Probing High-Temperature QCD
Matter
at the Relativistic Heavy-Ion
Collider (RHIC)
Saskia Mioduszewski
18 September 2008
Group Members
Postdocs:
Rory F. Clarke
Ahmed Hamed
Graduate Students:
Matthew Cervantes
Martin Codrington (Chemistry)
Supported by D.O.E. and Sloan Foundation
Goal of RHIC: To Study
Fundamental Puzzles of Hadrons
• Confinement
nuclear matter
p, n
– Quarks do not exist as free particles
• Generation of mass
– Free quark mass ~ 5-7 MeV
– Quarks become “fat” in hadrons,
constituent mass ~ 300-400 MeV
• Complex structure of hadrons
– Sea anti-/quarks
– Gluons
– Origin of Spin of the nucleon
These phenomena must have occurred with formation of hadrons
~ 10 ms after Big Bang
Hadron Synthesis
strong force binds
quarks and gluons in massive objects:
protons, neutrons mass ~ 1 GeV/c2
~ 100 s after Big Bang
Nuclear Synthesis
strong force binds protons and
neutrons in nuclei
Expectation from Numerical Simulations of
Finite-Temperature QCD
Stefan-Boltzmann
limit
Expectation: create a “weakly coupled gas of quarks and
gluons” by reaching Tc in high-energy heavy-ion collisions
(Year 2000)
New State of Matter created at CERN
At a special seminar on 10
February, spokespersons
from the experiments on
CERN's Heavy Ion
programme presented
compelling evidence for
the existence of a new
state of matter in which
quarks, instead of being
bound up into more
complex particles such as
protons and neutrons, are
liberated to roam freely.
Pb+Pb collisions at √sNN = 17 GeV at the SPS
“Travel” Back in Time
early universe
Quest of heavy-ion collisions:
T
RHIC
& LHC
heat and compress nuclear matter
Quark Matter
RHIC
&
SPS
SPS
TC~170 MeV
AGS
Hadron
Resonance Gas
SIS
Nuclear
Matter
baryon chemical potential 940 MeV
neutron stars
1200-1700 MeV
mB
– create Quark Gluon Plasma (QGP) as transient state in
heavy ion collisions (e.g. Au+Au collisions)
– verify existence of QGP
– study properties of QGP
– study QCD confinement and how hadrons get their masses
Relativistic Heavy Ion Collider
• RHIC was proposed in 1983
• RHIC began providing collisions in 2000
• √sNN = 200 GeV = 10 x Collision-Energy at
SPS
 New probe available
High-pT particles from “hard” scattering
RHIC Specifications
• 3.83 km circumference
• Two independent rings
– 120 bunches/ring
– 106 ns crossing time
• Capable of colliding
~any nuclear species
on
~any other species
• Energy:
 22-500 GeV for p-p
 5-200 GeV for Au-Au
(per N-N collision)
• Luminosity
– Au-Au: 5 x 1027 cm-2 s-1
– p-p : 1.5x1032 cm-2 s-1
(polarized)
The RHIC Experiments
STAR
PHENIX
STAR
Characterizing the collisions
• Different centralities, i.e. size of overlap
region
• Asymmetry of reaction zones
• How does the matter behave?
• Can we probe the matter that exists only
for a short time?
Not all A+A collisions are the same
-- “Centrality”
Spectators
Participants
For a given b,
“billiard ball” model
predicts Npart
(No. participants)
and Nbinary
15 fm
0
0
b
Npart
Nbinary
0 fm
394
~1000
(No. binary collisions)
Kinematics for colliders

pT
p||
Pseudo-rapidity:
Mid-rapidity:
η = 4:
   ln tan  2
η = 0, perpendicular to the incident beams
Scattering at θ = 2.1o in the CM (or lab) frame
Transverse momentum (pT) and pseudorapidity ()
provide a convenient description
Radial Flow
– Collective Expansion of system due to
pressure
– Heavier particles shifted to higher pT
– Observable: <bT> from slopes
as a function of mass and/or
centrality
– Spectra can be described by
hydrodynamic models for
pT< 2-3 GeV/c and mid-peripheral
to central events
<bT>
Single Particle Spectra (low pT)
• Decreasing slope for
increasing particle mass
and centrality
central
peripheral
Elliptic Flow in Non-central Collisions
Momentum space:
final asymmetry
Coordinate space:
initial asymmetry
py
multiple collisions
(pressure)
Early state manifestation of collective behavior:
• Asymmetry generated early in collision, quenched by expansion
 observed asymmetry emphasizes early time
Fourier Expansion: dN/df ~ 1 + 2 v2(pT) cos (2 f) + ...
Second Fourier coefficient v2:
v2  cos2f
f  atan
py
px
Data compared to Hydro
f
Hydrodynamics with 0 viscosity
v2
Reaction Plane
(Angle Y2)
pT [GeV/c]
 Thermalization in < 1 fm/c
How does the expected
“Quark Gluon Plasma”
compare with the
“Perfect Fluid” that we
have found at RHIC?
Can we quantify the
properties of this new
form of matter?
Same behavior as observed in gases of
strongly coupled Li atoms
K. M. O’Hara et al, Science 298, 2179
The matter we have created at RHIC
behaves like a strongly coupled
fluid, not like “weakly coupled gas of
quarks and gluons”
How small can viscosity be?
AdS/CFT for calculating properties of
strongly-coupled gauge theories
Conjectured lower
bound on
viscosity/entropy = 1/4p
/S [1/4p]
P.K. Kovtun, D.T. Son, and
A.O. Starinets, Phys. Rev.
Lett. 94:111601, 2005.
RHIC “fluid” might
be at ~2-3 on this
scale (at T~1012 K)
Probing the Medium
The QCD analogue of x-ray tomography
• Need an external
calibrated source
• Calculate absorption
cross sections
 Interpret the results
“Hard” processes to probe the matter
• Large momentum transfer – or close distance
• Can resolve partons: valence quarks, sea quarks
and gluons – scattered parton fragments into a “jet”
• Coupling is weak - pQCD applicable
h
1
A
f
a
c
d
dt
B
f
p
p
p
d
D
b/ A
Fragmentation
Function
Dh c
1
a/ A
b
Jet
h d
2
h
2
quark
or
gluon
Jets in heavy ion collisions
hard-scattered
hard-scattered
parton during Au+Au
parton in p+p
cone of hadrons “jet”
hadron distribution
softened, jets broadened?
increased
gluon-radiation
within plasma?
p
p
Hard scattering
Production cross section of p0
p+p collisions = “baseline”
• Good agreement with NLO
perturbative QCD calculations
Thermallyshaped Soft
Production
Hard
Scattering
• High pT particle yields serve as
a calibrated probe of the nuclear
medium in nucleus+nucleus
(A+A) and deuteron+nucleus
(d+A) collisions
Systematizing Our Expectations
• Describe in terms of
scaled ratio RAA
R AA
Yield AuAu

 N binary  AuAu  Yield pp
= 1 for “baseline
expectations”
• Will present most of
Au+Au and d+Au data
in terms of this ratio
“no effect”
Discovery of Strong Suppression
peripheral
Nbinary = 12.3  4.0

central
Nbinary = 975  94
Scaling of calibrated probe works in peripheral Au+Au,
but strong suppression in central Au+Au
Nuclear Modification Factor
Yield central
 N binary  central  Yield pp
Yield peripheral
 N binary  peripheral  Yield pp
 Comparison of
peripheral to central
RHIC 200 GeV
central Suppression
peripheral –
Nbinary scaling
binary scaling
Theoretical Understanding?
Understood in an approach that calculates energy loss of hardscattered parton through gluon radiation in a dense partonic
medium (15 GeV/fm3 ~100 x normal nuclear matter)
Au+Au suppression (I. Vitev and M. Gyulassy, hep-ph/0208108)
d+Au enhancement (I. Vitev, nucl-th/0302002 )
* Note deuteron-gold control
experiment with no suppression
 Our high pT probes
have been calibrated
and are now being
used to explore
properties
of the medium
d-Au
Au-Au
What have we learned?
• Nuclear matter created at RHIC is very opaque
and dense (estimates of 100 x normal nuclear
matter density)
• Strong collective behavior
• Coupling must be strong for v2 to be so large
Now we want to characterize this new matter more
quantitatively (viscosity, transport coefficients,
color charge density)
Jet Reconstruction in Au+Au Collisions
e+e  q q
(OPAL@LEP)
pp jet+jet
(STAR@RHIC)
Au+Au ???
(STAR@RHIC)
Jet Studies via Correlations

dN/d
pT,trig > 4 GeV/c
pT,assoc = 2-4 GeV/c
-p/2
0
p

pT,trig – pT of the trigger particle
pT,assoc bin – range of pT selected to
associate with the trigger particle
Azimuthal distributions in Au+Au
Escaping
Au+Au
Jet -“Near
peripheral
Side”
Au+Au central
pedestal and flow subtracted
Lost
-“Away
Side”
Phys
RevJet
Lett
90, 082302
Near-side: peripheral and central Au+Au similar to p+p
Strong suppression of back-to-back correlations
in central Au+Au collisions
“Reappearance of away-side jet”
With increasing trigger pT, away-side jet correlation reappears
4 < pT,trig< 6 GeV/c, 2< pT,assoc< pT,trig
Increasing pT,trig
Increasing pT,assoc
Medium Modification to Fragmentation
Function
Are we probing the medium? Or is it simply too opaque?
8 < pT,trig< 15 GeV/c,
pT,assoc > 6 GeV/c
Or
just tangential
Punch-through
Jet ?
emission ?
Centrality
Is there any particle not affected by
the opaque medium?
increased
gluon-radiation
within plasma?
g
• If g is produced in hard
scattering, instead of q or
g, expect it to escape
without interaction 
calibrated probe
• Then could study jet on
opposite side as a function
of the energy of photon
Hard Scattering  g + jet
Effect of Dense Medium on Direct
Photons
Hadrons are suppressed, photons are not – photons serve
as the “control” experiment
R
γ
AA
Yield γ central

 N binary  central  Yield γ pp
PHENIX, Phys. Rev. Lett. 96, 202301 (2006)
Fragmentation Function
Fragmentation Function - Study the particle distribution in a jet
Calculate yields as a function of
pT,assoc/pT,trig from correlation function
•
gEinitial
g-rich triggers
p0 triggers
Integrate yields
0
Modified Jet
p
• Compare distribution in vacuum to
medium to look for medium modification
Direct Measure of Medium Modification
to Fragmentation Function
A. Hamed, Hard Probes 2008
Modified Jet
Associated yields per trigger
gEinitial
Direct g
p0
Ratio of Central Au+Au to Peripheral
(~ Medium/Vacuum) Jet Yields
STAR Preliminary
Within the current uncertainty in the scaling the medium effect
on jets associated to a direct g trigger is similar to jets associated
to p0 trigger.
Summary
• RHIC has been successfully operating since 2000
• The expectation of QGP as a weakly coupled gas of
quarks and gluons has been challenged by data
• Medium created is strongly interacting (liquid-like)
and very opaque
• Currently experiments are trying to make
measurements that can characterize the medium
properties more quantitatively
• g+jet measurement holds promise to be one of such
probes
• Higher luminosity needed for definitive g+jet
measurement
• Future at RHIC is exciting
Extra Slides
Results: Method of extract direct g associated yield
O(αs2α(1/αs+g))
Extraction of directg away-side yields
near
near
R=Yg-rich+h/Yp0+h
Assume no near-side yield
for direct g
then the away-side yields per
trigger obey
away
away
0
p
Yg+h = (Yg-rich+h - RYp0+h )/(1-R)
This procedure removes correlations due to contamination (asymmetric
decay photons+fragmentation photons) with assumption that correlation is similar to
p0 – triggered correlation at the same pT.
A. Hamed STAR Experiment ICHEP08 Philadelphia, PA July 29th -August 5th.
This atomic system may also be near the bound.
T. Schafer, arXiv:0707.1540v1 (2007).
What do we learn from RAA?
Effect of collision medium on hadron pT spectra:
• Parton scattering with large momentum transfer
 Hard-scattered partons (jets) present in early stages of
collisions
• Hot and dense medium
 Hard-scattered partons sensitive to hot/dense medium
Theory predicts radiative energy loss of parton in QGP
• Emission of hadrons
 High pT hadrons (jet fragments)
Dense medium (QGP) would cause depletion in spectrum
of leading hadron at high pT - “jet quenching”
High-pT Predictions
X-N. Wang, Phys. Rev. C58 (1998) 2321
It has been predicted that jet production will be affected by
medium effects due to the production of hot dense matter
in high energy relativistic heavy ion collisions
Scaling from p+p to
A+A
• For hard-scattering processes, expect point-like
scaling. For inclusive cross sections :
σ AA
 the ratio of the number of point - like sources  A 2
σ pp
• For semi-inclusive yields, expect :
Yield AA
 number of Nucleon - Nucleon binary collisions
Yield pp
  N binary  for the A + A centrality class
Jet Studies via Correlations
Elliptic flow
pTtrig > 4 GeV/c
dN/
d

pTassoc = 2-4 GeV/c
-p/2
0
p

pTtrig – pT of the trigger particle
pTassoc bin – range of pT selected to
associate with the trigger particle
An example of Nbinary ~ A*B scaling
• Small cross section
processes scale as
though scattering
occurs incoherently
off nucleons in
nucleus
• scale as
A1.0 in m+A
• scale as
Nbinary ~A*B in A+B
7.2 GeV muons on various targets.
M. May et al., Phys. Rev. Lett. 35, 407, (1975)
“Binary-Scaling” and RAA
• The probability for a “hard” collision for any two
nucleons is small
• The total probability in A+A collision is multiplied
by the number of times we try, i.e. – the cross-section
scales with the number of binary collisions - Nbinary
• Define Nuclear Modification Factor RAA
Yield central /  N binary  central
Yield
/  N binary  peripheral
peripheral
Yield pp
Yield
Yield central /  N binary  central
Yield peripheral /  N binary  peripheral
 Effect of nuclear medium on yields
pp
Yield of p0 measured by PHENIX
p+p collisions
Au+Au collisions
Evolution of Jet Structure
At higher trigger pT (6 < pT,trig < 10 GeV/c),
away-side yield varies with pT,assoc
4 < pT,trig< 6 GeV/c, 2 < pT,assoc< pT,trig
For lower pT,assoc (1.3 < pT,assoc <1.8
GeV/c), away-side correlation has
non-gaussian shape  becomes
pedestal and flow
doubly-peaked
for lower pT,trig
subtracted