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GOING WITH THE FLOW
What the data from RHIC
have taught us so far
Berndt Mueller (Duke University)
大阪大学 , 14 October 2005
The quest for simplicity
Before 1975, nuclear matter at
high energy density was
considered a real mess !
QCD predicts that hot matter
becomes simple – the QGP
(not necessarily weakly
interacting!).
Characteristic features:
deconfinement and chiral
symmetry restoration (i.e.
quarks lose their dynamically
generated mass).
W f0 h
S* L K a1
N r N* p S
h’ a
X
0 D f
p
Hadronic resonance gas
_g
s
d
_
d s g
_ g d
u
d
g
g_
g u_
u g u
Quark-gluon plasma
The QCD phase diagram
RHIC
T
Critical
endpoint ?
QuarkGluon
Plasma
Tc
Chiral symmetry
restored
Hadronic
matter
1st order
line ?
Chiral symmetry
broken
Nuclei
Colour
superconductor
Neutron stars
B
QCD equation of state
20%
Free massless
particle limits
p 2
30
Tc = 175 10 MeV
Lattice gauge theory provides a model independent answer (for B=0).
T
4
The space-time picture
Thermal freezeout
Hadronization
Equilibration
The path to the Q-G plasma…
…Is Hexagonal and 2.4 Miles Long
The Relativistic Heavy Ion Collider at
Brookhaven National Laboratory
STAR
RHIC data collection
Charged particle tracks from
a central Au+Au collision
RHIC has had runs
with:
Au+Au at 200, 130, 62
and 19.6 GeV
Cu+Cu at 200, 62 GeV
d+Au at 200 GeV
p+p at 200, 130 GeV
Frequently asked questions
How do we know that we have produced equilibrated
matter, not just a huge bunch of particles ?
What makes this matter special ?
How do we measure its properties ?
Which evidence do we have that quarks are
deconfined for a brief moment (about 10-23 s) ?
Which evidence do we have for temporary chiral
symmetry restoration ?
What do we still need to learn ?
Translation: When can RHIC be closed down ?
FAQ #1
How do we know that we produced equilibrated matter,
not just a bunch of particles ?
Answer:
Particles are thermally distributed and flow collectively !
Chemical equilibrium
Chemical equilibrium fits
work, except where they
should not (resonances
with large rescattering).
RHIC Au+Au @ 200 GeV
= 160 10 MeV
µB = 24 5 MeV
Tch
Central Au-Au √s=200 GeV
STAR Preliminary
10
The “elliptic” flow (v2)
Coordinate
space:
initial
asymmetry
Momentum
space:
final
asymmetry
y
Pressure
gradient
py
x
collective
flow
Two-particle correlations
dN/d(f1- f2) 1 + 2v22cos(2[f1- f2])
FAQ #2
What makes this matter special ?
Answer:
It flows astonishingly smoothly !
“The least viscous non-superfluid ever seen”
v2 requires low viscosity
Relativistic viscous fluid dynamics:
T 0
with
T ( P)u u Pg h ( u u trace)
Shear viscosity h tends to smear out the effects of sharp gradients
pQCD:
h
4T 3
r p 2 1
3 s ln s
Dimensionless quantity
shear viscosity h
1
entropy density s 15 s2 ln 1s
Viscosity must be ultra-low
v2 data comparison with (2D) relativistic hydrodynamics
results suggests h/s 0.1
Recent excitement:
D. Teaney
Quantum lower bound on h/s :
h/s = 1/4p (Kovtun, Son, Starinets)
Realized in strongly coupled (g1)
N = 4 SUSY YM theory, also in QCD ?
QGP(T≈Tc) = sQGP
h/s = 1/4p implies f ≈ (5 T)-1 ≈ 0.3 d
An sQGP liquid?
For realistic gE, perturbative quasiparticles are short-lived:
Mass: m*g (0)
1
3
g ET 1.2 T
Width: g (0) 2 g (0)
1
2p
(for g E 2)
g E2 T 1.5 T
Similar relationship for quarks: /m* ≈ 1.3
Suggestive scenario:
As T Tc+0, /m* increases, QGP quasiparticles (gluons,
quarks, plasmons, plasminos) become broad and short-lived.
As T Tc-0, /m* increases, hadrons (mesons, baryons)
become broad and short-lived resonances.
Schematic scenario
Hadrons exchange
quarks rapidly and
become short-lived
resonances
HG
Quarks and gluons
collide frequently
and form shortlived “resonances”
sHad sQGP
liquid
Hagedorn
Tc
QGP
????
T
FAQ #3
How do we unambiguously measure its properties ?
Answer:
With hard QCD probes,
such as jets, photons, or heavy quarks
Parton energy loss (aka: jet quenching)
High-energy parton loses energy by
rescattering in dense, hot medium.
q
q
Radiative energy loss:
dE / dx r L kT 2
L
Scattering centers = color charges
q
q
Density of
scattering centers
g
d
2
2
qˆ r q dq
r kT
2
dq
2
Scattering power of
the QCD medium:
2
Range of color force
Pions vs. photons
Deviation from binary NN collision scaling:
RAA
p /
N AA
p /
N coll N pp
Photons
Hadrons
Energy loss at RHIC
Data are described by a very large loss parameter for
central collisions: (Dainese, Loizides, Paic, hep-ph/0406201)
RHIC data
qˆ 5 10 GeV2 /fm
sQGP
QGP
R. Baier
Pion gas
Cold nuclear matter
pT = 4.5 – 10 GeV/c
Larger than expected from
perturbation theory ?
Test case: RAA for charm
Heavy quarks (c, b) should lose
less energy by gluon radiation,
but…
…experiment (STAR, PHENIX)
observe strong suppression up
to RAA ~ 0.2 observed in most
central events.
Is collisional energy loss much
larger than expected?
FAQ #4
Which evidence do we have that quarks are deconfined
for a brief moment (about 10-23 s) ?
Answer:
Baryons and mesons are formed
from independently flowing quarks
Baryons vs. mesons
What makes baryons
different from mesons ?
Hadronization mechanisms
Meson
q
Meson
q q
q
q
q q q
Baryon
Recombination
Fragmentation
Baryon
Meson
1
Baryon
1
Meson
pM 2 pQ
from dense system
pB 3 pQ
Recombination always wins …
… for a thermal source
Fragmentation
still wins for a
power law tail
Baryons compete
with mesons
Recombination - fragmentation
R.J. Fries, BM, C. Nonaka, S.A. Bass
pQCD spectrum
shifted by 2.2 GeV
Teff = 350 MeV
blue-shifted
temperature
T = 180 MeV
Hadron v2 reflects quark flow !
Recombination model
suggests that hadronic
flow reflects partonic
flow (n = number of
valence quarks):
v had
2
had
pT
Provides measurement
of partonic v2 !
part
nv 2
part
npT
FAQ #5
Which evidence do we have for temporary
chiral symmetry restoration ?
Strangeness at RHIC
Mass (MeV)
1000000
QC D mass
100000
Hig g s mass
10000
1000
(sss)
QCD mass
disappears
(qss)
100
(qqs)
10
1
u
d
s
c
Flavor
b
t
FAQ #6:
What do we still need to (or want to) learn ?
Number of degrees of freedom:
via energy density – entropy relation.
Color screening:
via dissolution of heavy quark bound states (J/Y).
Chiral symmetry restoration:
modification of hadron masses via e+espectroscopy.
Quantitative determination of transport properties:
viscosity, stopping power, sound velocity, etc.
What exactly is the “s”QGP ?
QCD equation of state
20%
p 2
30
Challenge: Devise method for determining
from data
T
4
from and s
BM & K. Rajagopal, hep-ph/0502174
Eliminate T from and s :
p2 4
T
30
2p 2 3
s
T
45
1215 s 4
s4
0.96 3
2
3
128p
Lower limit on requires lower limit on s
and upper limit on .
Measuring and s
Entropy is related to produced particle number and is
conserved in the expansion of the (nearly) ideal fluid:
dN/dy → S → s = S/V.
dS/dy = 5100 ± 400 for Au+Au (6% central, 200 GeV/NN)
Yields: s = (dS/dy)/(pR2t0) = 33 ± 3 fm-3
Energy density is more difficult to determine:
Energy contained in transverse degrees of freedom is not
conserved during hydrodynamical expansion.
Focus in the past has been on obtaining a lower limit on ; here
we need an upper limit.
New aspect at RHIC: parton energy loss.
Where does Eloss go?
p+p
Away-side jet
Au+Au
Trigger jet
Lost energy of away-side jet is redistributed to rather large angles!
Wakes in the QGP
J. Ruppert and B. Müller, Phys. Lett. B 618 (2005) 123
Mach cone requires
collective mode with w(k) < k:
Colorless sound
? Colored sound = longitudinal gluons
? Transverse gluons
pQCD (HTL)
dispersion relation
Collective modes in medium
Longitudinal
(sound) modes
“Colored”
sound
Normal
sound
Transverse modes
Mach cone structures from a spacelike longitudinal plasmon branch:
Cherenkov-like gluon radiation into a
space-like transverse gluon branch:
J. Ruppert & B. Müller, Phys. Lett. B 618 (2005) 123
I. Dremin
A. Majumder, X.-N. Wang, hep-ph/0507062
Mach cone from sonic boom:
H. Stoecker
J. Casalderrey-Solana & E. Shuryak
Jet-Medium Interactions
Renk & Ruppert. hep-ph/0509036
Angular distribution and size of
off-jet axis peak depends on:
Energy fraction in
collective mode
Propagation velocity
Collective flow pattern
Note: f = 0.9 is a very large
collective fraction requiring an
extremely efficient energy
transfer mechanism!
Outlook
The “discovery phase” of RHIC has already uncovered
several surprises: near-ideal liquid flow, valence quark
number scaling of v2; very large partonic energy loss.
Several important observables are still waiting to be
explored. Run-4 and -5 data (just coming out!) are
beginning to provide some of the needed information.
The RHIC data are posing many well defined theoretical
challenges, such as:
Structure of QCD matter near Tc ?
Thermalization mechanisms in gauge theories ?
Transport coefficients in gauge theories ?
A new window of calculable hadronization ?
Special thanks to…
Steffen Bass
Jörg Ruppert
Chiho Nonaka
Thorsten Renk
Rainer Fries
Yuki Asakawa