Transcript No Slide Title

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 (g1)
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