Intro. Relativistic Heavy
Ion Collisions
Introduction and History of the Field.
Manuel Calderón de la Barca Sánchez
A relativistic heavy ion collision:
Two nuclei colliding at √s ~ 1 – 10000 GeV
Thousands of new particles are produced.
The product of the collision is NOT a simple
superposition of elementary nucleon-nucleon
collisions.
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1950’s, the early days
Natural accelerator: cosmic
rays.
Location of lab:
Stratosphere! Balloon
flights.
Detector: Nuclear emulsions
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Fermi: Description of high-energy hadronic
collisions using a statistical thermal model.
Formation of a highly excited intermediate
state: fireball
Thermal equilibrium is reached in fireball.
Decay into final state particles follows statistical rules
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Landau :
Energy is deposited in small volume.
~ size of Lorentz-contracted nuclear overlap.
Leads to formation of transient state.
State undergoes hydrodynamical expansion.
System cools down while expanding.
Reaches a freeze out temperature. Tf ~ mp
Below Tf, hadrons become free particles.
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Hagedorn:
Study mass spectrum of hadronic
resonances.
Many of these were just being discovered.
Observed a limiting temperature in mT
spectra.
Conjecture: A multi-hadron state should be described by
thermodynamics with a limiting temperature.
Assume spectrum of resonant states is exponential.
As higher states are populated, T increases.
If number of states increases exponentially, T saturates.
Hagedorn temperature ~ 160 MeV ~ mp.
r(m)µ ma exp(m / B) Þ Critical Temperature TC = B
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mid-1970s: Collins and Perry
PRL 34 (1975) 1353
“Superdense matter: Neutrons or Asymptotically free quarks?”
QFT approach to relativistic many body problem
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mid-1970s: Cabibbo and Parisi
PLB 59 (1975) 67
“Exponential hadronic spectrum and Quark Liberation”
Applied to MIT “Bag” model:
Expect phase transition both at
high T and at high density.
First “phase diagram” for hadronic matter
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Realization from QCD:
At high temperatures and densities, hadronic
matter should undergo a phase transition to a
state of ~free quarks and gluons: the QGP.
Lattice QCD: numerical calculations of QCD on
a discrete space-time.
More precise predictions.
Slightly more elaborate phase diagrams...
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Phase diagram of
nuclear matter in
equilibrium
rC @ (1- 2)GeV / fm 3
TC @ (150 -170)MeV
Where to explore
these regimes?
Early universe
Ultrarelativistic
heavy ion collisions
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From the 1983 NSAC Long Range Plan.
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Temperature
The phase diagram of QCD.
Early universe
quark-gluon plasma
Tc
critical point ?
hadron gas
nucleon gas
vacuum
nuclei
r0
color
superconductor
Color-Flavor
Locked Phase
Neutron stars baryon density
Need experiments to explore the phase diagram of QCD
Heavy Ion Collisions at RHIC and LHC create conditions sufficient to “melt” matter into a
quark gluon plasma
11
10-44 sec
Quantum Gravity
Unification of all 4 forces
1032 K
10-35 sec
Grand Unification
E-M/Weak = Strong force
1027 K
universe exponentially
expands by 1026
E-M = weak force
1027 K
creation of nucleons
1013 K
creation of electrons
6⋅109 K
10-35 sec? Inflation
2 10-10 sec Electroweak
unification
2·10-6 sec p-p-bar pairs
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1015 K
6 sec
e+e- pairs
3 min
Nucleosynthesis light elements formed
109 K
106 yrs
Microwave
Background
recombination transparent to photons
3000 K
109 yrs ?
Galaxy formation
bulges and halos of
normal galaxies form
20 K
12
Quark-Hadron Transition in the
Early Universe
K.A. Olive, Science 251 (1991) 1194
Initial Hot and Dense Epoch
Universe expands and cools.
Einstein’s Equations +
Energy conservation +
homogeneous/isotropic radiationdominated universe:
t sT
2
2.4
N(T )
7
N(200MeV ) = [2(N C2 -1)+ N C N f ]
2
-5
t s (200MeV ) » 10 s
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“The Quark-Hadron Transition
in the Early Universe”
E. Suhonen.
PLB 119 (1982) 81
Eq 1 and 2b: Einstein field equations, plus
energy conservation, written in terms of the
energy density
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Because we can study the
Thermodynamics of the Strong
Force.
The strong force exhibits
intriguing phenomena.
Confinement.
Chiral-Symmetry breaking.
Strong interactions give rise to
most of the mass we see!
We are only just beginning to
understand how the strongest
of all the forces behaves.
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Bevalac-LBL, and SIS-GSI fixed target
max. 2.2 GeV
1980s
AGS-BNL fixed target
1992
Au+Au
1994
Pb+Pb
E864/941, E802/859/866/917,
E814/877, E858/878,
E810/891, E895, E910 …
max. 4.8 GeV
SPS-CERN fixed target
max. 17.2 GeV
NA35/49, NA44, NA38/50/51,
NA45, NA52, NA57, WA80/98,
WA97, …
Nuclear Fragmentation
Resonance Production
Strangeness near
threshold
Resonances Dominate
Large Net-Baryon
Density
Strangeness Important
Charm production
TEVATRON-FNAL (fixed target p-A)
2000
Au+Au
2010
Pb+Pb
max. 38.7 GeV
RHIC-BNL Collider
BRAHMS, PHENIX, PHOBOS, STAR
Low Net-Baryon Density
Hard Parton Scattering
max. 200.0 GeV
LHC-CERN Collider
ALICE, ATLAS, CMS
Beauty Production
max. 2.76 TeV (5.5 TeV to be done)
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Longitudinal Expansion (left, middle)
Projectile and Target nuclei (forward/backward light cone)
Central region (z~0, yCM): Deconfined QGP
Interactions bring system into local statistical equilibrium. Thermalization.
Evolution described by relativistic hydrodynamics.
Note: Hydrodynamic evolution needs to start at t < 1 fm/c.
Surfaces of constant t : hyperbolae, “hypersurfaces”
Transverse expansion (right)
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Chemical Freezeout (Tch ≤ Tc ) : inelastic scattering stops
Kinetic Freezeout (Tfo ≤ Tc ) : elastic scattering stops
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Bjorken Hydrodynamics: Boost invariant midrapidity region.
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Nucleons interpenetrate opposing nucleus.
Baryons remain in the forward/backward
pancakes. (g>>1)
Consider system of quanta in region between
the pancakes.
d E
3 dN ch
For a nucleon-nucleon collision dy » 2 dy E
At midrapidity, we can measure dNch/dy
Assume nucleus is a dilute gas of nucleons
i.e. Each nucleon is separated by r > 1 fm.
Then, Energy production is additive.
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Lorentz-boost invariant observables:
Transverse Momentum: pT
æE+ p ö
1
z
Rapidity: y = ln ç
÷
2 è E - pz ø
Boost in z: y ® y - tanh-1 b = y - y'
Pseudo-Rapidity:
æ æ q öö 1 æ p + pz ö
h = -ln ç tan ç ÷÷ = ln çç
÷÷
è è 2 øø 2 è p - pz ø
Transverse Energy: E = E sin(q )
T
Invariant Cross-Section:
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Ed 3s
d 3s
=
3
dp
df dypT dpT
21
Average energy per particle.
At midrapidity: E = mT
cosh(y) » mT
Number of particles per unit
rapidity
dN ch dN ch
dN ch
=
J y ( pT ) »
dy
dh
dh
Formation time: tf.
Effective overlap area: S.
For central collisions of
identical nuclei:
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S » pR
2
22
Negatively charged hadron
spectra
STAR, PRL 87, 112303 (2001)
pT = 0.508 ± 0.012 GeV/c
dN hdh
= 280 ±1± 20
Including extrapolation to
b=0, Jacobian, average mass,
Nh- to Nch , r0=1.16 fm, t<1fm
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Energy density e ≥ 4 GeV/fm3 : ~ 7×eC.
Secondary particle spectra: Tch~170 MeV
First evidence that we reached the high
temperature phase of QCD.
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Substantial collective flow
The system behaves more like a liquid
than a gas.
Jet quenching
The system is opaque to fast partons.
The liquid has almost zero viscosity
Properties close to those of a perfect
fluid.
Quark number scaling observed in flow
of different particles
Suggestive of a quark intermediate state:
“partonic collectivity”
Bottomonium is suppressed
A probe of Deconfinement at high
temperature?
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