The Physics of
Relativistic Heavy Ion Collisions
Lecture #2
18th National Nuclear Physics Summer School
Lectures July 31-August 3, 2006
Associate Professor Jamie Nagle
University of Colorado, Boulder
Heavy Ion Experiments
Need 10,000,000,000,000 Kelvin Bunsen Burner
How to Access This Physics?
Big Bang
Only one chance…
Lattice QCD
Who wants to wait?…
RHIC
Neutron stars
Slide from Jeff Mitchell
Kinetic Energy  Thermal Energy
Energy Frontier History
Bevalac-LBL and SIS-GSI fixed target
max. 2.2 GeV
1992
Au-Au
AGS-BNL fixed target
max. 4.8 GeV
E864/941, E802/859/866/917, E814/877,
E858/878, E810/891, E896, E910 …
1994
Pb-Pb
SPS-CERN fixed target
max. 17.3 GeV
NA35/49, NA44, NA38/50/51, NA45,
NA52, NA57, WA80/98, WA97, …
TEVATRON-FNAL (fixed target p-A)
max. 38.7 GeV
2000
Au-Au
RHIC-BNL collider
max. 200.0 GeV
2007?
Pb-Pb
LHC-CERN collider
max. 2760.0 GeV
BRAHMS, PHENIX, PHOBOS, STAR
ALICE, ATLAS, CMS
Why Energy Matters?
Many basic goals of the field
have remained the same over
the last 20 years.
However, the character of the
system created is a strong
function of energy.
Many new probes and
theoretical handles are available
at higher energies.
Temperature Tch [MeV]
AGS-BNL
4.8 GeV
SPS-CERN
17.3 GeV
Nuclear Fragmentation
Resonance Production
Strangeness Near Threshold
Resonances Dominate
Large Net Baryon Density
Strangeness Important
Charm Production Starts
TEVATRON-FNAL
38.7 GeV
250
RHIC/LHC
200
quark-gluon plasma
150
SPS
RHIC-BNL
AGS
200.0 GeV
100
LBL/SIS
hadron
gas
50
atomic nuclei
0
Bevalac-LBL
2.2 GeV
0
200
400
600
800 1000 1200
Net Baryon Density ~ Potential B [MeV]
Low Net Baryon Density
Hard Parton Scattering
LHC-CERN
2760.0 GeV
Beauty Production
RHIC is doing great !
STAR
PHENIX
Hadronic Observables over a Large
Acceptance
Event-by-Event Capabilities
Electrons, Muons, Photons and Hadrons
Measurement Capabilities
Focus on Rare Probes: J/y, high-pT
Solenoidal magnetic field
Large coverage Time-Projection
Chamber
Silicon Tracking, RICH, EMC, TOF
Two central spectrometers with tracking
and electron/photon PID
Two forward muon spectrometers
BRAHMS
PHOBOS
Hadron PID over broad rapidity
acceptance
Charged Hadrons in Central
Spectrometer
Nearly 4p coverage multiplicity counters
Two conventional beam line
spectrometers
Magnets, Tracking Chambers, TOF, RICH
Silicon Multiplicity Rings
Magnetic field, Silicon Strips, TOF
Paddle Trigger Counter
TOF
Spectrometer
Ring Counters
Octagon+Vertex
What Are
Protons and Nuclei?
Structure of the Proton
See the whole proton
Momentum transfer
Q2 = 0.1 GeV2
Wavelength l = h/p
See the quark substructure
Q2 = 1.0 GeV2
See many partons (quarks and gluons)
Q2 = 20.0 GeV2
Parton Distribution Functions
Quarks
Gluons
30!
sea
valence
• Structure functions rise rapidly at low-x
• More rapid for gluons than quarks
Limitless Gluons?
When protons are viewed at short wavelength, there is a
large increase in low x gluons.
Is there a limit to the low x gluon density?
Gluon Saturation
probe rest frame
ggg
r/
Wavefunction of low x
gluons overlap and the selfcoupling gluons fuse, thus
saturating the density of
gluons in the initial state
target rest frame
l ~1/x
Transverse size of the quark-antiquark cloud
c ~ 2 10-14cm/ Q (GeV)
is determined by r ~ 1/Q
Fluctuations from dipole
increase and the unitary
limit of the photon cross
section in deep inelastic
scattering is the equivalent
to saturation.
1
J.P Blaizot, A.H. Mueller, Nucl. Phys. B289, 847 (1987).
Saturation in the Proton
HERA deep inelastic scattering data has been interpreted in
the context of gluon saturation models.
Lowest x data is at modest Q2
(should QCD+DGLAP work?)
Recent HERA running may not
resolve these issues since
machine changes limit the
coverage at low-x.
Future Electron-Ion Collider at
RHIC or HERA upgrade may be
necessary.
K. Golec-Biernat, Wuesthoff, others
What about Nuclei?
Nucleon structure functions are known to be modified in nuclei.
Can be modeled as recombination effect due to high gluon
density at low x (in the frame where the nucleus is moving fast).
Fermi Effect
enhancement
Saturation?
EMC effect
shadowin
g
x  .1
x  .1
RHIC probes x 
2p T
s
 102
x
Gluon Number Density
Gluon number density:
g = A xGN(x,Q2)/pR2
Gluon density depends on the nuclear overlap area
(pR2 a A2/3) and the momentum scale (Q2) since DGLAP
evolution requires:
G(x, Q2) ~ ln (Q2 / LQCD2)
HERA tests gluon density in the proton at very low x.
RHIC can test similar gluon density at significantly higher
x values. LHC heavy ion collisions probe even higher
gluon densities.
Color Glass Condensate
Put many nucleons into a nucleus and
Lorentz boost to the infinite momentum frame
Creates a 2-dimensional sheet of very high
density color charges set by a saturation scale.
High density of gluons (saturation) allows for the
simplification of Quantum Chromodynamics
Color fields can be described as classical wave
solutions to the Yang-Mills equation
Experimental Comparisons
In this saturation regime (sometimes termed the Color Glass
Condensate), with one parameter (saturation scale Qs) defines
the physics. In this classical approximation one can calculate
the collision output distribution of gluons. If one assumes a
mapping of partons to hadrons, one can compare with data.
l
 s  2 l y  Qs2e l y
dN
cosh y

 cN part    e
ln  2
 L
2
2
2
d
s
mT pT  sinh y
 o
 QCD
4

 
  1  l y 1  Qs el y / 2  
 
s

 
 
Saturation Regime?
The agreement appears impressive, but at the lowest energy one is no
where near the saturation condition.
Also, when the particle yield is matched, the transverse energy per particle
is a factor of 2 too large. Perhaps this is longitudinal work, but no detailed
calculation accounts for this yet.
Lower x?
For a 2  2 parton scattering process (LO), if both partons
scatter at 90 degrees, then x1=x2= 2pT/Ecm
pT ~ 2 GeV
Ecm ~ 200 GeV
x ~ 0.04
x2
x1
One can probe lower x values if x1 >> x2 and look at
particles away from 90 degrees (forward rapidity).
Rapidity y=0 (x~0.01), y=2.0 (x~0.001), y=4.0 (x~0.0001) for
pT ~ 2 GeV.
x2
x1
Suppression Factor R
d 2 N AA / dpT d
RAA ( pT ) 
TAAd 2 NN / dpT d
R = 1 (binary collision scaling)
Binary
Collisions
b
Participant
In deuteron-Gold collisions, forward rapidity probes low x in the Gold
nucleus. BRAHMS observes a suppression of particles that could be
related to saturation of the gluon density in the Gold nucleus.
d+Gold Probes
Suppression of forward hadrons generically consistent
with saturation of low-x gluons.
Suppression Factor
dd
d
x ~ 10-1
x ~ 10-2
Au
Au
Au
x ~ 10-3
MonoJets?
“Mono-jet”
Dilute parton
system
(deuteron)
p0
STAR Experiment
PT is balanced
by many gluons
Dense gluon
field (Au)
Tagged photons and jets at forward angles will give precise
information on x dependence of saturation effect.
No MonoJets at y=2?
PHENIX has measured the
correlation between y=2
hadrons and y=0 hadrons.
There appears to be no
decrease in away side partners
as predicted by saturation
models.
However, these predictions
were for more forward rapidity
(probing lower x) regions.
What do they have in common?
1. Scaling of the total p-p
cross section
2. Growth of low x gluons
in the proton
3. Shadowing of structure
functions in nuclei
x
4. Particle production in
nucleus-nucleus reactions
Saturation Summary
Interesting hints at non-linear saturation effects of partons in protons at
HERA. Current HERA running does not focus on this physics, and facility
will soon be shut down.
Interesting hints in proton (deuteron) nucleus reactions at RHIC, but at a
rather soft scale. Photon Jet or Jet Jet correlations that pin down x1 and x2
may shed more light.
Key future is much larger x reach at high Q2 at the LHC, or with Deep
Inelastic Scattering at future electron ion collider (EIC or eRHIC).
Collision Dynamics
RHIC = Gluon Collider
10,000 gluons, quarks, and antiquarks
are made physical in the laboratory !
What is the nature of this ensemble of partons?
End of the World!
Can be dismissed with some
basic General Relativity
RS  2GM
c2
 10 49 meters
R  10 15 meters
much less
than
Planck length !
Even if it could form, it
would evaporate by
Hawking Radiation in
10-83 seconds !
Start with Simpler System
OPAL Event Display
Electron-Positron Annihilation
e+e-  qq  hadron jets
Quark radiates gluons and
eventually forms hadrons in a jet
cone.
q
e-
e+
N ch  a sA exp( B / a s )
q
QCD calculation of
gluon multiplicity
times a hadron scale
factor gives excellent
agreement with data.
(Mueller 1983)
Thermal / Statistical Model
If we assume everything is produced statistically (phase
space) or from thermal equilibrium, we get a reasonable
description too.
Key feature is that strangeness is suppressed relative to its
mass and energy.
Becattini et al., hep-ph/9701275
pQCD versus Statistical Models
Event to Event fluctuations or within Event fluctuations can be
discriminating.
For example, some events have quark jets and some also
have gluon jets.
QGP in Proton Proton Reactions?
Bjorken speculated that in the “interiors of
large fireballs produced in very high-energy pp
collisions, vacuum states of the strong
interactions are produced with anomalous
chiral order parameters.”
“Baked Alaska”
Fermi (1950)
“High Energy Nuclear Events”,
Prog. Theor. Phys. 5, 570 (1950)
Groundwork for statistical
approach to particle production
in strong interactions:
“Since the interactions of the
pion field are strong, we may
expect that rapidly this energy
will be distributed among the
various degrees of freedom
present in this volume
according to statistical laws.”
Landau (1955)
Significant extension of Fermi’s
approach
Considers fundamental roles of
– Hydrodynamic evolution
– Entropy
“The defects of Fermi’s
theory arise mainly because
the expansion of the
compound system is not
correctly taken into
account…(The) expansion
of the system can be
considered on the basis of
relativistic hydrodynamics.”
QGP Signatures?
Experiments (E735, UA1, others) observe substantially
larger source volumes in high multiplicity pp (pp)
events via particle correlations and boosted pt spectra.
Strangeness Enhancement
Strangeness is enhanced in high multiplicity pp events,
but not up to statistical equilibrium.
Experiment E735
Watch out for autocorrelations. Higher multiplicity events
have gluon jets which have higher strangeness!
RHIC experiments can add a lot to these measurements.
Thermal / Statistical Model
Again, the statistical model works, with a remaining strangeness
suppression.
Multiplicity Scaling
Both the Landau model (thermal fireball) and the pQCD
(radiated gluon counting) give very similar scaling of
multiplicity versus energy (?)
Why Heavy Ions?
• Higher energy density may be achieved in protonproton, but the partonic re-interaction time scale
of order 1 fm/c.
• It is difficult to select events with different
geometries and avoid autocorrelations.
• We will see that probes with long paths through the
medium are key.
We should not rule out pp reactions, but rather study
the similarities and differences with AA reactions.
Heavy Ion Time Evolution
1. Initial Nuclei Collide
2. Partons are Freed from Nuclear Wavefunction
3. Partons interact and potentially form a Quark-Gluon Plasma
4. System expands and cools off
5. System Hadronizes and further Re-Scatters
6. Hadrons and Leptons stream towards our detectors
0 fm/c
2 fm/c
7 fm/c
>7 fm/c
Diagram from Peter Steinberg
Collision Characterization
The impact parameter determines the number of nucleons
that participate in the collision.
Binary collisions
Participating
nucleons
Spectators
Participants = 2 x 197 - Spectators
Zero
Degree
Calorimeter
n
n
n
p
Participants
p
p
Spectators
26 TeV of Available Energy !
Out of a maximum energy of 39.4 TeV in central
Gold Gold reactions, 26 TeV is made available for
heating the system.
Bjorken Energy Density
• At t=tform, the hatched
volume contains all
particles w/ b<dz/tform:
dN 
dz dN
dz dN

; (dy  d|| @ y  0)
t form d|| t form dy
• At y=b||=0, E=mT, thus:
 (t form ) 

E dN  mT  dN (t form )  mT 


V
dz  A
dy
t form  A
• We can equate dN<mT>
& dET and have:
 BJ (t form ) 
1
dET (t form )
t form  A
dy
Two nuclei pass through one another
leaving a region of produced particles
between them.
Energy Density
Energy density far above transition value predicted by lattice.
 Bj
1
1

pR 2 2ct
 dET
 2
 dy



pR2
2ct
PHENIX: Central Au-Au yields
dET
d
 503  2GeV
 0
Grand Canonical Ensemble
We start out with a system completely out of equilibrium and
lots of kinetic energy.
We can try to use the Grand Canonical Ensemble to
calculate the abundances of all the final measured particles.
ns 
1
e
(  s   ) / kT
Fermions or Bosons
1
Depends on Temperature and Chemical Potential.
Grand Canonical Ensemble
Infinite heat bath with which
my system can exchange
energy and particles, hence
we have a temperature and
chemical potential.
My system.
Ni  giV 
3
d p
 2p 
1
3
e
( p 2  m2   B ) / T
1
Heavy Ions GCE
Works very well again, but now almost no additional
suppression of strangeness.
Consider canonical ensemble in smaller systems?
Canonical Ensemble
Statistical Model using Grand Canonical Ensemble
One can use the GCE even when energy and other quantum
numbers are conserved. The temperature and chemical
potentials simply reflect characteristics of the system. Fluctuation
calculations are not valid.
If the volume of the system is
large, GCE is appropriate. For
small volumes, you must conserve
quantum numbers (for example
strangeness) in every event !
Thus the Canonical Ensemble is
relevant. In the CE, strangeness is
suppressed for very small volumes
and reaches the GCE limit for
large volumes.
Strangeness Enhancement
Hadronic rescattering can
equilibrate overall strangeness
(ie. K+, K-, L) in 10-100 fm/c and
strange antibaryons (L, X, W) in
over 1000 fm/c !
Quark-gluon plasma may
equilibrate all strange
particles in 3-6 fm/c !
Heavy Ion collision lifetime
is of order 10-15 fm/c
before free streaming.
“A particularly striking aspect of this apparent ‘chemical
equilibrium’ at the quark-hadron transition temperature is the
observed enhancement of hadrons containing strange quark
relative to proton-included collisions.
Since the hadron abundances appear to be frozen in at the point
of hadron formation, this enhancement signals a new and faster
strangeness-producing process before or during hadronization,
involving intense rescattering among quarks and gluons.”
Strangeness Suppression
ls 
2 ss
uu  dd
factor ~2
RHIC
Becattini et al hep-ph/0011322, hep-ph/0002267
Strange Patterns
The enhancement of total strangeness appears quite similar
at AGS, SPS, and now RHIC !
This challenges any model QGP model for enhancement. All
systems are approaching something that looks statistically
equilibrated, and we already see this trend in proton induced
collisions.
Strangeness Enhancement
NA57 (open)
STAR (filled)
Collision Dynamic Summary
- Depositing majority of kinetic energy into new medium
- Energy density appears above phase transition value
- Energy is distributed into particle production statistically
including equivalent strangeness production
- No sharp global feature distinct from smaller hadron
collisions, but instead gradual changes