Heavy Ion Collisions at RHIC
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Transcript Heavy Ion Collisions at RHIC
Heavy Ion Collisions at RHIC and
at the LHC: Physics Challenges
Urs Achim Wiedemann
SUNY Stony Brook and RIKEN BNL
Trieste, 25 May 2006
From elementary interactions to collective phenomena
1973: asymptotic freedom
QCD = quark model
+ gauge invariance
Today: mature theory with
a precision frontier
• background in search
for new physics
• TH laboratory for non-abelian
gauge theories
How do collective phenomena and macroscopic properties of matter
emerge from fundamental interactions?
QCD much richer than QED:
• non-abelian theory
2
• degrees of freedom change with Q
Question:
Why do we need collider energies
sNN 200GeV [RHIC]
sNN 5500GeV [LHC]
to test properties of dense QCD matter
which arise on typical scales
T 150 MeV , Qs 1 2 GeV ?
Answer 1: Large quantitative gains
Increasing the center of mass energy implies
Denser initial system
Longer lifetime
Bigger spatial extension
Stronger collective phenomena
A large body of experimental data from the CERN SPS
and RHIC supports this argument.
Answer 2: Qualitatively novel access to properties
of dense matter
2
To test properties of QCD matter, large- Q processes provide wellcontrolled tools (example: DIS).
Heavy Ion Collisions produce auto-generated probes at high sNN
Q T 150 MeV
Q: How sensitive are such ‘hard probes’?
Bjorken’s original estimate and its correction
Bjorken 1982: consider jet in p+p collision, hard parton interacts with
underlying event
collisional energy loss
dE coll dL 10 GeV fm
(error in estimate!)
Bjorken conjectured monojet phenomenon in proton-proton
But: radiative energy loss expected to dominate
E rad sqˆL2
• p+p:
Baier Dokshitzer Mueller Peigne Schiff 1995
L 0.5 fm, E rad 100 MeV
• A+A: L 5 fm, E rad 10 GeV
Negligible !
Monojet phenomenon!
Observed at RHIC
High pT Hadron Spectra
dN AA dpT d
RAA ( pT ,)
ncoll dN NN dpT d
0-5%
70-90%
Centrality dependence:
L large
L small
Centrality dependence: Au+Au vs. d+Au
●
Final state suppression
partonic
energy loss
●
Initial state enhancement
The medium-modified Final State Parton Shower
Gyulassy, X.N. Wang, BDMPS, Zakharov,GLV, ….
Wiedemann, NPB 588 (2000) 303
dI
sCR
2Re dy dy
2 2
d ln dkT (2 )
0
y
due
d n v u
ikT u y
Radiation off
produced parton
e
. K(s 0, y;u, y | )
u s
Target average includes Brownian motion:
y
2
2
K s, y;u, y | Drexp d i rÝ 2 14 qˆ ( )r
y
s r(y )
u r(y )
exp 14 qˆ (y y) r 2
• BDMPS transport coefficient is only model parameter sensitive to medium
• BDMPS transport coefficient can be defined model-independent as the
short-distance behavior of particular light-like Wilson loop in adjoint representation
W A (C) expqˆ L L2 /4
T
The medium-modified Final State Parton Shower
Baier, Dokshitzer, Mueller, Peigne, Schiff (1996); Zakharov (1997); Wiedemann (2000); Gyulassy, Levai, Vitev (2000); Wang ...
Medium characterized by
transport coefficient:
Model
2
qˆ
n density assumption
●
energy loss of leading parton
●
pt-broadening of shower
c 32
10
c
c qˆL2 2
c 3.2
qˆ L
Salgado,Wiedemann PRD68:014008 (2003)
c 1
2
k
2 T
qˆ L
Energy Loss in a Strongly Expanding Medium
●
In A-A collisions, the density of scattering centers is time-dependent:
qˆ( ) qˆ0 ( 0 )
●
= 1.5, 1.0, 0.5, 0
Dynamical Scaling Law:
same spectrum obtained for
equivalent static transport coefficient:
2
ˆq 2
L
●
Salgado, Wiedemann PRL 89, 092303 (2002)
qˆ( ) d
L 0
0
0
Calculations for a static medium
apply to expanding systems
Rescaled spectrum
The suppression of leading hadrons
Parton energy loss calculations account for:
• Nuclear modification factor
• Centrality dependence
• Back-to-back correlations
Eskola, Honkanen, Salgado, Wiedemann
NPA747 (2005) 511
• RAA = 0.2 is a natural limit
due to surface emission
?
indicates very opaque medium.
R. Baier,
NPA715 (2003) 209
• Numerics at face value:
34
QGP ?
ˆq( ) ?
c ( ) c
2
ideal
c 5 c QGP
ideal ?
Open questions:
- tests of the microscopic dynamics
underlying high-pt hadron suppression?
- relation of qˆ to model-independent
calculation in QCD?
BDMPS coefficient of N=4 SYM from AdS/CFT
Hong Liu, Krishna Rajagopal, Urs Achim Wiedemann, hep-ph/0605178
• AdS/CFT: calculating thermal Wilson loop in Minkowski space
W F (C)
T
expS(C)
is equivalent to calculating the minimal surface in 5-dimensional space with
AdS black hole metric. For N=4 SYM-theory:
ds
2
f dx dx
r2
2
R
1
2
r2
R2
f
2
2
f dx dx
r2
R2
1
r2
R2
2
2
2
1
dx
dx
dr
2 3 f
r04
r4
Here, R curvature radius of AdS space,
r0 black hole horizon
• Translation into field theoretic quantities:
Hawking temperature
is QGP temperature
String tension 1 4 '
determines t’Hooft coupling
2
gSYM
N
r0
TH
T
2
R
R2
'
Picturing the loop
Wilson loop C
in our world
Our world, (3+1)-dim brane
r
Surface S(C) with
boundary C in our
world
r0
horizon
Extra dimension
r, the bulk with
AdS black hole
metric.
Finding surface x x , , ,,2,3,r
amounts to extremizing Nambu-Goto action
1
S(C)
4 '
d d
det g
Induced metric
g G x x on worldsheet
Symmetries of loop C imply:
x , x2
x const., x 3 const.
Boundary:
Symmetry:
r L2
r r
Calculating the surface
The Nambu-Goto action reads
2r02L L / 2
r'2 R2
S(C)
d 1
2
2 ' R 0
f r2
r' r
Euler-Lagrange equations of motion:
r2 f
r'
R2
2
2
For integration constant 0 , turning point r' 0 0 implies
that f 0 0 and thus: r 0 r
0
descends up to horizon. Knowing that allows to determine
Surface
S(C)
L LT
2 2
2
2
1
4a
2T 2 L2
a 45 43 1.311
This action accounts for the interaction between the q-qbar pair and
the medium, as well as for the self-energy of q and qbar (quarks not
seeing each other). We must subtract self-energy …
The BDMPS coefficient
Self-energy of quark and anti-quark is given by two disconnected worldsheets
descending from r to r r0 at constant x 2
a LT
S0
2
Subtracting this term leads to (use small distance limit LT 1 )
2SI 2S 2S0
2
L L2T 3 OL L4 T 5
4 2a
The corresponding BDMPS transport coefficient reads
qˆSYM
3 / 243
245
T 3 18.87 SYM N c T 3
What do we learn?
Hong Liu, Krishna Rajagopal, Urs Achim Wiedemann, hep-ph/0605178
qˆSYM
3 / 243
245
T 3 18.87 SYM N c T 3
• Transport coefficient is not proportional to number of degrees of freedom N c
not proportional to ‘gluon number density’ or ‘number of scattering centers’.
(calculation
of (p+1)-dim SYM shows that in general, also temperature
dependence differs from that of a density)
2
• BDMPS transport coefficient is better thought of as measuring
• Numerically, for N=4 SYM with
qˆSYM 3.2 GeV
fm
qˆSYM 7.5 GeV
fm
2
for T = 300 MeV
2
qˆSYM 14.7 GeV
fm
N c 3 and
T3
SYM 1 2
for T = 400 MeV
2
for T = 500 MeV
• Would be interesting to repeat calculation in other thermal QFTs with gravity
dual to see whether result is universal or on what it depends.
Back-up
Better tests of microscopic dynamics
Underlying parton energy loss:
Parton energy loss - a simple estimate
Medium characterized by
transport coefficient:
2
qˆ
n density
●
How much energy is lost ?
Phase accumulated in medium:
kT2
z
Number of coherent scatterings: N coh
Gluon energy distribution:
Average energy loss
qˆ L2 c
2
2
t coh
,
where
t coh
Characteristic
gluon energy
2
qˆ
2
kT
kT2 qˆ t coh
dImed
1
dI1
qˆ
s
d dz N coh d dz
L
c
dI
E 0 dz 0 d med ~ s c ~ sqˆ L2
d dz
The medium-modified Final State Parton Shower
Baier, Dokshitzer, Mueller, Peigne, Schiff (1996); Zakharov (1997); Wiedemann (2000); Gyulassy, Levai, Vitev (2000); Wang ...
• Energy loss of leading parton
E rad sqˆL2
dI
med
• pT - broadening of parton shower
d dkT
kT2 qˆ L
2
• Expectation value of two light-like Wilson lines determines medium dependence
N(x, y) 1 TrW A (x)W A (y)
xy 0
med
qˆ L (x y) 2
W x P exp i dz T a Aa x,z
•
Radiation for expanding medium related to that of static medium
2 L 0
qˆ 2 0 qˆ( ) d
L 0
LHC: the richness of hard probes
The probes:
• Jets
• identified hadron specta
• D-,B-mesons
• Quarkonia
• Photons
• Z-boson tags
The range:
Q2 ,x, A, luminosity
Abundant yield
of hard probes
+ robust signal
(medium sensitivity
>> uncertainties)
= detailed understanding
of dense QCD matter
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