INTRODUCTION TO CPC:
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The elementary model of the CPC is our baryon-model:
([H.W.Fricke, C.C.Noack, Phys. Rev. Let. 80, 3014, (1998)])
 
 
Our baryon-model (model of four classical point-particles): A junction (J) is binding the valence quarks (1,2,3) by a confinement potential. The junction carries the average momentum of the sea quarks and gluonic degrees of freedom.
 

The relativistic equation of motion for this model s obtained by using the constraint-dynamics [J. Samuel, Phys. Rev. D 26, 3474 (1982)]. A quasi-potential depending on the distance between the junction (J) and the valence quarks (1,2,3) will model the confinement potential. This quasi-potential should affect the effective mass of the junction (p_(J))^2, because pushing away a valence quark will increase the number of sea quarks and gluons, which are modeled by the junction. For simplicity, we will assume the valence quarks to always remain on mass shell. The above physical requirements are embodied in the following constraints:
Full picture
where P is the total four-momentum of the system. The baryon-model's parameter are the current quark masses (m_i), and one interaction strength (\kappa), determined by the proton radius.
 

Just with this model and no further input, we obtain remarkably good fit to the valence quark structure functions of the baryon. We define the longitudinal momentum fraction of particle i in terms of the light-cone variables:
Full picture

We have Monte-Carlo sampled distributions of these momentum fractions and compared with the Q^2-independent structure functions:

Full picture Sampled distributions of the valence quark longitudinal momentum fraction x u_v(x) (up quark) and x d_v(x) (down quarks). The solid and dashed lines are the results obtained with the parameterization of [E. Eichten, et al, Rev. of Mod. Phys 56, 579 (1984)].

By introducing an additional phenomenological mass term in the constraint of the junction, we obtain a good fit to the Q^2-dependent structure functions:
Full picture Sampled distributions of the valence quark longitudinal momentum fraction x u_v(x) (up quark)  and  x  u_d(x) (down quark), at Q^2=200 (GeV)^2. The solid lines are the results obtained with the parameterization of [M. Glück, et al, Z. Phys. C 67, 433, (1995)]. 
Full picture Sampled integrated momentum fractions of the valence up quarks (boxes) and the valence down quarks (diamonds), as a function of Q^2. The solid and the dashed lines are the results obtained with the parameterization of [M. Glück, et al, Z. Phys. C 67, 433, (1995)].



The CPC includes:
([H.W.Fricke, preliminary Ph.D. thesis, (1999)])
 

Evolution:
The CPC is a full Poincare-covariant cascade. For the evolution of the hadrons and parton we use a generalized baryon-model for many baryon, mesons and partons per hadron.

Scattering:
Scattering is included by using a simplified differential cross-section of the parton-model:
(using the fact, that the baryon-model reproduces the parton structure functions.)
Full picture
where we use 'gluon-masses' to avoid the infrared divergences. This cross-section is used for hard and soft processes.

Three kinds of scattering are included:

1.: parton-parton scattering:

                before                                   after
Two partons transfer a momentum t given by Monte-Carlo sampling the differential cross-section.

2.: parton-junction scattering:

               before                                  after
A parton-anti-parton pair is created inside the junction using the Q^2-dependent structure functions of the sea-quarks and gluons. So to say, the junction (averaging the sea-quarks and gluons) is dissolved into its partons. Then the original parton scatters with one of the pair using the parton-parton scattering method.
 
3.: junction-junction scattering:
A parton-anti-parton pair is created inside both junctions.
 
Fragmentation:
Fragmentation is introduced by using the fragmentation model of the yo-yo strings:
(using the fact, that the baryon-model includes a confinement potential.)

After scattering the partons of a hadron may have high relative momentums and the distances between the partons and the junction may be far. Now, there is a lot of energy stored in the color-rope and spontaneous pair creation can take place. The hadron decays into two hadrons. We have separate decay for every junction-parton connection. The probability for the decay of a color-rope is (like the radioactive decay):

where \Lambda is the partial effective mass of the junction. Energy, momentum and flavor are locally conserved. Every parton is always connected with a junction.
Full picture
A hadron decays into two hadrons. The decay is introduced by the parton 2. The color rope breaks and a parton-anti-parton pair is created.


The CPC reproduces experimental data of:
([H.W.Fricke, preliminary Ph.D. thesis, (1999)])
 

SPS-energies:
                            p-p
                            S-S
                            Pb-Pb

RHIC-energies:
                            p-\bar p
                            S-S
                            Au-Au
  



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