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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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