The Flavors of the
Quark-Gluon Plasma
Berndt Mueller
SQM 2008
北京 - October 6-10, 2008
The QGP is a strange
state of matter
2
QCD phase diagram
T
Strange quarks play crucial role in
shaping the QCD phase diagram:
QuarkGluon
Critical
end point?
•
•
•
Plasma
Hadronic
matter
Chiral
symmetry
broken
1st order
line
Chiral symmetry
restored
U(1)A critical
end point ?
Nuclei
Location of critical point(s)
Stability of neutron stars
Structure of CSC phase
Color superconductor
Neutron stars
µB
3
QGP & quark flavor
quark-gluon
plasma
nucleons +
mesons
Melting nuclear matter
s, c, and b quarks are important
probes of hadronic matter:
- they are hard to produce
(s below Tc ; c and b above Tc)
- quark flavor conserved under
strong interactions
c and b are also hard probes, i. e.
their production can be reliably
calculated in pQCD.
4
Color screening
Induced color density
φa
Static color charge
(heavy quark) generates
screened potential
5
Quark masses
Higgs
quark
field
Quark
quark
condensate
Heat “melts” the quark condensate:
QCD mass disappears above Tc.
(Partial) chiral symmetry restoration
6
Confinement

The mechanism behind quark confinement in the vacuum is still not
well understood, but it is quantitatively described by lattice QCD.

Quark confinement above Tc disappears due to color screening.

Effective description of quark confinement and the deconfinement
transition exists: Polyakov loop model (P-NJL).
!
Lr = P exp ig
3 = N

−1
c
"
β
0
dτ Ab4
( tr L3 ) = ( e
1
3
iφ1
λbr
(x, τ )
2
+e
iφ2
+e
#
−i(φ1 − φ2 )
P-loop average projects color rep’s.
)
〈tr L〉= 0 → Confinement
〈tr L〉= 1 → Deconfinement
Interplay between P-loop and quark condensate explains coincidence
of Tc for deconfinement and chiral symmetry restoration.
7
PNJL phenomenology
Fukushima; Roessner, Ratti, Weise; ...
8
Strangeness enhanced
2
The original idea (Rafelski):
N(s ) 1 ⎛ ms ⎞
= ⎜ ⎟ K 2 ( ms / T ) eµB /(3T ) = 1 5
N(q ) 2 ⎝ T ⎠
“We almost always have more s than u or d quarks. When
quark matter reassembles into hadrons, some of the numerous
s quarks may, instead of being bound into kaons, form multiply
strange antibaryons, such as Λ, Ξ, Ω .”
gg → ss is essential for rapid strangeness equilibration ! (JR & BM)
Almost 30 years of investigation: The liberation of quark and gluon
degrees of freedom (not necessarily thermalization) is required for
strangeness equilibration.
9
s-enhancement at RHIC
(sss)
(qss)
(qqs)
★ STAR
★ STAR
10
s-production revisited
3-flavor PNJL model (Fukushima):
fq (k) =
Hung-Ming Tsai
!!3 "λ+ + 2!!3 "λ2+ + λ3+
1 + 3!!3 "λ+ + 3!!3 "λ2+ + λ3+
!q̄q"
!!3 "λ− + 2!!3 "λ2− + λ3−
fq̄ (k) =
1 + 3!!3 "λ− +
3!!3 "λ2−
+
λ3−
!!8 "4/9
λ± = exp[−(E(k) ∓ µ)/T ]
with
!!3 "
∞
!
1
fg (k) =
!tr Ln8 "e−n|k|/T
8 n=1
1
Aq =
2
!
1
Ag =
2
∞
4m2s
!
dss
∞
4m2s
"
$
4m2q #
2
1−
δ s − (k1 + k2 ) σ̄qq̄→ss̄ (s)
s
"
2
dss δ s − (k1 + k2 )
#
σ̄gg→ss̄ (s)
!s̄s"
!
!
d3 k1
d3 k2
(2 × 36)fq (k1 )fq̄ (k2 )
3
3
(2π) E(k1 ) (2π) E(k2 )
d3 k2
1
d3 k1
( × 256)fg (k1 )fg (k2 )
3
3
(2π) |k1 | (2π) |k2 | 2
11
Parton distributions
Ratio of quark distribitions functions for µ=0.1 GeV
Ratio of gluon distribitions functions
1.2
T=0.3 GeV
T=0.2 GeV
1
T=0.18 GeV
1
T=0.2 GeV
T=0.18 GeV
T = 300 MeV
0.8
0.8
Quarks
f g / f BE
f q / f FD
T=0.3 GeV
Hung-Ming Tsai
0.6
T = 300 MeV
0.6
T = 200 MeV
0.4
0.4
Gluons
T = 200 MeV
0.2
0.2
T = 180 MeV
T = 180 MeV
0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
k (GeV)
fi ( k; P )
T
/ fi ( k )
2
0
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
k (GeV)
2
Gluons more strongly suppressed near Tc than quarks,
in spite of additional mechanism for quarks (χSB).
12
ss rate in PNJL model
Hung-Ming Tsai
gg → ss
dominates
qq → ss
q and g disappear,
hadrons dominate
(hadronic rates
calculable in, e.g.:
(P)NJL model;
UrQMD, JAM)
13
Hadro-Chemistry
14
Chemical equilibrium
γ s / γ q = 1.00 ± 0.01
“Sudden” hadronization from deconfined state ?
15
Statistical model
Particle/antiparticle yield:
⎛ Ei ( p)  µi ⎞
Yi ( p) = γ i exp ⎜ −
⎟⎠
⎝
T
Baryons, e.g., Λ = (uds):
γ Λ = γ q2γ s , µ Λ = 2 µq + µ s
Mesons, e.g., K- = (sū):
γ K = γ sγ q , µ K = µ s − µ q
±
γ s / γ q = 1 implies relative equilibration of strange quarks.
γ s , γ q > 1 implies over-abundance of baryons.
RHIC data:
γs = γq = 1 for Tch ≈ 160-170 MeV;
or: γs > γq > 1 for Tch ≈ 140 MeV.
16
Out of equilibrium
Quality of data on identified hadrons and even resonances suggests that a
comprehensive assessment of the interplay between dynamical hadronization
and final-state hadron chemical reactions is timely.
It is well known that particle number changing reactions incrementally cease
as the hadron gas expands and cools, and γs,γq become greater than 1, even
if γs = γq =1 at hadronization: Chemical equilibrium at Tf,kin ≈ 100 MeV
underpredicts protons and antiprotons by factor ≈3 !
Theoretical tools (e.g. UrQMD or JAM cascades following hadronization)
exist to study the implications of any conceivable hadronization scenario.
Systematic comparisons of different scenarios in light of the RHIC (and SPS,
and soon LHC) data is missing.
Opportunity for Theory-Experiment collaboration.
17
v2(pT)
hadronization
Failure of ideal
hydrodynamics
tells us how
hadrons form:
New at RHIC !
Mass splitting characteristic
property of hydrodynamics
18
Quark number scaling of v2
In the recombination regime, meson and baryon v2 can be obtained
from the quark v2 :
v
M
2
( pT ) = 2v ( pT / 2 )
q
2
v
B
2
( pT ) = 3v ( pT / 3)
q
2
T,µ,v
Emitting medium is composed
of unconfined, flowing quarks.
19
Sudden hadronization ?
Precocious quark number scaling:
Accident or indicator of sudden hadronization ?
Bulk viscosity is large near Tc
H. Meyer
(quenched QCD)
peff = p − ς ∇ ⋅ v
ζ/s
Large ζ can induce thermodynamic instability
(Fries, BM, Schäfer, arXiv:0807.4333) or hydrodynamic
instabilities (Torrieri & Mishustin, arXiv:0805.0442),
forcing fireball to hadronize suddenly.
20
Probing beyond the hadronic horizon
with hadrons containing only
s-, c-, and b-quarks
21
Ω/ϕ probes
“ϕ-mesons are produced via coalescence of apparently thermalized quarks
in central Au+Au collisions. This observation implies hot and dense matter
with partonic collectivity has been formed at RHIC.” (STAR)
22
Heavy flavors: c, b

Production process is
unaffected by medium.

Transport & hadronization are
affected by medium - evidence:
RAA and v2 seen at RHIC.

Bound states dissolve in the
medium due to color screening
and thermal ionization - and
form by recombination near Tc ?

Comprehensive QCD-based
theoretical framework missing:
HQET + QCD-SR + HTL ?
Electrons from heavy flavor decays
23
Thermal charmonium?
Partonic flow ?
f (mT )  exp ( −mT / Ts )
J/ψ
Ω
★ STAR
Ξ
ϕ
24
Statistical charmonium ?
Formation of J/ψ by statistical recombination of perturbatively produced, later
thermalized charm quarks provides best representation of RHIC data:
Andronic, Braun-Munzinger,
Redlich & Stachel
25
The Future
26
Detector upgrades
STAR
forward meson spectrometer
DAQ & TPC electronics
Time of Flight barrel
heavy flavor tracker
barrel silicon tracker
forward tracker
PHENIX
-completed –
ongoing
in preparation
hadron blind detector
muon Trigger
silicon vertex barrel (VTX)
forward silicon
forward EM calorimeter
27
Higher energies…
CMS
LHC
ATLAS
ALICE
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Theory
★
Identify the model independent medium properties which can be determined
with the help of quark flavor probes (susceptibilities, chemical relaxation times,
diffusion coefficients, correlation/screening lengths, etc.) and develop robust
observables which can be measured with precision.
★
Develop a program involving collaboration among theorists and between
theorists and experimentalists to extract physics from data.
★
Adopt / join TEC-HQM model for hadronization and charm dynamics ?
https://wiki.bnl.gov/TECHQM/index.php
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THE END
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