarized and polarized QCD structure functions.

abstract

We solve a unified integral equation (the CCFM equation) for the gluon distribution of a proton in the small \(x\) regime. Here \(x\) is the longitudinal momentum fraction of a gluon probed at a scale \(Q\). The equation generates a gluon with a steep \(x^{-\lambda }\) behaviour, with \(\lambda \sim 0.5\). 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. We examine what the consequences of this gluon evolution are for the structure function, \(F_2(x, Q^2)\), as measured by the HERA electron–proton collider. Following this we investigate the effect of imposing an additional kinematic constraint, \(k^2_T \lt q^2_T/z\), on the CCFM equation. In particular we examine its implications for \(F_2(x, Q^2)\) as a function of \(Q^2\), the charm component, \(F_2^c(x, Q^2)\) and diffractive \(J/\psi \) photoproduction.

abstract

The first measurement of diffractive processes in deep inelastic scattering at the HERA collider is analysed in terms of a “soft” pomeron exchange model. The partonic structure of the pomeron which emerges in this picture is determined using the QCD parton model. The important role of the gluonic component in the partonic interpretation of the data is particularly emphasized.

abstract

A model for the longitudinal structure function \(F_L\) in the region of low \(x\) and low \(Q^2\) is discussed. It is constructed using the \(k_T\) factorization theorem and a photon–gluon fusion mechanism suitably extrapolated to the region of low \(Q^2\). A phenomenological model for higher twist is presented, which is based on the assumption that the contribution of quarks having limited transverse momenta is dominated by the soft pomeron exchange mechanism.

abstract

The idea of “dynamically” generated parton distribution functions, based on regular initial conditions at low momentum scale, is reanalyzed with particular emphasize paid to its compatibility with the factorization mechanism. Basic consequences of this approach are discussed and compared to those of the conventional approach, employing singular initial distribution functions.

abstract

Two-jet cross sections in deep inelastic scattering at HERA are calculated in next-to-leading order. The importance of higher order corrections and recombination scheme dependencies is studied for various jet algorithms. Some implications for the determination of \(\alpha _s(\mu ^2_R)\), the determination of the gluon density and the associated forward jet production in the low \(x\) regime at HERA are briefly discussed.

abstract

The spin-averaged structure function of the neutron, \(F_2^n\), is extracted from the latest deuteron data, taking into account the most recent developments in the treatment of nuclear effects in the deuteron. At small \(x\), the \(F_2^D/F_2^p\) ratio measured by the New Muon and Fermilab E665 Collaborations is interpreted to suggest a small amount of shadowing in deuterium, which acts to enhance \(F^n_2\) for \(x \lesssim 0.1\). A careful treatment of Fermi motion, binding and nucleon off-shell effects in the deuteron also indicates that the neutron/proton structure function ratio as \(x \to 1\) is consistent with the perturbative QCD expectation of 3/7, but larger than the traditional value of 1/4.

abstract

We discuss nuclear effects in deep inelastic lepton scattering. At small values of the Bjorken variable \(x \lt 0.1\) shadowing effects are due to the coherent interaction of hadronic Fock components of the exchanged, virtual photon. It turns out that in the kinematic regime of current experiments the contribution of the vector mesons are of major importance. At moderate and large \(x \gt 0.2\) nuclear effects are caused by binding and Fermi motion, but also by off-shell modifications of bound nucleon structure functions.

abstract

We discuss the evaluation of the nucleon isoscalar axial coupling, \(g^{(0)}_A\), in the instanton vacuum using the \(1/N_c\) expansion. This approach allows a fully consistent treatment of the \(U(1)_A\) anomaly. We compute the nucleon matrix element of the topological charge, \(\langle N|F \tilde F|N \rangle \), and show that it reduces to the matrix element of the isoscalar axial quark current. Our arguments show that the usual evaluation of \(g^{(0)}_A\) in the chiral quark soliton model is consistent with the \(U(1)_A\) anomaly in leading order of \(1/N_c\). Such calculations give \(g^{(0)}_A = 0.36\), which is in agreement with the recent estimate by Ellis and Karliner.

abstract

The main problems discussed during the Conference were connected with the following topics:

• 1. Deep inelastic scattering at low \(x\).
• 2. Deep inelastic diffraction.
• 3. Nuclear effects in deep inelastic scattering.
• 4. High energy limit of QCD and formal theoretical issues.