New Directions” - Duke University
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Transcript New Directions” - Duke University
Quark-Gluon Plasma
From Concepts
To “Precision” Science
Berndt Mueller
RHIC Users Meeting
BNL - March 28, 2008
1
Part 1…
The Quest for the
Quark-Gluon Plasma
2
QCD phase diagram
T
RHIC
Critical
point?
QuarkGluon
Plasma
quarkgluon
plasm
a
nucleons
+
mesons
Melting nuclear
matter
Chiral symmetry
restored
Hadronic
matter
Chiral symmetry
broken
1st
order
line
Nuclei
Color
superconductor
Neutron stars
B
3
QCD equation of state
gluons
quarks
Degrees of freedom : (2 8) (2 3 N f ) 1 O( g )
2
7
4
spin
2
30
170
RHIC
color
340
spin
510
color flavor
MeV
Weak or
strong
coupling?
Lattice QCD
4
The QCD EoS (at =0)
The precise value of Tc is still under debate:
Tc = 170 ± 20 MeV with 20 - 30 MeV width.
EoS near Tc is far from ideal ultrarelativistic gas!
Sound velocity cs2 = P/ << 1/3.
5
Lattice - susceptibilities
C XS 3
XS X
S
2
S
S
2
pQGP
B
R4,2
4 ln Z / B 4
ln Z / B
2
2
:
B4
B2
Eijiri
Karsch
Redlic
h
QCD matter above Tc may be a highly correlated system, but what is
correlated are quarks and not hadrons! (What about gluons?)
6
Part 2…
The 6 Stages of the Collision
7
Liberation of
saturated low-x
glue fields (CGC)
teq
initial state
Pre-equil. phase
pre-equilibrium
QGP and
hydrodynamic expansion
hadronization
hadronic phase
and freeze-out
A multi-stage reaction
8
Stage 1
Decoherence of
the initial state
9
The initial state
The Color Glass Condensate model is based on a brilliant idea:
Baryon c1 qqq c2 qqqg c3 qqqqq L c435 qqq ggL g L
123
30
None of these components of the
baryon wave function are
calculable…
…but this one is,
because it contains a
large scale
What applies to the proton (at high energy!), applies much better to
a large nucleus, and at lower energy, because the gluon density per
area is enhanced by a factor A1/3.
10
Gluon saturation
Gribov, Levin, Ryskin ’83
Blaizot, A. Mueller ’87
~ 1/Q2
Qs2 ( x, A)
McLerran, Venugopalan ‘94
A1/ 3 x 0.3
gluon density area :
1
2
Qs
Universal saturated state at small x: Qs >> QCD
“Color glass condensate” (CGC)
/sat
x
p
A
Evolution in x is described by BK
or JIMWLK equations. Location of
the onset of saturation is
determined by fluctuations (Iancu,
Peschanski,…)
11
CGC: Gluon production
Fields carried by moving sources interact
non-linearly and generate classical
spectrum of gluonic modes. This requires
numerical solution of YM eqs. with CGC
initial cond’s.
Krasnitz-Nara-Venugopalan, Lappi,
Gelis
QuickT ime™ and a
decompressor
are needed to see t his picture.
Simulation of T(x,t)
possible.
Classical 2-particle rapidity correlations
(Dumitru et al. ‘08)
12
Stage 2
Entropy:
From 0 to (dS/dy=) 5000 in
0.000 000 000 000 000 000 000 002
seconds
13
Final entropy
Bjorken’s formula
dN (t ) / dy
s (t )
dV (t ) / dy
(dN / dy )final
2
R t
Phase space analysis (Pal & Pratt):
dS
dy
final
d 3rd 3 p
fi ln fi (1 fi )ln(1 fi )
3
(2 ) dy
i
5600 500
[for 6% central Au+Au @ 200]
Chemical analysis (BM & Rajagopal):
dS
dy
final
dNi
(S / N )i
5100 200
dy
i
[for same cond.]
Assuming isentropic expansion up to Tch, averaging over R2 with
R = 7 fm, and using lattice EOS:
s(t 0 1 fm/c) 33 fm-3 T(t 0 ) 300 MeV
How is this entropy produced?
14
Decoherence
Coherent
state:
Sdeco
e
/2
2
n
n!
mn n
decoherence
n
2
mn
n
1
ln 2 N 1 O N 1
2
with
N 3
2
Counting causally disconnected transverse
domains:
2 2
dSdec Qs R s 2CF ln 2
1 dS
ln
1 1500
2
dy
2
s
3 dy
In D dimensions after
equilibration:
(D)
eq
S
for Qs2 2 GeV2
final
4
DN
3
Clearly, fully 3-dimensional equilibration is essential - how and
when?
15
From 2D to 3D
1/Qs
Nielsen-Olesen instability of
longitudinal color-magnetic field
(Itakura & Fujii, Iwazaki)
2
(k
gA
)
1
z
gBz 0
2
2
t
t t
t
2
16
Weibel instability
v
v
rv
rv
B
17
Color “turbulence”
Wavelength and growth rate of unstable modes
can be calculated perturbatively:
kz ~ gQs , g ~ gQs < kz
Mrowczynski
Rebhan,Romatschke,
Strickland
Arnold, Moore, Yaffe
Dumitru, Schenke
Exponential growth
saturates when
B2 > g2 T4.
Turbulent power
spectrum
18
Turbulent color fields
Color
correlation
length
M. Strickland, hepph/0511212
Time
Nonabelia
n
Quasi
abelia
n
Noise
Length (z)
Extended domains of coherent color field can create “anomalous” contributions
to transport coefficients and accelerate equilibration (as in EM plasmas).
19
Stage 3
The (almost) perfect liquid
20
Collision Geometry: Elliptic Flow
Reaction
plane
Bulk evolution described by
relativistic fluid dynamics,
assumes that the medium is in
local thermal equilibrium,
but no details of how equilibrium
was reached.
Input: (x,ti), P(), (,etc.).
z
y
x
Elliptic flow (v2):
• Gradients of almond-shape surface will lead
to preferential expansion in the reaction plane
• Anisotropy of emission is quantified by 2nd
Fourier coefficient of angular distribution: v2
prediction of fluid dynamics
21
v2(pT) vs. hydrodynamics
Mass splitting characteristic
property of hydrodynamics
22
Elliptic flow “measures” QGP
Relativistic viscous
hydrodynamics:
T 0 with
T ( P)u u Pg
d
du
t
u u
u
u
trace
d
t
d
t
np f
1
3
p
3 tr
Boost invariant hydrodynamics with
T0t0 ~ 1 requires /s ≤ 0.1
Small shear viscosity implies:
Romatschke &
Romatschke
The QGP is an almost perfect
liquid
23
String theory weighs in
General argument [Kovtun, Son & Starinets, PRL 94 (2005) 111601]
based on duality between thermal QFT and string theory on
curved background with the “black-brane” metric:
(3+1)-D world
(t,x)
(0,0
)
r0
horizon
1
r0
T
Dominated by absorption of (thermal) gravitons by the black hole:
abs
8 G
3
i t
dt
d
x
e
T
t,
x
,T
0,0
a (horizon area)
0
xy
xy
Therefore:
abs (0) 4G 1
s 16 G a 4
24
An age-old problem solved!
Shear and bulk viscosity are defined as coefficients in the
expansion of the stress tensor in gradients of the velocity field:
Tik ui uk P ik ui uk i uk k ui 23 ik u ik u
Unfortunately, this renders relativistic viscous hydrodynamics a-causal !
Solution, in principle: include time derivatives (Israel,Stewart, Müller - 1960s).
Full second-order expression for shear stress in conformal limit finally given by
Baier, Romatschke, Son, Starinets & Stephanov (arXiv:0712.2451):
u
t s u
d 1
1 2
2 3
25
Viscosity of RHIC
Tc
Peq
PL
PT
1
PT Peq
2
PT Peq
R.J.Fries, BM,
A. Schäfer, tbp
d 4
4t s
1 2
ts
1
2
dt
3t
3t
2
d
tb
dt t
z H1êfm^3L, h H1êfm^3L
/ s, / s
PL (t 0 ) 0
from lattice
2 0.0
1 0.0
5 .0
2 .0
1 .0
0 .5
0 .2
Lattice EOS
0 .1
0 .1
0 .2
Tc
2 ln 2
ts tb
2 T
0 .3
0 .4
0 .5
0 .6
T HGeVL
(N 4 SUSY)
26
Stage 4
Hadronizing the
Quark-Gluon Plasma
27
v2(pT) vs. hydrodynamics
Failure of ideal
hydrodynamics
tells us how
hadrons form
28
Quark number scaling of v2
In the recombination regime, meson and baryon v2 can be obtained
from the quark v2 :
pt
v pt 2v
2
M
2
q
2
pt
v pt 3v
3
B
2
q
2
qqq
T,,v
qq
Emitting medium is composed of
unconfined, flowing quarks.
29
CEP Observables
Observables that are not be sensitive to final state interactions
Critical fluctuations, the primary signature of the CEP, are modified
During expansion until chemical or kinetic freeze-out, in addition to
being suppressed near CEP by critical slowing down.
After Freeze-out, no effect of final state interactions
Chemical Freeze-out
T
Critical
point?
•
usually assumed to be
momentum independent
•
but this is not right
B
chemical freeze-out time
is pT (or yT) dependent
Larger pT (or yT),
earlier ch. Freeze-out
30
Emission Time Distribution
Emission Time
•
Larger yT, earlier emission
•
To minimize resonance effect,
yT is used instead of pT
•
No CEP effect (UrQMD)
31
Focus on chemistry
Tc
pT
Tc
Asakawa, Bass,
BM, Nonaka ‘08
p / p ratio near CEP falling with pT
32
RHIC can do it!
STAR PRELIMINARY
33
Part 3…
Probing the structure
of the Quark-Gluon Plasma
34
Energy loss in QCD
Radiative
energy loss:
q
sC2
dE
ö
qL
dx
4
q
Density of
scattering centers
d
2
i
qö q dq
kT dx Fi (x )F (0)
2
dq
2
2
Scattering power of
the QCD medium:
Nonradiative energy loss:
Range of color force
dE
sC2 2
y
ET
mD 1 2 lnc 2
dx
4
mD
ug
35
Towards q-hat
3-D ideal hydrodynamics with
radiative energy loss only
ASW HT AMY
qˆ0 (GeV/fm3 ) ~10
~2
~4
~20 ~4
T3
3/4
Bass, Majumder, Qin, Renk et al. (tbp)
Numbers change by up to factor
of 2, depending on whether q-hat
is scaled with T3, s, or 3/4 !
Other unresolved issues:
Consistent treatment of virtuality
of parton created by hard
scattering;
Nature of scattering centers
36
Closing in on q-hat
RAA vs. reaction
plane
More differential measurements
of jet quenching with very high
statistics are needed, as well as
consistent theories of jet
quenching for these observables.
Bass et al.
Zhang et al.
(using higher
twist energy
loss theory +
back-to-back
coincidences)
37
Collisions + radiation
Qin, Ruppert, Gale, Jeon, Moore & Mustafa, PRL 100,072301 (2007)
collisons
radiation
coll+rad
collisons
radiation
coll+rad
Inclusion of collisional energy
loss leads to reduction of s
from 0.33 to 0.27, corresponding
to a reduction of extracted value
of q-hat by 33%.
Contributions from collisional and radiative energy loss may be separated due to their
different fluctuations (Poisson vs. intermittent) by comparing singles quenching (RAA)
with coincident back-to-back quenching (IAA), and by their different quark mass
dependence by comparing with charm RAA.
38
Connecting jets with the medium
Hard partons probe the medium via the density of colored scattering
centers:
qö q 2 dq 2 d / dq 2 : dx F (x )F (0)
If kinetic theory applies, thermal gluons are quasi-particles that
experience the same medium. Then the shear1 viscosity is:1
p
p f ( p)
3
tr ( p)
In QCD, small angle scattering
dominates:
With p ~ 3T and s
3.6 (for gluons) one
finds:
From RHIC
data:
T3
1.25
s
qˆ
3 tr ( p)
2qˆ
p
2
A. Majumder, BM, X-N. Wang,
PRL 99 (2007) 192301
T0 335 MeV, qˆ0 2.8 GeV2 /fm ( / s)0 0.10
39
An interesting question
How does a fast parton
interact with the quarkgluon plasma ?
QuickTime™ and a
decompressor
are needed to see this picture.
Trigger jet
Back jet
What happens to the
energy and momentum
lost by a fast parton on
its passage through the
hot medium ?
How does the energy
and momentum
perturbation of the
medium propagate ?
Hard
scattering
QuickTime™ and a
decompressor
are needed to see this picture.
Thanks to:
E. Wenger
(PHOBOS)
What happens here ?!?
40
Parton-medium coupling
p
E x p D(x, p) p f0 x, p C f0
with
t
r
r r
Dij (x, p) dt ' Fi x,t Fj x v(t ' t),t ' .
T
J
x
Color field of moving
parton interacts with the
quanta of the medium
Space-time
distribution
of
collisional
eneregy
Tloss
T p u u pg
diss
with
J
dp
p
p D(x, p) p f (x, p)
41
Unscreened source
For an unscreened color charge, an analytical result is obtained in u1
limit:
r
0 r 0
R.B. Neufeld
J (x) J , uJ JV with
z
J 0 (x) f ( , z,t) g u 2 1 2 2
z
r
JV (x) f ( , z,t)
f ( , z,t)
1/2
r r 2 2
x ut
2g z (u 2 2) 2
u44
1/2
2
2 2
2
2
2
g z
g z
2 g 2 z 2
g 2Q%2 mD2
32 g (z ut)
2
g u 2
z
2
2 2
g
z
2
2
2
3/2
3/2
2uz
g
, z z ut
Spatial integral over deposited energy and momentum distribution equals
collisional energy loss; radiated gluons increase effective color charge.
42
Linearized hydro
Linearize hydro eqs. for a weak source: T00 + , T0i
gi .
r
r
4
r
r
0
2
g J
g cs
g J
t
t
0 p0 3
Solve in Fourier space for longitudinal sound:
i k J
i
2
0
s
k JL
2 cs2 k 2 i s k 2
cs2 k J 0 J L
gL i 2
cs2 k 2 i s k 2
JT
… and dissipative transverse perturbation: gT i
43 i s k 2
Use:
u 0.99955c,
1
c ,
3
2
s
1
s
3 T
for T 350 MeV.
See: J. Casalderrey-Solana, E.V. Shuryak and D. Teaney, arXiv:hepph/0602183
43
pQCD vs. N=4 SYM
u = 0.99955 c
Neufeld et al.
arXiv:0802.225
4
Chesler &
Yaffe
arXiv:0712.005
0
u = 0.75 c
44
Mach cone: cs and η
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
Plasma behind
jet:
Correlated flow,
not just thermal !
/ s 0.13
[Xu & Greiner]
/ s 0.48
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
[Arnold, Moore
& Yaffe (AMY)]
45
RHIC data
Away side shape modification
Central Au+Au 0-12% (STAR)
2.5 < pTtrig< 4 GeV/c
1< pTassoc < 2.5 GeV/c
Technique: Measure 2- and 3particle correlations on the awayside triggered by “high” pT hadron in
central coll’s. Cone-shaped
emission should show up in 3particle correlations as signal on
both sides of backward direction.
(1-2)/2
46
Summary 1
The RHIC program has shown that
• equilibrated matter is rapidly formed in heavy ion collisions;
• new, powerful probes become available at collider energies;
• systematic study of matter properties is possible.
QGP appears to be a strongly coupled, maybe turbulent color liquid with
novel and unanticipated transport properties.
Experimental and theoretical surprises have opened a gold mine for
theorists:
• extreme opaqueness of matter to colored probes;
• collective flow phenomena;
• collective medium response to jets;
• large enhancement of baryon production;
• connection to string theory and AdS/CFT duality.
47
Summary 2
Ultimate success of the RHIC program requires:
• precision data for key (often rare) observables;
• continued progress of our understanding of thermal QCD;
• sustained collaboration between theorists and experimentalists on
precision data interpretation.
Superficially different observables (flow, jet quenching, two-particle
correlations) are connected at a deep level.
Their exploration in a comprehensive framework will lead to deep insights
into how bulk QCD matter behaves and, ultimately, to the fulfillment of the
scientific promise of RHIC.
The LHC heavy ion program will help resolve ambiguities, due to its
extended kinematic range for critical observables.
48
Summary 3
Experimental and theoretical surprises have opened a gold mine for
theorists, but to extract the gold, painstaking work will be required in
collaboration between theorists and experimentalists.
The first steps have been taken:
QuickTime™ and a
decompressor
are needed to see this picture.
For report and details see:
https://wiki.bnl.gov/TECHQM/index.php/Main_Page
49
THE END
50