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Semi-inclusive Deep Inelastic Scattering

Nearly all existing data on quark distributions in hadrons have been obtained by inclusive scattering of high energy particles. In such reactions, one strikes quarks with considerable momentum and energy and reconstructs quark distributions from scattering data. This is possible because of a property of factorisation of the scattering amplitudes in quantum field theory. This property has allowed theory to find a firm basis for the partonic description and to go beyond the original model proposed by Feynman and Bjørken. The experimental observation amounts to an average over all the possible quark configurations in the nucleus. In addition to fundamental tests of QCD, the measurements of structure functions have lead to the discovery of the importance of gluons in the momentum and spin distributions in the proton.
    

Figure: The strange nucleon: the simple quark model of the nucleon and quark dynamics imply that $\phi$ production should be suppressed relative to $\omega$ production in various processess (shown by the line). However $\overline{p}$ annihilation data show clear violation of the expectations.

  

Additional information on the quark and gluon structure is obtained by looking at produced particles in the final state. At sufficiently high energies this semi-inclusive process factorises into distribution functions and fragmentation functions for quarks and gluons. The specific flavour composition of some hadrons can then be used to tag the struck quark in the hard process, e.g. fast K^--mesons to tag strange quarks, D-mesons (or their decay products) to tag charmed quarks. The fragmentation functions themselves also form a source of information on quark and gluon dynamics. Just as for the distribution functions the spin transfer from hadron to quark has shown surprising results, the spin transfer from quark to hadron may have surprises. Detection of a particle in the final state also serves to provide sensitivity to transverse directions in the hard scattering process. It enables one to enter the field of quark-gluon correlations. Unlike the quark and gluon densities most of the correlations appear in the cross section via power-suppressed (1/Q) terms. A full exploitation of the possibilities of semi-inclusive processes requires polarised beams and targets in combination with sufficiently high energies in the range $\sqrt{s} \simeq 10 - 30$ GeV. This energy regime is adapted to the correlation length for quark and gluon fields of the order of 0.3 fm and allows to cover the transition from the perturbative to the non-perturbative regime of QCD. It would be a qualitative leap towards precision experiments if luminosities of about 10³³ cm^-2s^-1 could be reached in a collider geometry with both beams highly polarised. These are the design features of the electron-electron collider (ENC), proposed at GSI, a double ring system colliding electrons of 2.5 to 7.5 GeV with nucleons of nuclei of 10 to 30 GeV/u. This collider with full acceptance for the final hadronic state would be well suited for the study of semi-inclusive reactions.