Wolfgang CassingWolfgang Cassing

CERN, 04.06.2007CERN, 04.06.2007

Properties of the sQGP at Properties of the sQGP at RHIC and LHC energiesRHIC and LHC energies

Aim:Aim: Transport study of relativistic Transport study of relativistic many-body systemsmany-body systems

Transport theoryTransport theory: : off-shell Kadanoff-Baym equations off-shell Kadanoff-Baym equations for the Green-functions Gfor the Green-functions G<<

hh(x,p) in phase-space representation(x,p) in phase-space representation

Actual solutions: Actual solutions: Monte Carlo simulations with a large number of test-

particles

Scetch of an ultrarelativistic nucleus-nucleus collision (S. A. Bass)Scetch of an ultrarelativistic nucleus-nucleus collision (S. A. Bass)

= Parton-Hadron-String-Dynamics (PHSD)

what are the properties of the new medium?what are the properties of the new medium?

Ask lattice QCD Ask lattice QCD effective approach! effective approach!

At RHIC the strong QGP (At RHIC the strong QGP (sQGPsQGP) was found, but) was found, but

0.2

0.4

0.6

0.8

1.0

wp

/30,s

/s 0

w / 3p0

s/ s0

1 2 3 4

T / T c

0

2

4

/T

c,M

/T

c

M

From lattice QCD to gluon quasiparticle propertiesFrom lattice QCD to gluon quasiparticle properties

quasiparticle entropy:quasiparticle entropy:

mass:mass:

width:width:

coupling:coupling:

spectral function:spectral function:

Andre Peshier, PRD 70 (2004) 034016Andre Peshier, PRD 70 (2004) 034016

==-3p-3p

entropyentropy

massmass

widthwidth

Gluonic quasiparticles of the sQGPGluonic quasiparticles of the sQGP

T = 1.053 TT = 1.053 Tcc T = 1.35 TT = 1.35 Tcc T = 3 TT = 3 Tcc

Andre Peshier, PRD 70 (2004) 034016

broad distributions in (broad distributions in (,k),k)

average glue-glue cross section:average glue-glue cross section:

percolation parameter:percolation parameter:

plasma parameter:plasma parameter:

shear viscosity:shear viscosity:

PRL 94 (2005) 172301PRL 94 (2005) 172301

=> The QGP looks like an almost perfect liquid !=> The QGP looks like an almost perfect liquid !

The Dynamical QuasiParticle Model (DQPM)The Dynamical QuasiParticle Model (DQPM)

The quasiparticle entropy density:The quasiparticle entropy density:

gluonsgluons

quarksquarks

antiquarksantiquarks

Complex selfenergies, e.g. :Complex selfenergies, e.g. :

+ some thermodynamics:+ some thermodynamics:

energy density:energy density:

pressure Ppressure P

interaction measure:interaction measure:

The DQPM model assumptionsThe DQPM model assumptions

Spectral functions for partonic degrees of freedom (g, (g, q, qq, qbarbar):):

gluon mass:gluon mass:

gluon width:gluon width:

quark width:quark width:

quark mass:quark mass:

1 2 3 4 5 6 7 8 9 100.0

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0.8

1.0

1.2

1 2 3 4 5 6 7 8 9 100.0

0.1

0.2

0.3

0.4

0.5

0.6

gluons

g

. TC/T

M. TC/T

[GeV

]

T/TC

quarks

q

. TC/T

m. TC/T

T/TC

The strong coupling gThe strong coupling g22

3 parameters:3 parameters: TTss/T/Tcc=0.46; c=28.8; =0.46; c=28.8; =2.42=2.42

Quasiparticle properties Quasiparticle properties (N(Nff=3; T=3; Tcc = 0.185 GeV) = 0.185 GeV)

1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

2.0

2.5

T/TC

N=8

S(T)

DQPM thermodynamics (NDQPM thermodynamics (Nff=3)=3)

1 100.0

0.5

1.0

1.5

2.0

p . (T

C/T)4W. (T

C/T)4

TC=0.185 GeV

T00. (T

C/T)4

. (T

C/T)4

# [G

eV/f

m3 ]

T/TC

some short-hand notations:some short-hand notations:

+: time-like+: time-like-: space-like-: space-like

Time-like and space-like quantities Time-like and space-like quantities

0.0 0.5 1.0 1.50.0

0.5

1.0

1.5

Quarks: I(,p)T=1.05 T

C

time-like

space-likep=

p [GeV/c]

[G

eV]

1E-5

2.8E-5

4.6E-5

6.4E-5

8.2E-5

1E-4

0 1 2 3 4 50

1

2

3

4

5p=Quarks: I(,p)

T=3 TC

time-like

space-like

p [GeV/c]

[G

eV]

5E-4

1.4E-3

2.3E-3

3.2E-3

4.1E-3

5E-3

Example:Example:

Time-like and space-like densities Time-like and space-like densities

1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

2.0

1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

2.0

2.5

3.0

NS

N

N

N

NSB

NSB

TC=0.185 GeV

# (

TC/T

)3 [fm

-3]

gluons

T/TC

NS

N

N

N

TC=0.185 GeV

quarks

T/TC

‚‚densities‘:densities‘:

scalar densities:scalar densities:

time-like densities are small except close to Tc !

Time-like and space-like energy densitiesTime-like and space-like energy densities

1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

T00

T00

T00

TC=0.185 GeV

ener

gy d

ensi

ty(T

C/T

)4 [G

eV f

m-3] gluons

T/TC

T00

T00

T00

TC=0.185 GeV

quarks

T/TC

space-like energy densities dominate except close to Tc ! space-like parts are identified with potential energy densities!

Thermodynamical consistency ?Thermodynamical consistency ?

Total energy density:Total energy density:

1 100.0

0.5

1.0

1.5

2.0

p . (T

C/T)4W. (T

C/T)4

TC=0.185 GeV

T00. (T

C/T)4

. (T

C/T)4

# [G

eV/f

m3 ]

T/TC

=> matches well the thermodynamical energy density!

Potential energy per time-like partonPotential energy per time-like parton

1 100.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1 100

1

2

3

4

5

6

=<

V>

/<T

kin>

Vqq

/Nq

+. T

C/T

Vgg

/Ng

+. T

C/T

# [G

eV]

T/TC

gluons

quarks

T/TC

Plasma parameters:Plasma parameters:

Potential energy:Potential energy:

huge !huge !

liquidliquid

gasgas

Partonic liquid should persist at Partonic liquid should persist at LHC !LHC !

Potential energy versus parton densityPotential energy versus parton density

Potential energy:Potential energy:

Parton density:Parton density:

Gluon fraction:Gluon fraction:

PHSDPHSD

1 10 100 10000

1

2

3

4

5

6

7

8

9

10

1 10 100 1000

0.18

0.20

0.22

0.24

0.26

0.28

0.30

fit

gluo

n fr

acti

onV/

P

P [fm-3]

# [G

eV]

P [fm-3]

fit

Self-energies of time-like partonsSelf-energies of time-like partons

1 10 100 10000

5

10

15

20

10 100 10001.8

1.9

2.0

2.1

2.2

2.3

rati

o

Uq

Ug

P [fm-3]

U [

GeV

]

P [fm-3]

Ug/U

q

gluonsgluons

quarksquarks

PHSDPHSD

Effective 2-body interactions of time-like partonsEffective 2-body interactions of time-like partons

1 10 100 1000

-0.4

-0.2

0.0

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0.4

0.6

10 100 10000

1

2

3

4

5

6

7

qq

gg

qg

P [fm-3]

inte

ract

ion

stre

nght

[G

eV f

m3 ]

P [fm-3]

qg

/qq

gg

/qq

2nd derivatives ofinteraction densities

effective interactions turn strongly attractive below 2.2 fmeffective interactions turn strongly attractive below 2.2 fm -3-3 ! ! PHSDPHSD

Finite quark chemical potentialsFinite quark chemical potentials

1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

2.0

1 2 3 4 5 6 7 8 9 100.0

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1.0

1.5

1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

2.0

=0.3 GeV

=0

* (

T4 C

0 / T

4 ) [G

eV f

m-3]

=0.3 GeV

=0

P*

(T3 C

0 / T

3 ) [f

m-3]

=0

=0.3 GeV

# *

(TC

0 / T

) [G

eV]

P*

(T4 C

0 / T

4 ) [G

eV f

m-3]

T/TC()

=0.3 GeV

=0 T00 g

/ N +

g

T00 q+qbar

/ N +

q+qbar

T/TC()

energy densityenergy density

pressurepressure

parton densityparton density

pot. energy per particlepot. energy per particle

slight increase with chemical potential close to Tslight increase with chemical potential close to Tcc

Fermion potential energy per particle practically independent !Fermion potential energy per particle practically independent !

Parton densities and gluon fractionParton densities and gluon fraction

1 2 3 4 5 6 7 8 9100.0

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1.0

1.2

1.4

1.6

1.8

1 2 3 4 5 6 7 8 9100.00

0.05

0.10

0.15

0.20

0.25

0.30

N q+qbar

=0

=0.3 GeV

Ng

Ng

N +

q+qbar

# *

(T3 C

0 / T

3 ) [f

m-3]

T/TC()

glu

on f

ract

ion

* (T

3 C0 /

T3 )

=0.3 GeV

=0

T/TC()

• fermion densities fermion densities increase with quark chemical potentialincrease with quark chemical potential• gluon densities gluon densities slightly decrease !slightly decrease !

Parton energy densitiesParton energy densities

1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

1 2 3 4 5 6 7 8 9 100.0

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0.2

0.3

0.4

0.5

0.6

1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

=0.3 GeV

=0

# *

(T4 C

0 / T

4 ) [G

eV f

m-3]

# *

(T4 C

0 / T

4 ) [G

eV f

m-3]

# *

(T4 C

0 / T

4 ) [G

eV f

m-3]

T00 q+qbar

T00 q+qbar

# *

(T4 C

0 / T

4 ) [G

eV f

m-3]

=0

T00 qbar

T00 q

=0.3 GeV

=0.3 GeV

q qbar

T00 g

T00 g

T/TC()

=0

T00 q

T00 qbar=0.3 GeV

=0.3 GeV

q qbar

T/TC()

increase with chemical potential close to Tincrease with chemical potential close to Tcc ; ;

gluon potential energy density practically independent !gluon potential energy density practically independent !

Net fermion densitiesNet fermion densities

1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

=0

# *

(T2 C

0 / T

2 ) [f

m-3G

eV-1]

=0.3 GeV

q+ * (

T2 C

0 / T

2 ) [f

m-3]

T/TC()

q

/

q

+ /

T/TC()

Net fermion densitiesNet fermion densities approximately scale with T approximately scale with T22 and and chemical potential chemical potential qq ! !

Net fermion density – comparison to lQCDNet fermion density – comparison to lQCD

Comparison to lQCDComparison to lQCD : looks quite reasonable !1.0 1.2 1.4 1.6 1.8 2.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.2

0.4

0.6

0.8

/TC0

= 1.0

lQCD, Nf=2

q / T

3

T/TC0

NNff=2; lQCD:=2; lQCD:C. R. Allton et al.,C. R. Allton et al.,PRD 68 (2003) 014507PRD 68 (2003) 014507

Dilepton ‚back-to-back‘ radiation from the sQGPDilepton ‚back-to-back‘ radiation from the sQGP

0 2 4 6 8 10 1210-13

10-12

10-11

10-10

10-9

10-8

10-7

T = 1.5 TC

lQCD, Nf=2

DQPM

Born approx.

/T

diff

eren

tial

dile

pton

rat

e

Born rate:Born rate:

DQPM rate:DQPM rate:

NNff=2; lQCD:=2; lQCD:F. Karsch et al.,F. Karsch et al.,PLB 530 (2002) 147PLB 530 (2002) 147

massive suppression massive suppression of low mass dileptonsof low mass dileptons in line with lQCD ! in line with lQCD !

Dilepton radiation from the sQGP – NA60Dilepton radiation from the sQGP – NA60

0.2 0.4 0.6 0.8 1.0 1.2 1.40

200

400

600

800

1000

1200

1400

1600 In+In, 160 GeV, Central, all pT

NA60 DDbar coctail , free s.f. , in-medium s.f. thermal dileptons sum=+thermal sum=+thermal+DDbar

dN/d

M p

er 2

0 M

eV

M [GeV/c2]

NA60 dataNA60 data

sQGP is here!sQGP is here!

Preliminary PHSD results:Preliminary PHSD results:

Conjecture: the sQGP shows up already at SPS energies !

SummarySummary

PHSD Conjecture:PHSD Conjecture: the sQGP shows up already at SPS energies ! the sQGP shows up already at SPS energies !

• The dynamical quasiparticle model (DQPM)The dynamical quasiparticle model (DQPM) well matches well matches lQCDlQCD (with only 3 parameters) !(with only 3 parameters) !

• DQPM allows to extrapolateDQPM allows to extrapolate to finite quark chemical potentials to finite quark chemical potentials presently out of reach for lQCD.presently out of reach for lQCD.

• DQPM DQPM separates lime-like quantities from space-likeseparates lime-like quantities from space-like (interaction) (interaction) regions (needed for off-shell transport). regions (needed for off-shell transport).

• DQPM provides DQPM provides mean-fields for gluons and quarksmean-fields for gluons and quarks as well as as well as effective 2-body interactionseffective 2-body interactions PHSDPHSDand gives and gives transition ratestransition rates for the formation of hadrons if the average for the formation of hadrons if the average distance is larger than 0.77 fm distance is larger than 0.77 fm PHSDPHSD . .

• The plasma parameter G suggests that the The plasma parameter G suggests that the sQGPsQGP and its related and its related experimental observations (scaling of elliptic flow with parton experimental observations (scaling of elliptic flow with parton number etc.) will persist number etc.) will persist at LHCat LHC (i.e. the partonic liquid). (i.e. the partonic liquid).

Dilepton radiation from the sQGP – NA60Dilepton radiation from the sQGP – NA60

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.010-5

10-4

10-3

10-2

10-1

100

101

102

M [GeV/c2]

HSD free 'coctail' QGP sum

Au+Au, 160 GeVb=0.5 fm

dN/d

M [

1/(G

eV/c

2 )]