properties of the sqgp at rhic and lhc energies
DESCRIPTION
Properties of the sQGP at RHIC and LHC energies. Wolfgang Cassing CERN, 04.06.2007. Aim: Transport study of relativistic many-body systems. Transport theory : off-shell Kadanoff-Baym equations for the Green-functions G < h (x,p) in phase-space representation. Actual solutions: - PowerPoint PPT PresentationTRANSCRIPT
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
0.2
0.4
0.6
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
0.2
0.4
0.6
10 100 10000
1
2
3
4
5
6
7
gg
qg
P [fm-3]
inte
ract
ion
stre
nght
[G
eV f
m3 ]
P [fm-3]
qg
gg
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
0.5
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
0.2
0.4
0.6
0.8
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
0.1
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 )]