The properties of parton- -hadron matter hadron matter The - - PowerPoint PPT Presentation
The properties of parton- -hadron matter hadron matter The properties of parton from heavy- -ion collisions ion collisions from heavy Elena lena Bratkovskaya Bratkovskaya E Institut f r Theoretische Physik r Theoretische Physik
1 1
Institut f Institut fü ür Theoretische Physik r Theoretische Physik & FIAS, Uni. Frankfurt & FIAS, Uni. Frankfurt
BLTP, BLTP, 7 August, 2013 7 August, 2013
2 2
3 min nucleons deuterons α α α α− − − −particles 10-3sec quarks gluons photons
T~160 MeV
300000 years atoms 15 Mrd years
3 3
1 event: Au+Au, 21.3 TeV
Relativistic-
Heavy-
Ion-
Collider – – RHIC RHIC -
(Brookhaven): Au+Au at 21.3 A TeV Au+Au at 21.3 A TeV
Future facilities: FAIR (GSI), NICA (Dubna) FAIR (GSI), NICA (Dubna)
Large Hadron Collider Hadron Collider -
LHC -
(CERN): Pb+Pb at 574 A TeV Pb+Pb at 574 A TeV
L=3.8 km L=3.8 km
STAR detector at RHIC STAR detector at RHIC NICA NICA
SPS SPS L=27 km L=27 km
4 4
0.5 1.0 1.5 2.0 2.5 3.0 2 4 6 8 10 12 14
µ
µ µ µB=0
µ
µ µ µB=530 MeV
T/Tc
ε ε ε ε/T
4
T Tc
c = 160 MeV
= 160 MeV
energy density versus temperature energy density versus temperature Q Quantum uantum C Chromo hromo D Dynamics : ynamics : predicts strong increase of predicts strong increase of the the energy density energy density ε ε ε ε ε ε ε ε at a critical at a critical temperature temperature T TC
C ~160 MeV
~160 MeV ⇒ ⇒ Possible Possible phase transition phase transition from from hadronic to hadronic to partonic matter partonic matter (quarks, gluons) at critical energy (quarks, gluons) at critical energy density density ε ε ε ε ε ε ε εC
C ~0.5 GeV/fm
~0.5 GeV/fm3
3
Critical conditions Critical conditions -
ε ε ε ε ε ε εC
C ~0.5 GeV/fm
~0.5 GeV/fm3
3 , T
, TC
C ~160 MeV
~160 MeV -
can be reached in in heavy heavy-
ion experiments at bombarding energies at bombarding energies > 5 GeV/A > 5 GeV/A
QGP QGP
hadrons hadrons
5 5
Study of the phase phase transition transition from from hadronic to partonic hadronic to partonic matter matter – – Quark Quark-
Gluon-
Plasma
Search for the critical point critical point
Study of the in in-
medium properties of hadrons at high baryon density properties of hadrons at high baryon density and temperature and temperature
The phase diagram of QCD The phase diagram of QCD
6 6
PHSD PHSD
7 7
Multi-
strange particle enhancement in A+A
Charm suppression
Collective flow (v1
1, v
, v2
2)
)
Thermal dileptons
Jet quenching and angular correlations
High pT
T suppression of hadrons
suppression of hadrons
Nonstatistical event by event fluctuations and correlations
...
8 8
basic assumption basic assumption: system is described by a (grand) canonical ensemble of : system is described by a (grand) canonical ensemble of non non-
interacting fermions and bosons in thermal and chemical equilibrium thermal and chemical equilibrium [ [ -
no dynamics]
basic assumption basic assumption: conservation laws + equation of state; assumption of : conservation laws + equation of state; assumption of local thermal and chemical equilibrium local thermal and chemical equilibrium [ [ -
simplified dynamics]
based on transport theory of relativistic quantum many based on transport theory of relativistic quantum many-
body systems -
Actual solutions: Monte Carlo simulations Monte Carlo simulations [ [+:
full dynamics | -
very complicated]
Microscopic transport models provide a unique dynamical dynamical description description
nonequilibrium effects in heavy effects in heavy-
ion collisions
9 9
coll p r r
t f ) t , p , r ( f ) t , r ( U ) t , p , r ( f m p ) t , p , r ( f t ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ = = = = ∇ ∇ ∇ ∇ ∇ ∇ ∇ ∇ − − − − ∇ ∇ ∇ ∇ + + + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
Boltzmann -
Uehling-
Uhlenbeck equation (non (non-
relativistic formulation)
propagation of particles in the self self-
generated Hartree-
Fock mean-
field potential potential U(r,t) U(r,t) with an on with an on-
shell collision term: collision term:
) term Fock ( ) t , p , r ( f ) t , r r ( V p d r d ) 2 ( 1 ) t , r ( U
3 3 3
+ + + + ′ ′ ′ ′ ′ ′ ′ ′ − − − − ′ ′ ′ ′ = = = =
β β β
π π π π
) t , p , r ( f
is the single particle phase single particle phase-
space distribution function
probability to find the particle at position r r with momentum with momentum p p at time at time t t
self-
generated Hartree Hartree-
Fock mean-
field potential:
Ludwig Boltzmann
collision term: collision term: eleastic and eleastic and inelastic reactions inelastic reactions P ) 4 3 2 1 ( d d ) p p p p ( | | d p d p d ) 2 ( 4 I
4 3 2 1 3 12 3 3 2 3 3 coll
⋅ ⋅ ⋅ ⋅ + + + + → → → → + + + + ⋅ ⋅ ⋅ ⋅ − − − − − − − − + + + + = = = =
Ω Ω Ω Ω σ σ σ σ δ δ δ δ υ υ υ υ Ω Ω Ω Ω π π π π
Probability including Pauli blocking of fermions: Pauli blocking of fermions:
) f 1 )( f 1 ( f f ) f 1 )( f 1 ( f f P
4 3 2 1 2 1 4 3
− − − − − − − − − − − − − − − − − − − − = = = =
Gain term: 3+4 Gain term: 3+4
1+2 Loss term: 1+2 Loss term: 1+2
3+4 Collision term Collision term for 1+2 for 1+2
3+4 (let‘ ‘s consider fermions) s consider fermions) : : 1 2 3 4
t ∆ ∆ ∆ ∆
12
υ υ υ υ
10 10
Semi-
classical BUU
solution for weakly interacting systems of particles How to describe How to describe strongly interacting systems?! strongly interacting systems?!
Quantum field theory
Kadanoff-
Baym dynamics for resummed(!) single for resummed(!) single-
particle Green functions S<
<
(1962) (1962)
Leo Kadanoff Leo Kadanoff Gordon Baym Gordon Baym
) M ( S ˆ
2 x x 1 x
+ + + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ − − − − ≡ ≡ ≡ ≡
− − − − µ µ µ µ µ µ µ µ
advanced S S S S S retarded S S S S S
a xy xy xy c xy adv xy a xy xy xy c xy ret xy
− − − − − − − − = = = = − − − − = = = = − − − − − − − − = = = = − − − − = = = =
< < < < > > > > > > > > < < < <
anticausal } ) y ( Φ ) x ( {Φ T iS causal } ) y ( Φ ) x ( {Φ T iS } ) x ( Φ ) y ( {Φ iS } ) x ( Φ ) y ( {Φ η iS
a a xy c c xy xy xy
− − − − 〉 〉 〉 〉 〈 〈 〈 〈 = = = = − − − − 〉 〉 〉 〉 〈 〈 〈 〈 = = = = 〉 〉 〉 〉 〈 〈 〈 〈 = = = = 〉 〉 〉 〉 〈 〈 〈 〈 = = = =
+ + + + + + + + + + + + > > > > + + + + < < < <
Green functions S Green functions S<
< /self
/self-
energies Σ: Σ: Σ: Σ: Σ: Σ: Σ: Σ:
time ) anti ( ) T ( T ) fermions / bosons ( 1
c a
− − − − − − − − − − − − ± ± ± ± = = = = η η η η
Integration over the intermediate spacetime Integration over the intermediate spacetime
11 11
After the After the first order gradient expansion of the Wigner transformed first order gradient expansion of the Wigner transformed Kadanoff Kadanoff-
Baym equations and separation into the real and imaginary parts one gets: and separation into the real and imaginary parts one gets:
drift term drift term Vlasov term Vlasov term collision term = collision term = ‚ ‚loss loss‘ ‘ term term -
‚gain gain‘ ‘ term term backflow term backflow term
Generalized transport equations (GTE): Generalized transport equations (GTE):
Backflow term Backflow term incorporates the incorporates the off
shell behavior in the particle propagation behavior in the particle propagation ! ! vanishes in the quasiparticle limit vanishes in the quasiparticle limit A AXP
XP
δ δ δ δ δ δ δ(p (p2
2-
M2
2)
) Spectral function: Spectral function: – – width of spectral function width of spectral function = = reaction rate reaction rate of particle (at phase
space position XP)
4 4-
dimentional generalizaton of the Poisson-
bracket:
(2000) 445
GTE: Propagation of the Green Propagation of the Green‘ ‘s function s function i iS S<
<XP XP=A
=AXP
XPN
NXP
XP , which carries information not
, which carries information not
number of particles ( (N NXP
XP)
), but also on their , but also on their properties, properties, interactions and interactions and correlations correlations (via (via A AXP
XP)
)
ret XP XP
ImΣ Σ Σ Σ Γ Γ Γ Γ − − − − = = = =
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HSD HSD – – H Hadron adron-
String tring-
Dynamics transport approach: ynamics transport approach:
solution of the the generalized off generalized off-
shell transport equations for for the phase the phase-
space density f fi
i(r,p,t)
(r,p,t) with with collision terms collision terms I Icoll
coll describing:
describing:
HSD is an open code: HSD is an open code: http://www.th.physik.uni-frankfurt.de/~brat/hsd.html
Low energy collisions: Low energy collisions:
binary 2< < < < < < < <− − − − − − − −>2 >2 >2 >2 >2 >2 >2 >2 and and 2 2< < < < < < < <− − − − − − − −> > > > > > > >3 reactions 3 reactions
1< < < < < < < <− − − − − − − −>2 >2 >2 >2 >2 >2 >2 >2 : formation and : formation and decay of baryonic and decay of baryonic and mesonic mesonic resonances resonances BB BB < < < < < < < <− − − − − − − −> > > > > > > > B´B´ B´B´ BB BB < < < < < < < <− − − − − − − −> > > > > > > > B´B´m B´B´m mB mB < < < < < < < <− − − − − − − −> > > > > > > > m´B´ m´B´ mB mB < < < < < < < <− − − − − − − −> > > > > > > > B´ B´ mm mm < < < < < < < <− − − − − − − −> > > > > > > > m´m´ m´m´ mm mm < < < < < < < <− − − − − − − −> > > > > > > > m´ m´ . . . . . . Baryons: Baryons: B = p, n, B = p, n, ∆(1232) ∆(1232) ∆(1232) ∆(1232) ∆(1232) ∆(1232) ∆(1232) ∆(1232), , N(1440), N(1535), ... N(1440), N(1535), ... Mesons: Mesons: M = M = π π π π π π π π, , η η η η η η η η, , ρ, ω, φ, ... ρ, ω, φ, ... ρ, ω, φ, ... ρ, ω, φ, ... ρ, ω, φ, ... ρ, ω, φ, ... ρ, ω, φ, ... ρ, ω, φ, ...
π π π π π π π π+
+p
p pp pp
High energy collisions: High energy collisions: (above s (above s1/2
1/2~2.5 GeV)
~2.5 GeV) Inclusive particle Inclusive particle production: production: BB BB − − − − − − − −> > > > > > > > X , mB X , mB − − − − − − − −> > > > > > > >X X X =many particles X =many particles described by described by strings strings (= excited color (= excited color singlet states singlet states q q-
qq, , q q-
qbar) ) formation and decay formation and decay
13 13
very good description of particle production in pp, pA, pp, pA, π π π π π π π πA, AA reactions A, AA reactions
unique description of nuclear dynamics from from low low (~100 MeV) (~100 MeV) to ultrarelativistic to ultrarelativistic (>20 TeV) energies (>20 TeV) energies
10
10 10
1
10
2
10
3
10
4
10
10
10
10 10
2
10
4
AGS SPS RHIC
HSD ' 99
__ D(c) J/Ψ
Ψ Ψ Ψ
D(c)
φ φ φ φ
K
− − − −
K
+
η η η η π π π π
+
Multiplicity
Au+Au (central)
Energy [A GeV]
HSD predictions from 1999; data from the new millenium HSD predictions from 1999; data from the new millenium
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10 10
1
10
2
10
3
10
4
0.00 0.05 0.10 0.15 0.20 0.25
E866 NA49 BRAHMS, 5%
HSD UrQMD
<K
+>/<π
π π π
+>
Elab/A [GeV] 1 10 100 0.10 0.15 0.20 0.25 0.30 0.35
s
1/2 [GeV]
E866 NA49 NA44 STAR BRAHMS PHENIX
Au+Au / Pb+Pb -> K
++X
T [GeV]
HSD HSD with Cronin eff. UrQMD
‚horn horn‘ ‘ in K in K+
+/
/π π π π π π π π+
+
‚step step‘ ‘ in slope T in slope T
string picture => evidence for => evidence for partonic degrees of partonic degrees of freedom freedom
PRC 69 (2004) 032302 PRC 69 (2004) 032302
elliptic flow
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How to model a QGP phase QGP phase in line with lQCD data? in line with lQCD data?
How to solve the hadronization problem hadronization problem? ?
Hybrid‘ ‘ models: models:
QGP phase: hydro hydro with QGP EoS with QGP EoS
hadronic freeze-
hadron-
string transport model
Hybrid-
UrQMD
microscopic transport description of the transport description of the partonic partonic and and hadronic phase hadronic phase in terms of strongly interacting in terms of strongly interacting dynamical dynamical quasi quasi-
particles and off and off-
shell hadrons
PHSD pQCD based models: pQCD based models:
QGP phase: pQCD cascade
hadronization: quark coalescence
AMPT, HIJING, BAMPS
16 16
In order to study the In order to study the phase transition phase transition from from hadronic to partonic matter hadronic to partonic matter – – Quark Quark-
Gluon-
Plasma – – we we need need a a consistent non consistent non-
equilibrium (transport) model with
explicit parton parton-
parton interactions (i.e. between quarks and gluons) (i.e. between quarks and gluons) beyond strings! beyond strings!
explicit phase transition phase transition from hadronic to partonic degrees of freedom from hadronic to partonic degrees of freedom
lQCD EoS for partonic phase for partonic phase
QGP phase QGP phase described by described by D Dynamical ynamical Q Quasi uasiP Particle article M Model
DQPM) Transport theory Transport theory: off : off-
shell Kadanoff-
Baym equations for the Green Green-
functions S<
< h h(x,p) in phase
(x,p) in phase-
space representation for the partonic partonic and and hadronic phase hadronic phase
A.
Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)
NPA831 (2009) 215; NPA831 (2009) 215;
EPJ ST PJ ST 168 168 (2009) (2009) 3 3
17 17
DQPM DQPM describes describes QCD QCD properties in terms of properties in terms of ‚ ‚resummed resummed‘ ‘ single single-
particle Green‘ ‘s s functions functions – – in the sense of a two in the sense of a two-
particle irreducible (2PI 2PI) approach: ) approach:
A.
Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)
the resummed resummed properties are specified by properties are specified by complex self complex self-
energies which depend on which depend on temperature temperature: :
the real part of self real part of self-
energies ( (Σ Σq
q,
, Π Π) ) describes a describes a dynamically generated dynamically generated mass mass ( (M Mq
q,M
,Mg
g)
); ;
the imaginary part imaginary part describes the describes the interaction width interaction width of
partons ( (Γ Γ Γ Γ Γ Γ Γ Γq
q,
, Γ Γ Γ Γ Γ Γ Γ Γg
g)
)
space-
like part of energy-
momentum tensor T Tµν
µν µν µν µν µν µν µν defines the potential energy
defines the potential energy density and the density and the mean mean-
field potential (1PI) for quarks and gluons (1PI) for quarks and gluons
2PI framew work
guaranti ies es a consistent description of the system a consistent description of the system in in-
and out-
equilibrium equilibrium on the basis of
Kadanoff-
Baym equations equations
Gluon propagator: Gluon propagator:
1 =P
=P2
2 -
Π gluon self gluon self-
energy: Π Π=M =Mg
g2 2-
i2Γ Γ Γ Γ Γ Γ Γ Γg
gω
ω Quark propagator: Quark propagator: S Sq
q
1 = P
= P2
2 -
Σq
q
quark self quark self-
energy: Σ Σq
q=M
=Mq
q2 2-
i2Γ Γ Γ Γ Γ Γ Γ Γq
qω
ω
18 18
Properties Properties of
interacting quasi-
particles: massive quarks and gluons massive quarks and gluons (g, q, q (g, q, qbar
bar)
) with with Lorentzian spectral functions : Lorentzian spectral functions :
DQPM: Peshier, Cassing, PRL 94 (2005) 172301; DQPM: Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)
with with 3 parameters: 3 parameters: T Ts
s/T
/Tc
c=0.46;
=0.46; c c=28.8; =28.8; λ λ λ λ λ λ λ λ=2.42 =2.42
(for pure glue N (for pure glue Nf
f=0)
=0)
fit to lattice (lQCD) results (e.g. entropy density) (e.g. entropy density)
(T) ω 4 (T) M p ω (T) ω 4 ) T , ( ρ
2 i 2 2 2 i 2 2 i i
Γ Γ Γ Γ Γ Γ Γ Γ ω ω ω ω + + + + − − − − − − − − = = = =
g , q , q i ( = = = =
running coupling (pure glue): (pure glue):
N Nc
c = 3, N
= 3, Nf
f=3
=3
mass: mass: width: width:
gluons:
quarks:
lQCD: pure glue lQCD: pure glue
Modeling of the quark/gluon masses and widths
HTL limit at high T
19 19
Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2 Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) 007) 365: NPA 793 (2007)
Quasiparticle properties:
large width and mass for gluons and quarks
DQPM matches well matches well lattice QCD lattice QCD
DQPM provides provides mean mean-
fields (1PI) for gluons and quarks as well as as well as effective 2 effective 2-
body interactions (2PI)
DQPM gives gives transition rates transition rates for the formation of hadrons for the formation of hadrons
PHSD
fit to lattice (lQCD) results (e.g. entropy density)
(e.g. entropy density)
* BMW lQCD data S. Borsanyi et al., JHEP 1009 (2010) 073 * BMW lQCD data S. Borsanyi et al., JHEP 1009 (2010) 073 Plot from Peshier, Plot from Peshier, PRD 70 (2004) PRD 70 (2004) 034016 034016
T TC
C=158 MeV
=158 MeV ε ε ε ε ε ε ε εC
C=0.5 GeV/fm
=0.5 GeV/fm3
3
20 20
Formation of QGP stage by dissolution of pre by dissolution of pre-
hadrons (all new produced secondary hadrons) (all new produced secondary hadrons) into into massive colored quarks + mean massive colored quarks + mean-
field energy based on the based on the Dynamical Quasi Dynamical Quasi-
Particle Model (DQPM) which defines which defines quark spectral functions, quark spectral functions, i.e. masses i.e. masses M Mq
q(
(ε ε ε ε ε ε ε ε) ) and widths and widths Γ Γ Γ Γ Γ Γ Γ Γq
q (
(ε ε ε ε ε ε ε ε) ) + + mean mean-
field potential U Uq
q at given
at given ε ε ε ε ε ε ε ε – – local energy density local energy density
( (ε ε ε ε ε ε ε ε related by lQCD EoS to related by lQCD EoS to T T -
temperature in the local cell)
Initial A+A collisions – – as in HSD: as in HSD:
string formation in primary NN collisions formation in primary NN collisions
string decay to pre pre-
hadrons ( (B B -
baryons, m m -
mesons)
NPA831 (2009) 215; NPA831 (2009) 215; E EPJ ST PJ ST 168 168 (2009) (2009) 3 3; ; N NP PA856 A856 (2011) (2011) 162 162. .
QGP phase: QGP phase: ε ε ε ε ε ε ε ε > > ε ε ε ε ε ε ε εcritical
critical
q
U q q m qqq, B ∀ ∀ ∀ ∀ → → → → → → → →
I.
From hadrons to QGP:
21 21
g g g g g q q + + + + → → → → + + + + → → → → + + + +
II.
Partonic phase -
QGP:
quarks and gluons (= quarks and gluons (= ‚ ‚dynamical quasiparticles dynamical quasiparticles‘ ‘) ) with with off
shell spectral functions (width, mass) defined by the DQPM (width, mass) defined by the DQPM
in self self-
generated mean-
field potential for quarks and gluons for quarks and gluons U Uq
q, U
, Ug
g
from the DQPM from the DQPM
EoS of partonic phase: ‚crossover‘ from lattice QCD ‚crossover‘ from lattice QCD (fitted by DQPM) (fitted by DQPM)
(quasi-
) elastic and inelastic parton parton-
parton interactions: using the effective cross sections from the DQPM using the effective cross sections from the DQPM
(quasi-
) elastic collisions:
inelastic collisions: (Breit (Breit-
Wigner cross sections)
q q g g q q + + + + → → → → → → → → + + + + q q q q q q q q q q q q + + + + → → → → + + + + + + + + → → → → + + + + + + + + → → → → + + + + g g g g q g q g q g q g + + + + → → → → + + + + + + + + → → → → + + + + + + + + → → → → + + + +
suppressed (<1%) suppressed (<1%) due to the large due to the large mass of gluons mass of gluons
22 22
III.
Hadronization:
Hadronization: based on DQPM based on DQPM
massive, off-
shell (anti-
)quarks with broad spectral functions hadronize to with broad spectral functions hadronize to
shell mesons and baryons or color neutral excited states -
‚strings strings‘ ‘ (strings act as (strings act as ‚ ‚doorway states doorway states‘ ‘ for hadrons) for hadrons)
) ' string (' baryon q q q ) ' string (' meson q q , q q g ↔ ↔ ↔ ↔ + + + + + + + + ↔ ↔ ↔ ↔ + + + + + + + + → → → →
IV.
Hadronic phase: hadron
hadron-
string interactions – – off
shell HSD
Local covariant off-
shell transition rate transition rate for q+qbar fusion for q+qbar fusion
meson formation:
Nj
j(x,p)
(x,p) is the phase is the phase-
space density of parton j at space-
time position x x and 4 and 4-
momentum p p
Wm
m is the phase
is the phase-
space distribution of the formed ‚ ‚pre pre-
hadrons‘ ‘ (Gaussian in phase space) (Gaussian in phase space)
|Μ |Μ |Μ |Μ |Μ |Μ |Μqq
qq|
| | | | | | |2
2 2 2 2 2 2 2 is the effective quark
is the effective quark-
antiquark interaction from the DQPM
( ( ( ( ) ) ) )
q q q q m 2 q q q q q q q q q q q q q q q q 4 q q 4 q q 4 4 m q q
p p , x x W | M | ) p ( ) p ( ) p , x ( N ) p , x ( N ) color , flavor ( x 2 x x ) p p p ( Tr Tr p d x d dN − − − − − − − − ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ − − − − + + + + − − − − − − − − = = = =
→ → → → + + + +
ρ ρ ρ ρ ω ω ω ω ρ ρ ρ ρ ω ω ω ω δ δ δ δ δ δ δ δ δ δ δ δ
23 23
24 24
25 25
26 26
The goal: The goal:
study of the dynamical equilibration dynamical equilibration of QGP within the non
equilibrium
shell PHSD PHSD transport approach transport approach
transport coefficients (shear and bulk viscosities) (shear and bulk viscosities) of
strongly interacting interacting partonic partonic matter matter
particle number fluctuations fluctuations (scaled variance, skewness, (scaled variance, skewness, kurtosis) kurtosis)
064903, , arXiv:1212.5393 arXiv:1212.5393
Realization: Realization:
Initialize the system in a finite box with finite box with periodic boundary conditions periodic boundary conditions with some with some energy density energy density ε ε and chemical potential and chemical potential q
q
Evolve the system in time until until equilibrium is achieved equilibrium is achieved
27 27
T=TC
C:
: η η η η η η η η/s /s shows shows a a minimum minimum (~0.1) (~0.1) close to the critical temperature close to the critical temperature
T>TC
C :
: QGP QGP -
pQCD limit limit at higher at higher temperatures temperatures
T<TC
C:
: fast increase of the ratio fast increase of the ratio η η η η η η η η/s /s for for hadronic matter hadronic matter
lower interaction rate of hadronic system system
smaller number of degrees of freedom (or entropy density) (or entropy density) for hadronic for hadronic matter compared to the QGP matter compared to the QGP
QGP QGP in PHSD in PHSD = = strongly strongly-
interacting liquid
η η η η η η η η/s /s using using Kubo formalism Kubo formalism and the and the relaxation time approximation relaxation time approximation (‚kinetic theory‘) (‚kinetic theory‘)
Virial expansion: Virial expansion: S.
Mattiello, , W.
Cassing, , Eur
. Phys. J. C 70, 243 (2010). (2010).
064903
QGP QGP
28 28
the QCD QCD matter matter even at T even at T~ ~ T Tc
c is a
is a much better much better electric conductor than Cu or Ag electric conductor than Cu or Ag (at room (at room temperature temperature) ) by a factor of 500 ! by a factor of 500 !
The response of the strongly-
interacting system in equilibrium to an system in equilibrium to an external electric external electric field field eE eEz
z defines the
defines the electric conductivity electric conductivity σ σ σ σ σ σ σ σ0
0:
:
29 29
T-
30 30
Central Pb + Pb at SPS energies Central Pb + Pb at SPS energies
PHSD gives harder m harder mT
T spectra
spectra and works better than HSD and works better than HSD at high energies at high energies – – RHIC, SPS (and top FAIR, NICA) RHIC, SPS (and top FAIR, NICA)
however, at low SPS (and low FAIR, NICA) energies the effect of the partonic phase the partonic phase decreases due to the decrease of the partonic fraction decreases due to the decrease of the partonic fraction Central Au+Au at RHIC Central Au+Au at RHIC
NPA856 (2011) 162 NPA856 (2011) 162
31 31
enhanced production of (multi-
) strange antibaryons in PHSD relative to HSD relative to HSD strange strange antibaryons antibaryons _ _ _ _ Λ Λ Λ Λ Λ Λ Λ Λ+ +Σ Σ Σ Σ Σ Σ Σ Σ0 multi multi-
strange antibaryon antibaryon _ _ Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ+
+
100 200 300 400 0.00 0.01 0.02 0.03 0.04 0.05 0.06 100 200 300 400 0.000 0.002 0.004 0.006 0.008 0.010
NA57 NA49 HSD PHSD
Λ
Λ Λ Λ+Σ Σ Σ Σ
Nwound Nwound
Pb+Pb, 158 A GeV, mid-rapidity
_ _ Λ+Σ
Λ+Σ Λ+Σ Λ+Σ
dN/dy | y=0 / Nwound
100 200 300 400 10
10
10
100 200 300 400 10
10
HSD PHSD NA57 NA49
Ξ
Ξ Ξ Ξ
− − − −
dN/dy | y=0 / Nwound
__ __ __ __
Ξ
Ξ Ξ Ξ
+ + + +
Pb+Pb, 158 A GeV, mid-rapidity
Nwound Nwound
multi multi-
strange baryon baryon Ξ Ξ Ξ Ξ Ξ Ξ Ξ Ξ
− − − − − − − −-
strange baryons baryons Λ Λ Λ Λ Λ Λ Λ Λ+ +Σ Σ Σ Σ Σ Σ Σ Σ0
Cassing & Bratkovskaya, NPA 831 (2009) 215 Cassing & Bratkovskaya, NPA 831 (2009) 215
32 32
x z
33 33
Non central Non central Au+Au Au+Au collisions : collisions :
interaction nteraction between constituents between constituents leads to a leads to a pressure pressure gradient gradient => spatial asymmetry => spatial asymmetry is is converted converted to to an an asymmetry in momentum space asymmetry in momentum space => => collective flow collective flow v v2
2 > 0
> 0 indicates indicates in in-
plane emission of particles emission of particles v v2
2 < 0
< 0 corresponds to a corresponds to a squeeze squeeze-
perpendicular to the reaction plane ( to the reaction plane (out
plane emission) emission) v v2
2 > 0
> 0
from S. A. Voloshin, arXiv:1111.7241 from S. A. Voloshin, arXiv:1111.7241
34 34
Flow coefficients reach their asymptotic values reach their asymptotic values by the time of 6 by the time of 6– –8 fm 8 fm/c /c after after the beginning of the collision the beginning of the collision
Time evolution of Time evolution of v vn
n for Au + Au collisions at
for Au + Au collisions at s s 1/2
1/2 = 200 GeV with impact
= 200 GeV with impact parameter parameter b b = 8 fm. = 8 fm.
35 35
2 vs. collision energy for Au+Au
v2
2 in PHSD is larger than in HSD
in PHSD is larger than in HSD due to due to the repulsive scalar mean the repulsive scalar mean-
field potential U Us
s(
(ρ ρ) for partons ) for partons
v2
2 grows with bombarding energy
grows with bombarding energy due to due to the increase of the parton fraction the increase of the parton fraction
36 36
The mass splitting at low pT
T is approximately reproduced as well as the
is approximately reproduced as well as the meson meson-
baryon splitting for pT
T > 2 GeV/c !
> 2 GeV/c !
The scaling of v scaling of v2
2 with the number of constituent quarks n
with the number of constituent quarks nq
q is roughly in
is roughly in line with the data at RHIC. line with the data at RHIC.
NPA856 (2011) 162 NPA856 (2011) 162
37 37
38 38
iessen Joachim Stroth
Dilepton sources: Dilepton sources:
from the QGP via partonic (q,qbar, g) interactions:
from hadronic sources:
direct decay of vector mesons ( mesons (ρ,ω,φ, ρ,ω,φ, ρ,ω,φ, ρ,ω,φ, ρ,ω,φ, ρ,ω,φ, ρ,ω,φ, ρ,ω,φ,J J/Ψ,Ψ /Ψ,Ψ /Ψ,Ψ /Ψ,Ψ /Ψ,Ψ /Ψ,Ψ /Ψ,Ψ /Ψ,Ψ‘ ‘) )
Dalitz decay of mesons and baryons ( and baryons (π π π π π π π π0
0,
,η η η η η η η η, , ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆, ,… …) )
correlated D+Dbar pairs
radiation from multi-
meson reactions (π π π π π π π π+ +π π π π π π π π, , π π π π π π π π+ +ρ ρ ρ ρ ρ ρ ρ ρ, , π π π π π π π π+ +ω ω ω ω ω ω ω ω, , ρ ρ ρ ρ ρ ρ ρ ρ+ +ρ ρ ρ ρ ρ ρ ρ ρ , , π π π π π π π π+a +a1
1)
) -
‚4 4π π π π π π π π‘ ‘
Dileptons are an ideal probe an ideal probe to study the to study the properties of the hot and dense medium properties of the hot and dense medium
γ γ γ γ γ γ γ γ* * g g γ γ γ γ γ γ γ γ* * γ γ γ γ γ γ γ γ* * q q l+ l-
γ γ γ γ γ γ γ*
*
q q q q q q q q q q q q g g g g q q
Dileptons are emitted from different stages of the reaction and not much effected by final not much effected by final-
state interactions
39 39
Mass region above 1 GeV GeV is dominated is dominated by by partonic partonic radiation radiation ! ! Acceptance corrected NA60 data Acceptance corrected NA60 data
and C. and C.-
054917
Contributions of “ “4 4π π π π π π π π” ” channels channels ( (radiation from multi radiation from multi-
meson reactions) are are small small
40 40
T spectra
Inverse slope parameter Teff
eff for
for dilepton spectra vs NA60 data dilepton spectra vs NA60 data Conjecture: Conjecture:
spectrum from sQGP is softer than from hadronic phase since quark since quark-
antiquark annihilation occurs dominantly before the collective radial flow annihilation occurs dominantly before the collective radial flow has developed (cf. has developed (cf. NA60) NA60)
and C. and C.-
054917
41 41
The partonic partonic channels channels dominate at M>1 dominate at M>1 GeV GeV
42 42
pT
T cut enhances the signal of
cut enhances the signal of QGP( QGP(qbar qbar-
q)
helin,
Phys.Rev. C87 (2013) 014905; arXiv:1208.1279 ; arXiv:1208.1279
QGP(qbar qbar-
q) dominates at M>1.2 dominates at M>1.2 GeV GeV ! ! D D-
, B-
mesons: from from Pol Pol-
Bernard Gossiaux Gossiaux and and J Jö örg Aichelin rg Aichelin J/ J/Ψ, Ψ Ψ, Ψ Ψ, Ψ Ψ, Ψ Ψ, Ψ Ψ, Ψ Ψ, Ψ Ψ, Ψ’ ’: : from C.M. from C.M. Ko Ko and T. Song and T. Song
43 43
PHSD provides a consistent description of provides a consistent description of off
shell parton dynamics in line with the lattice QCD equation of state in line with the lattice QCD equation of state (from the BMW (from the BMW collaboration) collaboration)
PHSD versus experimental observables experimental observables: : enhancement of meson m enhancement of meson mT
T slopes (at top SPS and RHIC)
slopes (at top SPS and RHIC) strange antibaryon enhancement (at SPS) strange antibaryon enhancement (at SPS) partonic emission of high mass dileptons at SPS and RHIC partonic emission of high mass dileptons at SPS and RHIC enhancement of collective flow v enhancement of collective flow v2
2 with increasing energy
with increasing energy quark number scaling of v quark number scaling of v2
2 (at RHIC)
(at RHIC) … …
44 44
What is the stage of matter close to T What is the stage of matter close to Tc
c :
:
1st order phase transition?
‚Mixed Mixed‘ ‘ phase = interaction of partonic phase = interaction of partonic and hadronic degrees of freedom? and hadronic degrees of freedom?
(V.D. Toneev et al.) (V.D. Toneev et al.)
Open problems: Open problems:
How to describe a first first-
transition transition in transport models? in transport models?
How to describe parton-
hadron interactions in a ‚mixed‘ phase a ‚mixed‘ phase? ?
Lattice EQS for Lattice EQS for µ µ µ µ µ µ µ µ=0 =0
‚crossover‘ , T > Tc
c
45 45
Baryonic matter Baryonic matter || || Meson and baryon Meson and baryon spectroscopy spectroscopy In In-
medium effects EoS EoS
0.1 1 10 100 1000 10000 100000
Low Low Intermediate Intermediate High High Ultra Ultra-
High E Ebeam
beam [A
[A GeV] GeV] SIS SIS FAIR FAIR NICA NICA SPS SPS RHIC RHIC LHC LHC
‚ ‚Mixed Mixed‘ ‘ phase: phase: hadrons (baryons, mesons) + hadrons (baryons, mesons) + quarks and gluons quarks and gluons || || In In-
medium effects Chiral symmetry restoration Chiral symmetry restoration Phase transition to sQGP Phase transition to sQGP Critical point in the QCD phase Critical point in the QCD phase diagram diagram QGP: quarks and gluons QGP: quarks and gluons || || Properties of sQGP Properties of sQGP
BM@N BM@N
46 46
Wolfgang Cassing Wolfgang Cassing (Giessen Univ.) (Giessen Univ.) Volodya Konchakovski Volodya Konchakovski (Giessen Univ.) (Giessen Univ.) Olena Linnyk Olena Linnyk (Giessen Univ.) (Giessen Univ.) Elena Bratkovskaya Elena Bratkovskaya (FIAS & ITP Frankfurt Univ.) (FIAS & ITP Frankfurt Univ.) Vitalii Ozvenchuk Vitalii Ozvenchuk (HGS (HGS-
HIRe, FIAS & ITP Frankfurt Univ.) Rudy Marty Rudy Marty (FIAS, Frankfurt Univ.) (FIAS, Frankfurt Univ.) Hamza Berrehrah Hamza Berrehrah (FIAS, Frankfurt Univ.) (FIAS, Frankfurt Univ.) Daniel Cabrera Daniel Cabrera (ITP&FIAS, Frankfurt Univ.) (ITP&FIAS, Frankfurt Univ.) External Collaborations: External Collaborations: SUBATECH, Nantes Univ. : SUBATECH, Nantes Univ. : J Jö örg Aichelin rg Aichelin Christoph Hartnack Christoph Hartnack Pol Pol-
Bernard Gossiaux Texas A&M Univ.: Texas A&M Univ.: Che Che-
Ming Ko JINR, Dubna: JINR, Dubna: Vadim Voronyuk Vadim Voronyuk Viatcheslav Toneev Viatcheslav Toneev Kiev Univ.: Kiev Univ.: Mark Gorenstein Mark Gorenstein Barcelona Univ. Barcelona Univ. Laura Tolos, Angel Ramos Laura Tolos, Angel Ramos Wayne State Uni. Wayne State Uni. Sergei Voloshin Sergei Voloshin