Introduction to Relativistic Heavy
Ion Collision Physics
Huan Z. Huang
黄焕中
Department of Physics and Astronomy
University of California, Los Angeles
Oct 2006 @Tsinghua
http://hep.tsinghua.edu.cn/talks/Huang/
Two Puzzles of Modern Physics
-- T.D.Lee
• Missing Symmetry – all present
theories are based on symmetry, but
most symmetry quantum numbers are
NOT conserved.
• Unseen Quarks – all hadrons are made
of quarks, yet NO individual quark has
been observed.
Vacuum As A Condensate
• Vacuum is everything but empty!
• The complex structure of the vacuum and the
response of the vacuum to the physical
world breaks the symmetry.
• Vacuum can be excited!
We do not understand vacuum at all !
A Pictorial View of Micro-Bangs at RHIC
Thin Pancakes
Lorentz g=100
Huge Stretch
Nuclei pass
The Last Epoch:
thru each other Transverse Expansion Final Freezeout-High Temperature (?!)
< 1 fm/c
Large Volume
Au+Au Head-on Collisions  40x1012 eV ~ 6 micro-Joule
Human Ear Sensitivity ~ 10-11 erg = 10-18 Joule
A very loud Bang, indeed, if E Sound……
Vacuum Engineering !
High Energy Nucleus-Nucleus Collisions
initial state
hadronic phase
and freeze-out
QGP and
hydrodynamic expansion
pre-equilibrium
hadronization
Physics:
1) Parton distributions in nuclei
2) Initial conditions of the collision
3) a new state of matter – Quark-Gluon Plasma and its properties
4) hadronization
Kinematic Variables
Rapidity:
1 E  PZ
y  ln(
)
2 E  PZ
1 P  PZ

)   ln(tan )
Pseudo-rapidity:   ln(
2 P  PZ
2
Transverse Momentum:
pT 
p p
Transverse Mass:
mT 
p m
2
X
2
T
2
Y
2
0
Useful Expressions
E  mT cosh y
pZ  mT sinh y
 z  tanh y
dpz  Edy
Feymann xF:
pL*
pL*
xF  *  S
pmax
2
q2  ( pi  p f )2 ; Q 2   q2
Bjorken x:
  (Ei  E f )
Q2
x
2 M
Light-cone x+:
( E  pz )
x 
( E  pz )beam
Cross Sections
sTotal =
Number of Reactions
Number of Beam Particles X Scattering Center / Area
Dimension [L2]
sTotal = sinel + sel
sinel= sSD + sND
SD: Singly Diffractive
ND: Non-Diffractive
3
d
Differential Cross Section: 3s
d p
d 3 p  dpx dp y dpz  p 2dp sin dd
Question: differential cross section vs total cross section?
Invariant Cross Sections
Invariant Differential Cross Section:
E d3s/d3p 
d 2s
2pT dpT dy
d 2s
2mT dmT dy
2
d
N
Invariant Multiplicity Density:
N ev 2pT dpT dy
E d3n/d3p 
d 2N
N ev 2mT dmT dy
Experimental Considerations: Efficiency, Acceptance, Decay
Correction, Target-out Correction.
Order of Magnitude
Geometrical CS:
pp r2 = (1fm)2 = 32 mb
Au+Au Collisions:
Rau = 1.2 A1/3 = 6.98 fm
bmax=(2R)2 = 6 barn
1 barn = 10-24 cm2
Regge Theory:
stotal=XS0.0808 + YS-0.4525
p-pbar 21.70
p-p
21.70
98.39 mb
56.08 mb
Pomeron r,w,f,a,….
HIJING: minijet production
Luminosity at Collider
L=
NB2 B v / U
A
B  Number of bunches per beam
NB  Number of particles per bunch
v  velocity of particles
U  circumference of the ring
A  beam cross section at the collision
Relativistic Heavy Ion Collider:
3
gN
L  f rev B
2
N 
N Invariant Transverse 95% Emittance
*  the beta function
2
B
*
RHIC Numbers
RHIC Design:
B
NB
L
sNN
Au Beam
57
109
2x1026
200 GeV
Collision Rate: L x s
1200 Hz
proton Beam
1011
1x1031 cm-2s-1
500 GeV
0.7 MHz
RHIC Complex
Relativistic Heavy Ion Collider --- RHIC
STAR
Au+Au 200 GeV N-N CM energy
Polarized p+p up to 500 GeV CM energy
Building Blocks of Hadron World
Molecules
Atoms
Nucleus
Proton
(uud)
Electrons
Neutron
(udd)
Hyperons
(s…)
Mesons Exotics
(q-q) (qqqq-q,…)
Strong interaction is due to color charges and mediated
by gluons. Gluons carry color charges too.
Baryon Density: r = baryon number/volume
normal nucleus r0 ~ 0.15 /fm3 ~ 0.25x1015 g/cm3
Temperature,
MeV ~ 1.16 x 1010 K
10-6 second after the Big Bang T~200 MeV
Energy Scale and Phase Transition
Entity
Energy
Dimension
Physics
Bulk Property
P/T
Atom
10’s eV
10-10 m
Ionization
e/Ion Plasma
No
Nucleus 8 MeV
10-14 m
Multifrag.
Liquid-Gas
Y(?)
QCD
200 MeV
10-15 m
Deconfine.
QGP
Y(?)
EW
100 GeV
10-18 m
P/CP
GUT
1015-16 GeV
Supersymmetry
TOE
1019 GeV
Superstring
Baryon Asymmetry Y(?)
Salient Feature of Strong Interaction
Asymptotic Freedom:
Quark Confinement:
Coupling Strength
庄子天下篇 ~ 300 B.C.
一尺之棰，日取其半，万世不竭
Take half from a foot long stick each day,
You will never exhaust it in million years.
q
QCD
q
Shorter distance 
q
(GeV)
Momentum Transfer
q q
q
Quark pairs can be produced from vacuum
No free quark can be observed
QCD on Lattice
Transition from quarks to hadrons – DOF !
QGP – not an ideal Boltzmann gas !
Lattice: current status
• technical progress: finer mesh size, physical quark masses, improved
fermion actions
 phase-transition: smooth, rapid cross-over
 EoS at finite μB: in reach, but with large systematic uncertainties
 critical temperature: TC180 MeV
Fodor & Katz, hep-lat/0110102
Rajagopal & Wilczek, hep-ph/0011333
Quark-Hadron Phase Transition
QGP – micro-second after the Big Bang
The Melting of Quarks and Gluons
-- Quark-Gluon Plasma -Matter Compression:
Vacuum Heating:
Deconfinement
High Baryon Density
-- low energy heavy ion collisions
-- neutron starquark star
High Temperature Vacuum
-- high energy heavy ion collisions
-- the Big Bang
QCD Phase Transition
early universe
Chemical Temperature Tch [MeV]
250
RHIC
200
quark-gluon plasma
SPS
150
AGS
Lattice QCD
deconfinement
chiral restoration
thermal freeze-out
100
SIS
hadron
gas
50
neutron stars
atomic nuclei
0
0
200
400
600
800
1000
1200
Baryonic Potential B [MeV]
What do experimental data points indicate and
how were these points obtained ?
Nuclear Collision Geometry
Number of Participants
Impact Parameter
Particle Production is assumed to be directly
related to the impact parameter or number of
participant nucleons.
Number of Participant Nucleons
a) Geometrical Interpretation of Observables
A monotonic relation between the observable and
collision centrality is assumed
b) Estimate from direct measurement
missing energy from Zero-degree calorimeter
from dn/dy of protons….
Directly Determining NPART
Best approach (for fixed target!):
– Directly measure in a “zero degree calorimeter”
– N PART  2   A  E ZDC (for A+A collisions)

E PerNucleon 
NA50
– Strongly (anti)-correlated
with produced
transverse energy:
ET
EZDC
ET
Number of Participant Nucleons
c) Dynamical Model
Tune to fit experimental measurement
From model to convert measurement to impact parameter
and number of participant nucleons
++ Fluctuations are included
- - Physical picture is biased to begin with
Spectrum Fit
mT spectrum: d2n/(2mT)dmTdy vs (mT-m0)
pT spectrum: d2n/(2pT)dpTdy vs pT
Boltzmann mT Fit:
d2n/(2mT)dmTdy ~ mT exp(-mT/slp)
slp  Slope Parameter
Why is this Boltzmann?
d3n/d3p ~ exp(-E/T)
Invariant Multiplicity Density:
Ed3n/d3p ~ E exp(-E/T)
E = mTcosh(y-ycm)
d2n/(2mT)dmTdy ~ mT cosh(y-ycm) exp(-mT cosh(y-ycm)/T)
Slp depends on rapidity for an isotropic thermal fireball
slp = T/cosh(y-ycm)
dn/dy =
(
2
d n
)2mT dmT  e
2mT dmT dy

( y  ycm ) 2
2s 2y
sy ~ 0.7-0.8
Naïve Expectations
• Thermal Isotropic Source  mT Scaling
, K and proton have the same slope parameter e-E/T
mid-rapidity
Tp = 565 MeV
TK = 300 MeV
T = 190 MeV
Data show a large difference among these particles  Expansion
Naïve Expectation 2
Slope parameter  Temperature
Rapidity density dn/dy  entropy or energy density
First Order Phase Transition:
<pT>
QGP
Mixed
hadron
dn/dy
Collision dynamics much more complicated !!
Collision Dynamics
Bjorken Scaling
Bjorken Ansatz: “…… at sufficient high energy there is a
‘central-plateau’ structure for the particle production as
a function of the rapidity variable.”
dn/dy
y
Physics must be invariant under Lorentz-boost:
1) Local thermodynamic quantity must be a function of
proper time
  t 2  z 2 only.
2) Longitudinal velocity
vz = z/t or y = 0.5 ln ((t+z)/(t-z))
Bjorken Energy Density
Energy density  =
E x DN
A x Dz
E  average energy per particle
A  transverse area of the collision volume
Dz  longitudinal interval
DN  number of particles in Dz interval
vz = z/t = tanh y; z =  sinh y
Dz =  cosh y Dy
E = mT cosh y
=
mT cosh y DN
A  cosh y Dy
mT dn/dy
A
Initial Energy Density Estimate
PRL 85, 3100 (00); 91, 052303 (03); 88, 22302 (02), 91, 052303 (03)
130 GeV
PHOBOS
19.6 GeV
200 GeV
Pseudo-rapidity
Within ||<0.5 the total transverse momentum
hminus:
created is 1.5x650x0.508 ~ 500 GeV
Central Au+Au <pT>=0.508GeV/c
from an initial transverse overlap
pp: 0.390GeV/c
area of R2 ~ 153 fm2 !
Energy density
 ~ 5-30 0 at early time
=0.2-1 fm/c !
Ideas for QGP Signatures
Strangeness Production: (J.Rafelski and B. Muller PRL 48, 1066 (1982))
s-s quark pair production from gluon fusions in QGP leads to
strangeness equilibration in QGP  most prominent in strange hyperon
production (L,X,W and anti-particles).
Parton Energy Loss in a QCD Color Medium:
(J.D. Bjorken Fermilab-pub-82-059 (1982)
X.N. Wang and M. Gyulassy, PRL 68, 1480 (1992))
Quark/gluon
dE/dx in color medium
is large!
Quark/gluon
Ideas for QGP Signatures
QCD Color Screening: (T. Matsui and H. Satz, Phys. Lett. B178, 416 (1986))
A color charge in a color medium is screened similar to Debye
screening in QED  the melting of J/y.
c
c
Charm quarks c-c may not bind
Into J/y in high T QCD medium
The J/y yield may be increased due to charm quark coalescence at
the final stage of hadronization (e.g., R.L. Thews, hep-ph/0302050)
Chiral Symmetry Restoration:
T = 0, m(u,d,s) > 0 – Spontaneous symmetry breaking
T> 150 MeV, m=0 – Chiral symmetry restored
Mass, width and decay branching ratios of resonances may
be different in dense medium .
F. Weber J.Phys. G27 (2001) 465
Models of Neutron Stars
“Strangeness" of dense matter ?
In-medium properties of hadrons ?
Compressibility of nuclear matter ?
Deconfinement at high baryon densities ?
The STAR Detector
1st year detectors
2nd year detectors
Magnet
Coils
TPC Endcap &
MWPC
Silicon Strip
Detector
installation in 2002
installation in 2003
Time Projection
Chamber
Silicon Vertex
Tracker
FTPCs
ZDC
ZDC
Endcap
Calorimeter
Barrel EM
Calorimeter
Vertex Position
Detectors
Central Trigger
Barrel
+ TOF
RICH