Institut für Theoretische Physik

Universität Heidelberg

Philosophenweg 19

D-69120 Heidelberg

**E-Mail**: H.J.Pirner at tphys.uni-heidelberg.de

**Tel.**: +49-6221-54-9441**Fax.**: +49-6221-54-9331

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We study proton-lead collisions with a new model for the Fock states of the incoming proton. The number of collisions that the proton experiences selects the appropriate Fock state of the proton, which generates a multiple of p p -like rapidity distributions. We take as input the p p maximum entropy distributions, shifting the respective center-of-mass rapidities and reducing the available energies. A comparison with existing data at 5 TeV is made, and results for 8 TeV are presented. We also explore the high multiplicity data in this model.

The main ideas underlying high energy proton-nucleus collisions are well established. It is easiest to consider the system in the reference frame where the nucleus is at rest. Then high energy excitations in the fast incoming proton become degenerate with the ground state. Their life-time at sufficiently high energy is significantly longer than the nuclear dimension, so these excitations can be treated as Fock components of the proton. In the large Nc approximation one can reorganise these excitations in a series of color neutral Fock states consisting of quark-antiquark pairs [1]. We consider only those Fock components of the proton, which are brought to mass shell by interactions, otherwise they remain being a virtual fluctuation of the proton. The n-th Fock state is actualized by n collisions with target nucleons. Data can be explained when in n collisions only (n+1)/2 as many particles are formed as in a single pp collision [2–4]. How can one understand the phenomenon that the fragmentation products do not multiply n times, given the two facts that there are n collisions and that the fragmenting two strings formed in each collision overlap strongly in rapidity space? This is explained in the paper published in Phys Rev of the same title.

A wide consensus has been that nucleus-nucleus scattering allows to study equilibrium thermodynamics of the quark-gluon plasmas at temperatures T varying between 700 MeV and 150 MeV. Special emphasis has been devoted to the cross over transition between the quark gluon plasma and the hadron resonance gas. The respective lattice calculations supplemented by hydrodynamic calculations of various observables like the azimuthal asymmetry $v_2$ give some evidence of hydrodynamical flow of hadronic matter under the assumptions that very early after the collision in the cm-system local equilibrium characterized by a local temperature has been reached.

The maximum entropy approach I propose is at variance with this consensus model. It emphasizes the phenomenological aspects of the reactions dynamics and is based on the unbalance between longitudinal and transverse motion in these high energy reactions. It agrees with the common wisdom that randomness is important to describe the momentum dependence of the inclusive and correlated cross sections. It disagrees however on the amount of order which is present in heavy ion reactions. Randomness comes about, because many low momentum partons/particles radiating new QCD partons at a primordial stage hadronize at the later stages. But there is very different dynamics in the longitudinal and transversal directions. Partons are best described by the Feyman parameters x which define the fraction of light cone momentum, and the transversal momenta. Consequently a random distribution must respect not only the mean energy pumped into the collision, like in a gas confined into a volume, but the conservation laws in longitudinal and transverse directions. This applies also locally in small samples of the configuration space.

The most random distribution with these constraints is the light cone plasma distribution. I think this distribution is reached at an intermediate time t≈ 1 fm/c in the cm-system. Much earlier the initial parton distributions dominate the process. Much later the hadronization and hadronic interactions in the resonance gas are important. Using parton-hadron duality Klaus Reygers, Boris Kopeliovich and myself determined purely phenomenologically a “transverse” temperature and a longitudinal “softness” of pp- and AA-collisions. These parameters form a data base which can be analyzed theoretically in a second step, e.g. the “effective” transverse temperature increases in nuclear collisions with centrality due to multiple scattering of partons in the other nucleus.

In the future I aim at determining the quark-and gluon light cone distributions underlying the observed hadronic spectra by unfolding the fragmentation process. The idea is simple: If the final hadrons distribution obeys a maximum entropy distribution, then also the earlier quark gluon distributions follows the same distribution. Preliminary studies show that the so obtained transverse momentum scale for quark and gluon distributions will will be around 1 GeV, not very much different from values obtained in the color glass picture.

Once this work is completed one will have a microscopic picture of the intermediate and late stage of the collision leading to low momentum particle production. The model is based on fragmentation of strings which are slightly modified because of their environment. It is exciting to see how far such a picture is valid and when it fails due to extremely high density.

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