Relativistic Hydrodynamics and heavy ion reactions - Clare, R. Ornik, R. Weiner, and G. Hydrodynamical beam jets in high energy hadronic collisions - A Simple evolution equation for rapidity distributions in nucleus-nucleus collisions - Dias de Deus, J. Parton based Gribov-Regge theory - Drescher, H.
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E12 Dependence of black fragment azimuthal and projected angular distributions on polar angle in silicon-emulsion collisions at 4. C69 Unified description of multiplicity distributions of final-state particles produced in collisions at high energies - Liu, Fu-Hu Nucl.
A Combining with Eqs. We introduce the di! Following steps similar to those described in Section 5. We recall from Section 4. Various data on di! Next, we introduce helicity dependent di! With inclusion of shadowing and the e! In the laboratory frame at small x 0. Consider therefore a single e! The deuteron form factors become approximately constant, i. Double scattering contribution to the tensor structure function b from .
Furthermore, the coherent interaction of the virtual photon with several nucleons causes shadowing.
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Accounting for both e! From the e! At small values x 0. Assuming again, as in Section 7. In the nuclear case, shadowing reduces the small-x contribution to the Bjorken integral. Consequently the non-singlet nuclear structure function must be enhanced, i. As a consequence a signi"cant antishadowing is obtained in this kinematic region. The use of deuterium as a target may have advantages since non-nucleonic admixtures are supposed to be smaller due to weaker nuclear binding. Incoherent interactions of the virtual photon with hadronic constituents of the nucleus dominate, and the usual starting point is a description based on the impulse approximation including nucleon degrees of freedom only [,,,].
This approach is not without question, but not much progress has so far been made beyond that level. This allows, as in the unpolarized case, to factorize nucleon and nuclear degrees of freedom, introducing structure functions of nucleons as bound quasi-particles.
The expressions in Eqs. The functions t p "1 A! For the transverse structure function g the target polarization is taken perpendicular to the momentum 2 transfer and denoted by N. The nucleon spin operators which multiply the spectral functions in Eqs. Furthermore, p is the transverse component of the nucleon , three-momentum, p" p , p , and S determines the transverse spin quantization axis relative to , X , the photon momentum which is taken along the z-direction. From Eqs. Relativistic contributions which lead beyond the convolution formula 7. Deviations from non-relativistic convolution were generally found to be small, except at very large x'0.
As a general rule, the structure functions at x 0. Further developments and perspectives We close this review with a short summary of the key physics points together with an outlook on several selected topics for which investigations are still actively under way. By selecting di! An even more stringent selection of such components can be achieved in exclusive photo- and electroproduction processes, and in particular in high-energy di!
Depending on energy and momentum transfer, the mechanism of vector meson formation can be quite di! For longitudinally polarized photons, b"const. The range of energy and momentum transfers covered by the experiment is 9 GeV l 20 GeV and 0. This implies coherence lengths in the range 0. Given the four-momenta q and k of the incoming virtual photon and the produced o meson, the t-channel momentum transfer to the nucleon is t" q! Such coherent processes fall o!
Consider now the incoherent production of vector mesons from nuclei. The open symbols represent data from previous experiments [,]. The dashed curve shows a Glauber calculation from Ref. More interesting e! The dashed curve in Fig. Further systematic investigations of such coherence length e! Once the energy transfer exceeds several tens of GeV, a further scale enters. To be speci"c, let D the observed vector meson again be a o. The small initial wave packet is generally not an eigenstate of the strong interaction Hamiltonian.
Now consider expanding the wave packet in hadronic eigenstates. Clearly, for a wave packet with a size small compared to typical hadronic dimensions, several such eigenstates are necessary to represent the wave function of the packet. Let one of those hadronic eigenstates in the expansion be the o meson itself mass m , let another one be M a neighboring state with larger mass say, m "m dm.
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The phase di! The time it takes to "lter out all but the o meson component when passing through the nucleus is then l.
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The interpretation of data in terms of color transparency is still under debate see e. Possible future developments with nuclei at HERA  could o! Such a study is possible due to recent data on di! One "nds that contributions from vector mesons are negligible at large momentum transfers since di!
Furthermore, the ZEUS data  on the ratio of di! In Section 5. This suggests a weak energy dependence of nuclear shadowing.
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On similar grounds the di! This increase of the gluon density with decreasing x can however not continue inde"nitely. At very small x the density of gluons becomes so large that G. Thus, one enters a new regime of very high parton densities where standard methods of perturbation theory are inappropriate despite small values for the coupling a , and resummation techniques to in"nite order have Q to be applied for references see e.
For further illustration let us view the scattering process in a frame where the target momentum is very large, P""P"PR. This rate involves the probability of "nding at least two partons per unit area in the nucleon [,]. However, phenomena related to high parton densities at small x should be magni"ed in nuclei since nuclear parton densities are enhanced. In Refs. The second term is the correction of interest here and describes the interaction of gluons from di! One "nds [,] that the x-range where non-linear e!
One is entering a new domain of QCD, dealing with partonic systems of high density, which presents new challenges. Acknowledgements We gratefully acknowledge many discussions and conversations with S. Brodsky, L. Frankfurt, P. Hoyer, B. Kopeliovich, S. Kulagin, L.