The Physics of Relativistic Heavy Ion Collisions

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The Physics of Relativistic Heavy Ion Collisions
Lecture 2
Associate Professor Jamie Nagle University of
Colorado, Boulder
18th National Nuclear Physics Summer
School Lectures July 31-August 3, 2006
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Heavy Ion Experiments
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Need 10,000,000,000,000 Kelvin Bunsen Burner
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How to Access This Physics?
Slide from Jeff Mitchell
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Kinetic Energy ? Thermal Energy
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Energy Frontier History
Bevalac-LBL and SIS-GSI fixed target
max. 2.2 GeV AGS-BNL fixed target max. 4.8
GeV SPS-CERN fixed target max. 17.3
GeV TEVATRON-FNAL (fixed target p-A) max. 38.7
GeV RHIC-BNL collider max. 200.0 GeV LHC-CERN
collider max. 2760.0 GeV
E864/941, E802/859/866/917, E814/877, E858/878,
E810/891, E896, E910
1992 Au-Au
NA35/49, NA44, NA38/50/51, NA45, NA52, NA57,
WA80/98, WA97,
1994 Pb-Pb
2000 Au-Au
BRAHMS, PHENIX, PHOBOS, STAR
2007? Pb-Pb
ALICE, ATLAS, CMS
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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.
Bevalac-LBL 2.2 GeV AGS-BNL 4.8
GeV SPS-CERN 17.3 GeV TEVATRON-FNAL 38.7
GeV RHIC-BNL 200.0 GeV LHC-CERN 2760.0 GeV
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RHIC/LHC
200
quark-gluon plasma
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SPS
AGS
Temperature Tch MeV
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LBL/SIS
hadron gas
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atomic nuclei
0
0
200
400
600
800
1000
1200
Net Baryon Density Potential ?B MeV
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STAR Hadronic Observables over a Large
Acceptance Event-by-Event Capabilities Solenoidal
magnetic field Large coverage Time-Projection
Chamber Silicon Tracking, RICH, EMC, TOF
PHENIX Electrons, Muons, Photons and Hadrons
Measurement Capabilities Focus on Rare Probes
J/y, high-pT Two central spectrometers with
tracking and electron/photon PID Two forward muon
spectrometers
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BRAHMS Hadron PID over broad rapidity
acceptance Two conventional beam line
spectrometers Magnets, Tracking Chambers, TOF,
RICH
PHOBOS Charged Hadrons in Central
Spectrometer Nearly 4p coverage multiplicity
counters Silicon Multiplicity Rings Magnetic
field, Silicon Strips, TOF
Paddle Trigger Counter
TOF
Spectrometer
OctagonVertex
Ring Counters
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What Are Protons and Nuclei?
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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
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Parton Distribution Functions
Quarks
Gluons
30!
sea
valence

• Structure functions rise rapidly at low-x
• More rapid for gluons than quarks

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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?
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Gluon Saturation
target rest frame
lc 1/x
Transverse size of the quark-antiquark cloud is
determined by r 1/Q 2 10-14cm/ Q (GeV)
Wavefunction of low x gluons overlap and the
self-coupling gluons fuse, thus saturating the
density of gluons in the initial state
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).
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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 QCDDGLAP 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
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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
shadowing
RHIC probes
x
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Gluon Number Density
Gluon number density ?g A xGN(x,Q2)/?R2
Gluon density depends on the nuclear overlap area
(?R2 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.
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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 Colo
r fields can be described as classical wave
solutions to the Yang-Mills equation
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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.
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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.
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Lower x?
For a 2 ?? 2 parton scattering process (LO), if
both partons scatter at 90 degrees, then x1x2
2pT/Ecm
pT 2 GeV Ecm 200 GeV x 0.04
x2
x1
One can probe lower x values if x1 gtgt x2 and look
at particles away from 90 degrees (forward
rapidity). Rapidity y0 (x0.01), y2.0
(x0.001), y4.0 (x0.0001) for pT 2 GeV.
x2
x1
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Suppression Factor R
R 1 (binary collision scaling)
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.
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dGold Probes
Suppression of forward hadrons generically
consistent with saturation of low-x gluons.
Suppression Factor
x 10-3
x 10-2
x 10-1
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MonoJets?
STAR Experiment
Tagged photons and jets at forward angles will
give precise information on x dependence of
saturation effect.
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No MonoJets at y2?
PHENIX has measured the correlation between y2
hadrons and y0 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.
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What do they have in common?

• Scaling of the total p-p
• cross section

• Shadowing of structure
• functions in nuclei

• Growth of low x gluons
• in the proton

• Particle production in
• nucleus-nucleus reactions

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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).
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Collision Dynamics
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RHIC Gluon Collider
10,000 gluons, quarks, and antiquarks are made
physical in the laboratory ! What is the nature
of this ensemble of partons?
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End of the World!
Can be dismissed with some basic General
Relativity
much less than Planck length !
Even if it could form, it would evaporate by
Hawking Radiation in 10-83 seconds !
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Start with Simpler System
Electron-Positron Annihilation
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ee- ? qq ? hadron jets
Quark radiates gluons and eventually forms
hadrons in a jet cone.
q
e
e-
q
QCD calculation of gluon multiplicity times a
hadron scale factor gives excellent agreement
with data.
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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
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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.
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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.
Time
Baked Alaska
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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.
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Landau (1955)

• Significant extension of Fermis approach
• Considers fundamental roles of
• Hydrodynamic evolution
• Entropy
• The defects of Fermis 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.

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QGP Signatures?
Experiments (E735, UA1, others) observe
substantially larger source volumes in high
multiplicity pp (pp) events via particle
correlations and boosted pt spectra.
p
k
Radius (fm)
ltptgt (GeV/c)
p
dNch/dh (charged)
dNch/dh (charged)
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Strangeness Enhancement
Strangeness is enhanced in high multiplicity pp
events, but not up to statistical equilibrium.
Experiment E735
dNch/dh
K/p
Ratio
Ratio
Nch
pt (GeV/c)
Watch out for autocorrelations. Higher
multiplicity events have gluon jets which have
higher strangeness! RHIC experiments can add a
lot to these measurements.
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Thermal / Statistical Model
Again, the statistical model works, with a
remaining strangeness suppression.
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Multiplicity Scaling
Both the Landau model (thermal fireball) and the
pQCD (radiated gluon counting) give very similar
scaling of multiplicity versus energy (?)
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Why Heavy Ions?

• Higher energy density may be achieved in
  proton-proton, 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.

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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
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Collision Characterization
The impact parameter determines the number of
nucleons that participate in the collision.
Binary collisions
Participating nucleons
Zero Degree Calorimeter
n
Spectators
Participants
Spectators
n
n
p
p
p
Participants 2 x 197 - Spectators
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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.
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Bjorken Energy Density

• At ttform, the hatched volume contains all
  particles w/ bltdz/tform
• At yb0, EmT, thus
• We can equate dNltmTgt dET and have

Two nuclei pass through one another leaving a
region of produced particles between them.
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Energy Density
Energy density far above transition value
predicted by lattice.
pR2
2ct
PHENIX Central Au-Au yields
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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.
Depends on Temperature and Chemical Potential.
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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.
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Heavy Ions GCE
Works very well again, but now almost no
additional suppression of strangeness. Consider
canonical ensemble in smaller systems?
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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.
Volume (fm3)
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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.
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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.
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Strangeness Suppression
Becattini et al hep-ph/0011322, hep-ph/0002267
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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.
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Strangeness Enhancement
NA57 (open) STAR (filled)
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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