Diffusion and local deconfinement in relativistic

systems

Diffusion and local deconfinement in relativistic

systems

Georg WolschinUniversität Heidelberg, Theor.

Physicshttp://wolschin.uni-hd.de

Georg WolschinUniversität Heidelberg, Theor.

Physicshttp://wolschin.uni-hd.de

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TopicsTopics

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?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))]

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Relativistic Diffusion ModelRelativistic 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 RDMLinear RDM

• The rapidity relaxation time y determines the peak positions

• The rapidity diffusion coefficient Dy is calculated fromy and the equilibrium temperature T in the weak-coupling limit

- For =1,q=2-=1 and a linear drift function J(y) = (yeq-y)/y

the mean value becomes

and the variance is

with

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RDM:p-induced transverse energy spectra

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 4acceptance

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

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Transverse energy spectra: SPSTransverse 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

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Rapidity density distributions: Net protons, SISRapidity 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)

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Rapidity density distributions: Net protons @AGSRapidity 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)

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Central Collisions at AGS, SPSCentral 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 spectraNet 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) see also GW, Eur. Phys. J. A5, 85 (1999).

High midrap.yield

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RDM-solutions for Au-AuRDM-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

GW, Phys. Rev. C 69, 024906 (2004)

ymax = 5.36

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RDM for Au-Au @ RHICRDM 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)

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Discontinuous evolution for Au-AuDiscontinuous 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 @ RHIC vs. SPSCentral 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)

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Central Au-Au at RHICCentral 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.

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Au-Au at RHICAu-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 SystemsHeavy Relativistic Systems

Parameters for heavy relativistic systems at AGS, SPS and RHIC energies. The beam rapidity is expressed in the c.m. system. The ratioint/y determines how fast the net-baryon system equilibrates in rapidity space. The effective rapidity diffusion coefficient is Dy

eff, 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 d-Au 200 GeV net protons

RDM-schematiccalculation for d-Au: 3 sources model yeq=0 Net protons D from Au-Au

(overestimated)

-6 -4 -2 0 2 4 6

y

10

20

30

40

0

dn/d

y

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d-Au 200 GeV net protonsd-Au 200 GeV net protons

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)-6 -4 -2 0 2 4 6

y

10

20

30

40

0

dn/d

y

6 4 2 0 2 4 60

10

20

30

4040

0

MS( )y

.MNE R eq( )y

66 .y y 1

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3 sources RDM: Charged-hadron (pseudo-) rapidity distributions

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))

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Produced particles in the 3 sources RDM:

Charged-hadron (pseudo-) rapidity distributions

Produced particles in the 3 sources RDM:

Charged-hadron (pseudo-) rapidity distributions

M. Biyajima et al., Prog. Theor. Phys.Suppl. 153, 344 (2004)

PHOBOS data at SNN=130, 200 GeV for charged hadronsCentral 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

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SummarySummaryThe Relativistic Diffusion Model describes/predicts net baryon and charged hadron transverse energy and rapidity distributions from SIS to RHIC accuratelyAt SPS energies, net-proton rapidity spectra (dN/dy) show no signals yet for QGP formationAt 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.