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Quark and Gluon Densities

In the regime of deep inelastic scattering, QCD is ideally suited to analyse quark and gluon dynamics in hadrons. The cross sections factorise into non-perturbative, or soft parts, and perturbatively calculable hard parts. Computational tools that have been developed over years enable accurate computation of the hard parts and to go to higher orders in perturbation theory. This is certainly one of the achievements in the last five years. This major progress is strikingly illustrated by the Q2 evolution of the Børken sum rule. This sum rule relates the first moment of the difference of polarised structure functions for proton and neutron measured in high-energy electron-proton, electron-deuteron and electron-3He scattering. Within this framework the soft part has been determined and detailed knowledge has been obtained on the quark and gluon distribution in the nucleon. The proton structure function F2 has been accurately determined by NMC ( x>10-2) and at HERA (down to $x\simeq 10^{-4}$). The gluon density G(x) has been determined at HERA down to $x\simeq 10^{-4}$. The spin structure of the nucleon has been studied at CERN (SMC), SLAC and DESY (HERMES). Fig. [*] is a summary of all existing data.
  
Figure: The polarised structure functions of the proton, of the deuteron and of the neutron measured at CERN, DESY and SLAC. The analysis of these data confirm the validity of QCD from the low energy region of $\beta$ -decay to the high energy deep inelastic region. These results demonstrate that a significant fraction of the nucleon spin is either carried by gluons or by strange quarks from the sea.
\begin{figure}\epsfig{file=hadron/fig6.eps, width=\columnwidth}\end{figure}
 

The results corroborate the Bjørken sum rule, when higher order QCD corrections are taken into account. This provides a beautiful confirmation that QCD accurately describes strong interactions over an energy range from $\beta$-decay to the highest collider energies. The surprise is that quarks carry only a small fraction of the nucleon spin. Yet, the quark model has been very successful in describing the phenomenology of strongly interacting particles. We know that constituent quarks are composite objects made of a quark interacting with a sea of gluons and of virtual quark-antiquark pairs. polarised electron and muon scattering experiments show that the role played by the sea is a significant effect. The possibility of a $s\bar{s}$ ``vacuum polarisation'' in the nucleon now needs to be determined with the best accuracy possible. An important issue is the size of the contribution of the ``axial anomaly'' and the closely related question of gluon polarisation. The various proposed theoretical ideas differ considerably in their predictions of the amount of spin carried by gluons. Several experiments have been proposed to measure the amount of gluon polarisation, at CERN (COMPASS), at HERA and at the new Relativistic Heavy Ion Collider (RHIC) being constructed at Brookhaven in the US. This future generation of polarised scattering experiments should resolve the enigma of the proton spin. Finally, new information on the flavour structure of the nucleon has been obtained by the NMC collaboration.. It appears that there are more anti-down than anti-up quarks in a proton. A possible explanation, only qualitative for the moment, could be the presence of pionic quark-antiquark correlations in the proton wavefunction. In the years to come one hopes to refine the knowledge on the nucleon spin decomposition over spin and orbital angular momentum of quarks and gluons. Experiments such as in leptoproduction of charm or Deeply Virtual Compton Scattering, COMPASS (CERN) and HERMES (DESY), are expected to contribute significantly to our insight. This may confirm improved theoretical understanding of nucleon structure as obtained from lattice gauge calculations or may inspire new approaches towards understanding confinement. At HERMES, the use of polarisation, as well as the detection of particles in semi-inclusive (in particular 1-particle inclusive) scattering processes, will allow the determination of nontrivial correlation functions. This requires particle identification in order to have flavour recognition and also good angular resolution in order to study azimuthal asymmetries which provide ways to study the dependence on the quark transverse momentum distribution. Furthermore, polarimetry in the final state is an important ingredient from which new information is expected. Such a study of non-leading effects in 1-particle inclusive lepton-hadron scattering will complement, or be complemented by, measurements in hadron-hadron scattering, especially Drell-Yan measurements (e.g. RHIC at Brookhaven) and fragmentation studies in e+e- annihilation at LEP. At HERA, the priority will be put on reaching the nominal luminosity (a few hundred pb-1) and getting more accurate data. The study of the properties of the hadronic final state could be undertaken and shed some light on the origin of the rapid rise of the proton structure function F2 at low x. More statistics on two jet events will lead to a more accurate determination of the gluon distribution G(x) and its evolution. A more systematic study of diffractive events will lead to a better understanding of the nature and the structure of the Pomeron. The detection of the recoiling proton at the most forward angles may not allow to take full advantage of the improved luminosity. 


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