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					    Diffusion and local
deconfinement in relativistic
         systems

          Georg Wolschin
   Universität Heidelberg, Theor.
               Physics
        http://wolschin.uni-hd.de
                    Topics
 Relativistic Diffusion Model for R(ET,y):
   net baryons and produced charged hadrons
 Transverse energy and rapidity distributions
  at SIS, AGS, SPS and RHIC energies
 Indications for local deconfinement and local
  thermal equilibrium (QGP formation) at RHIC
  (and possibly SPS) energies ?
 Collective longitudinal expansion


YITP2/05                                          2
  Indications for local deconfinement/qgp?




                                              Fig. Courtesy U Frankfurt


   1.Yes, in central collisions of Au-Au at √s=200 GeV/particle pair,
the partons in 14% of the incoming baryons are likely to be deconfined.
                [cf. GW, Phys. Rev. C 69, 024906(2004)]
 2.Yes, most of the produced particles are in local thermal equilibrium
             [cf. M. Biyajima et al., nucl-th/0309075 (2003))]
  YITP2/05                                                                3
                Relativistic Diffusion Model

                                             • Nonequilibrium-
                                               statistical approach to
                                               relativistic many-body
                                               collisions
-The drift function J(y) determines          • Macroscopic
 the shift of the mean rapidity                distribution function
 towards the equilibrium value                 R(y,t) for the rapidity y
                                             • Coupled to a
- The diffusion coefficient D(t)
 accounts for the broadening of the            corresponding evolution
 distributions due to interactions             eq. for pT, or ET
 and particle creations. It is related
 to J(y) via a dissipation-fluct. Theorem.
    YITP2/05                                                          4
                           Linear RDM
- For m=1,q=2-n=1 and a linear
  drift function J(y) = (yeq-y)/y   • The rapidity relaxation
   the mean value becomes              time y determines the
                                       peak positions
                                     • The rapidity diffusion
                                       coefficient Dy is
  and the variance is
                                       calculated from y and
                                       the equilibrium
                             with
                                       temperature T in the
                                       weak-coupling limit




YITP2/05                                                     5
           RDM:p-induced transverse energy
                        spectra

                          • RDM-calculation for
                            200GeV p + Au
                          • Selected weighted
                            solutions of the
                            transport eq. at various
                            impact parameters b
                          • NA 35 data scaled to 4
                            acceptance


                             GW, Z. Phys. A 355, 301 (1996)



YITP2/05                                                      6
           Transverse energy spectra: SPS

                          • RDM-prediction @SPS
                            energies, pL=157.7 A
                            GeV
                          • SNN = 17.3 GeV
                          • NA 49 data scaled to 4
                            acceptance
                          • Calorimeter data,
                            integrated over all
                            particle species




YITP2/05                                          7
Rapidity density distributions:
Net protons, SIS

• Linear Relativistic
  Diffusion Model-
  calculations @SIS
  energies

• Ni-Ni, Ecm = 1.06-1.93 A
  GeV; FOPI data: bell-
  shaped distributions
  (dashed: thermal equil.)

     GW, Eur. Phys. Lett. 47, 30 (1999)




YITP2/05                                  8
Rapidity density distributions:
Net protons @AGS

• Linear Relativistic
  Diffusion Model-
  calculations @AGS
  energies
• Si-Al, pL = 14.6 GeV/c;
  Au-Au, pL = 11.4 GeV/c;
  E 814/ E877 data


     GW, Eur. Phys. Lett. 47, 30 (1999)




YITP2/05                                  9
            Central Collisions at AGS, SPS



• Rapidity density distributions
  evolve from bell-shape to
  double-hump as the energy
  increases from AGS (4.9 GeV) to
  SPS (17.3 GeV)
• Diffusion-model solutions are
  shown for SPS energies



 YITP2/05                                    10
              Net proton rapidity spectra

• Linear RDM-calculations
  @SPS and RHIC
  energies

• SPS: Pb-Pb, SNN = 17.3
  GeV; NA 49 data
• RHIC: Au-Au, SNN =
  200 GeV; BRAHMS data

    GW, Phys. Rev. C 69, 024906 (2004) High midrap.yield
  see also GW, Eur. Phys. J. A5, 85 (1999).




YITP2/05                                                   11
                RDM-solutions for Au-Au

• Rapidity density
  distributions of net
  protons for various
  values of t/y
• Approach to thermal
  equilibrium for t/y>>1
• Continuous evolution of
  the distribution
  functions with time


                                          ymax = 5.36
    GW, Phys. Rev. C 69, 024906 (2004)



 YITP2/05                                               12
           RDM for Au-Au @ RHIC
• Net protons in central
  collisions
• Linear (solid curves) and
  nonlinear RDM-results;
  weak-coupling solution is
  dotted
• Midrapidity data require
  transition to thermal
  equilibrium (dashed area)
• Nonlinear solution:



                              GW, Phys. Lett. B 569, 67 (2003)



YITP2/05                                                         13
            Discontinuous evolution for Au-Au
• Rapidity density
  distributions of net
  protons for various
  values of t/y
• Disontinuous evolution
  of the distribution
  functions with time
  towards the local
  thermal equilibrium
  distribution
  (22 protons)

                                       Thermal equilibrium (expanding)

            GW, Phys. Rev. C 69, 024906 (2004)
 YITP2/05                                                                14
            Central Au-Au @ RHIC vs. SPS
                                                    • BRAHMS data at
                                                       SNN=200 GeV for net
                                                      protons
                                                    • Central 10% of the cross
                                                      section
                                                    • Relativistic Diffusion Model
                                                      for the nonequilibrium
                                                      contributions
                                                    • Discontinuous transition to
                                                      local statistical equilibrium
                                                      at midrapidity indicates
                                                      deconfinement.

GW, PLB 569, 67 (2003) and Phys. Rev. C 69 (2004)

YITP2/05                                                                         15
                       Central Au-Au at RHIC

                                                  • BRAHMS data at SNN=200
                                                    GeV for net protons
                                                  • Central 5% of the cross
                                                    section
                                                  • Relativistic Diffusion Model
                                                    for the nonequilibrium
                                                    contributions, plus
                                                  • Local statistical equilibrium
                                                    at midrapidity
                                                    (expanding source)
Calc. GW (2004); data P. Christiansen (BRAHMS),
                  Priv. comm.


YITP2/05                                                                       16
                 Au-Au at RHIC

RDM-prediction for 62.4 GeV
(the lower RHIC energy
  measured by BRAHMS; data
  analysis is underway)




YITP2/05                         17
               Heavy Relativistic Systems


Parameters for heavy relativistic
systems at AGS, SPS and RHIC
energies. The beam rapidity is
expressed in the c.m. system. The
ratio int/y determines how fast the
net-baryon system equilibrates in
rapidity space. The effective rapidity
diffusion coefficient is Dyeff, the
longitudinal expansion velocity vcoll.

 *At 62.4 GeV, Dyeff will need
 adjustement to forthcoming data.




YITP2/05                                    18
           d-Au 200 GeV net protons

RDM-schematic               40
calculation for
d-Au:                       30


                    dn/dy
 3 sources model
                            20
 yeq=0
 Net protons
 D from Au-Au              10
  (overestimated)
                             0
                                 -6   -4   -2   0   2   4        6

YITP2/05
                                                y           19
       d-Au 200 GeV net protons
                                          40

RDM-schematic                   40        40



calculation for
                                          30
d-Au:                             30


                       dn/dy
 3 sources model              MS( y )

 yeq as in GW,                   20      20
                               MNE. R eq( y )

   Z.Phys. A355, 301
   (1996)                                 10

 Net protons
                                  10
 D from Au-Au                             0
   (overestimated)                   0     0
                                                6    4    2      0     2   4        6
                                                6             y. y 1                6
                                          -6        -4   -2   0        2   4        6

YITP2/05
                                                                y              20
3 sources RDM: Charged-hadron (pseudo-)
          rapidity distributions
• BRAHMS data at
  SNN=200 GeV for
  charged hadrons
• Central collisions
• Relativistic Diffusion
  Model for the non-equil.
  plus equilibrium
  contributions (»3
  sources«)
• n=N/Nch; Nch≈ 4630,
  0-5%
                             M. Biyajima et al., Prog. Theor. Phys.Suppl. 153, 344 (2004))


  YITP2/05                                                                                   21
   Produced particles in the 3 sources RDM:
        Charged-hadron (pseudo-) rapidity distributions




  PHOBOS data at SNN=130, 200 GeV for charged hadrons                      Central collisions (0-6%)
     Number of particles in the 3 “sources”: 448:3134:448 @ 130 GeV
                                             551:3858:551 @ 200 GeV

Most of the produced charged hadrons at RHIC are in the equilibrated midrapidity region
                 M. Biyajima et al., Prog. Theor. Phys.Suppl. 153, 344 (2004)


  YITP2/05                                                                                         22
                         Summary
The Relativistic Diffusion Model describes/predicts net baryon and
charged hadron transverse energy and rapidity distributions from
SIS to RHIC accurately
At SPS energies, net-proton rapidity spectra (dN/dy) show no
signals yet for QGP formation
At RHIC energies, there are indications for QGP formation (»third
source«) from dN/dy :
   - A fraction of ≈22 net protons (≈55 net baryons) reaches
local thermal equilibrium.
- This transition is discontinuous and most likely due to an
intermediary deconfinement of the constituent partons
   (quarks and gluons).
Both nonequilibrium and equilibrium fractions of the distribution
show strong longitudinal collective expansion.



YITP2/05                                                         23

				
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