Diffusion and local deconfinement in relativistic systems

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Diffusion and local deconfinement in relativistic
systems

• Georg Wolschin
• Universität Heidelberg, Theor. Physics
• http//wolschin.uni-hd.de

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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
  

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Indications for local deconfinement/qgp?
Fig. Courtesy U Frankfurt
1.Yes, in central collisions of Au-Au at vs200
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))
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Relativistic Diffusion Model

• Nonequilibrium-statistical approach to
  relativistic many-body collisions
• Macroscopic distribution function R(y,t) for the
  rapidity y
• Coupled to a corresponding evolution eq. for pT,
  or ET

-The drift function J(y) determines the shift of
the mean rapidity towards the equilibrium
value - The diffusion coefficient D(t)
accounts for the broadening of the distributions
due to interactions and particle creations. It
is related to J(y) via a dissipation-fluct.
Theorem.
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Linear RDM
- For m1,q2-n1 and a linear drift function
J(y) (yeq-y)/?y the mean value becomes

• The rapidity relaxation time ?y determines the
  peak positions
• The rapidity diffusion coefficient Dy is
  calculated from ?y and the equilibrium
  temperature T in the weak-coupling limit

and the variance is
with
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RDMp-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)
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Transverse energy spectra SPS

• RDM-prediction _at_SPS energies, pL157.7 A GeV
• ?SNN 17.3 GeV
• NA 49 data scaled to 4? acceptance
• Calorimeter data, integrated over all particle
  species

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Rapidity density distributions Net protons, SIS

• Linear Relativistic Diffusion Model-calculations
  _at_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)

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Rapidity density distributions Net protons _at_AGS

• Linear Relativistic Diffusion Model-calculations
  _at_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)

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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

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Net proton rapidity spectra

• Linear RDM-calculations _at_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)
• see also GW, Eur. Phys. J. A5, 85 (1999).

High midrap.yield
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RDM-solutions for Au-Au

• Rapidity density distributions of net protons for
  various values of t/?y
• Approach to thermal equilibrium for t/?ygtgt1
• Continuous evolution of the distribution
  functions with time

ymax 5.36
GW, Phys. Rev. C 69, 024906 (2004)
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RDM for Au-Au _at_ 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)
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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)
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Central Au-Au _at_ RHIC vs. SPS

• BRAHMS data at
• ?SNN200 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)
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Central Au-Au at RHIC

• BRAHMS data at ?SNN200 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.
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Au-Au at RHIC
RDM-prediction for 62.4 GeV (the lower RHIC
energy measured by BRAHMS data analysis is
underway)
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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
tint/?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.
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d-Au 200 GeV net protons
40

• RDM-schematic
• calculation for
• d-Au
• 3 sources model
• yeq0
• Net protons
• D from Au-Au (overestimated)

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dn/dy
20
10
0
-6
-4
-2
0
2
4
6
y
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d-Au 200 GeV net protons
40

• RDM-schematic
• calculation for
• d-Au
• 3 sources model
• yeq as in GW, Z.Phys. A355, 301 (1996)
• Net protons
• D from Au-Au (overestimated)

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dn/dy
20
10
0
-6
-4
-2
0
2
4
6
y
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3 sources RDM Charged-hadron (pseudo-) rapidity
distributions

• BRAHMS data at
• ?SNN200 GeV for charged hadrons
• Central collisions
• Relativistic Diffusion Model for the non-equil.
  plus equilibrium contributions (3 sources)
• nN/Nch Nch 4630,
• 0-5

M. Biyajima et al., Prog. Theor. Phys.Suppl. 153,
344 (2004))
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Produced particles in the 3 sources RDM
Charged-hadron (pseudo-) rapidity distributions
PHOBOS data at ?SNN130, 200 GeV for charged
hadrons
Central collisions (0-6)
Number of particles in the 3 sources
4483134448 _at_ 130 GeV

5513858551 _at_ 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)
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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.