PHYSICS 224C
Nuclear Physics III Experimental High Energy
You can find this page at http://nuclear.ucdavis.edu/~cebra/classes/phys224/phys224c.html
QUARTER: Fall 2008
LECTURES: 432 Phys/Geo, TR 2:10 to 3:30
INSTRUCTOR: Daniel Cebra, 539 P/G, 752-4592, cebra@physics.ucdavis.edu
GRADERS: none
TEXT: No required text. The following could be useful:
R.L Vogt Ultrarelativistic Heavy Ion Collisions
C.Y. Wong Introduction to High-Energy Heavy-Ion Collisions
L.P. Csernai Introduction to Relativistic Heavy Ion Collisions
J. Letessier and J. Rafelski Hadrons and Quark-Gluon Plasma
HOMEWORK: There will be presentations assigned through the quarter.
EXAM: There will be no exams for this course
GRADE DETERMINATION: Grade will be determined presentations and class participation
OFFICE HOURS: Cebra (any time)
Course Overview: The class will be taught as a seminar class. We will alternate between lectures to
overview the concepts with readings and discussions of critical papers in the field. There will be no
homework assignments, no exams. Students are read the discussion papers ahead and to come
prepared for presentations.
Course Outline
I.
Overview and Historical Perspective
a.
b.
c.
I.
Hagedorn Bootstrap Model
Bjorken energy density
Basic Kinematics
Quantum Chromodynamics
a.
b.
c.
d.
II.
Asymptotic freedom
Confinement
Chirality
Drell-yan
Initial Conditions and First Collisions
a.
b.
c.
I.
Glauber Model --- pre-collision and initial geometry (impact parameter)
Color-Glass Condensate
Parton Cascade ---
Quark-Gluon Plasma Formation and Evolution
a.
b.
c.
II.
Lattice QCD
Hydrodynamics
Elliptic flow
Probes of the Dense Partonic Phase
a.
b.
c.
d.
e.
I.
J/y Suppression and open charm
Upsilon
Jets
Direct Photons
Di-Leptons
Hadronization
a.
b.
c.
II.
Recombination vs. Fragmentation
Chemical Equilibrium, Chemical freeze-out
Strangeness enhancement
Thermal Freeze-out
a.
b.
c.
I.
Pion production/Entropy
Radial Flow
HBT
Implications
a.
b.
c.
Big Bang Cosmology
BBN
Supernovae
d.
Neutron, Strange, and Quark Stars
Broad Historic Developments
1896 Discovery of Radioactivity (Becquerel)
1911 Nuclear Atom (Rutherford)
1932 Discovery of the neutron (Chadwick)
1935 Meson Hypothesis (Yukawa)
1939 Liquid-Drop model of nucear fission (Bohr and Wheeler)
1947 Discovery of the pion (Powell)
1949 Nuclear Shell Model (Mayer and Jensen)
1953 Strangeness Hypothesis (Gell-Mann and Nishjima)
1953 First production of strange particles (Brookhaven)
1955 Discovery of the anti-proton (Chamberlain and Segre)
1964 Quark model of hadrons (Gell-Mann and Zweig)
1967 Electroweak model proposed (Weinberg and Salam)
1970 Charm hypothesis (Glashow)
1974 Discovery of the J/y (Ricther, Ting)
1977 U Discovered and bottom inferred (Lederman)
1980 First Quark Matter meeting (Darmstadt, Germany)
1983 W and Z discovered (Rubbia)
1983 Isabelle cancelled
1984 RHIC Proposal
1986 Heavy-ion operations at the AGS and SPS
1992 Au beams at the AGS and Pb beams at the SPS
1995 Top quark observed (Fermilab)
2000 Au+Au operations at RHIC
2009? Pb+Pb operations at the LHC
3/22/2016
Physics 224C – Lecture 1 -- Cebra
3
A brief history of relativistic heavy-ion facilities
LBNL – Bevalac (1980 – 1992) [Au 0.1 to 1.15 AGeV]
EOS --- TPC : DLS --- DiLepton spectrometer
GSI – SIS () []
TAPS: KaoS: FoPi
BNL – AGS (1986-1995) [Si, 1994 Au 10 AGeV, 8, 6, 4, 2]
E802/866/917; E810/891; E877; E878; E864; E895; E896
CERN – SPS (1986-present) [O 60, 200 AGeV (1986-87); S 200 AGeV (1987-1992): Pb 158, 80, 40, 30, 20 AGeV
(1994-2000), In]
HELIOS(NA34); NA35/NA49/NA61(Shine); NA36; NA38/NA50/NA60; NA44; CERES(NA45); NA52
WA85/WA94/WA97/NA57;
WA80/WA9898
BNL – RHIC (2000-present) [Au+Au 130, 200, 62.4, 19.6, d+Au 200, Cu+Cu 200, 62.4, 22, p+p 200, 450]
STAR
PHENIX
Phobos
BRAHMS
pp2pp
CERN – LHC (2009?)[Pb+Pb]
ALICE
CMS
ATLAS
3/22/2016
Physics 224C – Lecture 1 -- Cebra
4
Quark-Gluon Plasma
3/22/2016
Physics 224C – Lecture 1 -- Cebra
5
Motivation for Relativistic Heavy Ion Collisions
Two big connections: cosmology and QCD
The phase diagram of QCD
Temperature
Early universe
critical point ?
quark-gluon plasma
Tc
colour
superconductor
hadron gas
nucleon gas
nuclei
CFL
r0
vacuum
baryon density
Neutron stars
Evolution of Forces in Nature
Going back in time…
Age
0
10-35 s
Energy
Matter in universe
1019 GeV
grand unified theory of all forces
1014 GeV
1st phase transition
(strong: q,g + electroweak: g, l,n)
10-10s
102 GeV
2nd phase transition
(strong: q,g + electro: g + weak: l,n)
10-5 s
0.2 GeV
3rd phase transition
RHIC, LHC & FAIR
0.1 MeV
RIA & FAIR nuclei
(strong:hadrons + electro:g + weak: l,n)
3 min.
6*105 years
0.3 eV
Now (1.5*109 years) 3*10-4 eV = 3 K
atoms
Connection to Cosmology
• Baryogenesis ?
• Dark Matter Formation ?
• Is matter generation in cosmic medium (plasma)
different than matter generation in vacuum ?
Sakharov (1967) – three conditions for baryogenesis
• Baryon number violation
• C- and CP-symmetry violation
• Interactions out of thermal equilibrium
•
Currently, there is no experimental evidence of particle interactions where the conservation of
baryon number is broken: all observed particle reactions have equal baryon number before and
after. Mathematically, the commutator of the baryon number quantum operator with the
Standard Model hamiltonian is zero: [B,H] = BH - HB = 0. This suggests physics beyond the
Standard Model
•
The second condition — violation of CP-symmetry — was discovered in 1964 (direct CP-violation,
that is violation of CP-symmetry in a decay process, was discovered later, in 1999). If CPTsymmetry is assumed, violation of CP-symmetry demands violation of time inversion symmetry,
or T-symmetry.
•
The last condition states that the rate of a reaction which generates baryon-asymmetry must be
less than the rate of expansion of the universe. In this situation the particles and their
corresponding antiparticles do not achieve thermal equilibrium due to rapid expansion
decreasing the occurrence of pair-annihilation.
Dark Matter in RHI collisions ? Possibly (not like dark energy)
The basic parameters: mass, charge
Basic Thermodynamics
dE  TdS  PdV
Hot
Hot
Hot
Hot
Cool
Sudden expansion, fluid fills empty
space without loss of energy.
dE = 0
PdV > 0 therefore dS > 0
Gradual expansion (equilibrium maintained),
fluid loses energy through PdV work.
dE = -PdV therefore dS = 0
Isentropic
Adiabatic
Nuclear Equation of State
Nuclear Equation of State

Golden Rule 1: Entropy per co-moving volume is conserved
Golden Rule 2: All entropy is in relativistic species
Expansion covers many decades in T, so typically either
T>>m (relativistic) or T<<m (frozen out)
Golden Rule 3: All chemical potentials are negligible
Entropy S in co - moving volume
Relativistic gas
  preserved
3
2 2  3 2 2 
S
3
 s   sParticle Type   
 T  
gS T
V
45 
 45 
Particle Type
Particle Type
gS  effective number of relativistic species
S
S 1 2 2
3
Entropy density


g
T
S
V  3 a 3
45
Golden Rule 4:
 13
T  gS 
1
a
g*S
1 Billion oK
1 Trillion oK
Start with light particles, no strong nuclear force
g*S
1 Billion oK
1 Trillion oK
Previous
Plot
Now add hadrons = feel strong nuclear force
g*S
1 Billion oK
1 Trillion oK
Previous
Plots
Keep adding more hadrons….

How many hadrons?
Density of hadron mass
states dN/dM increases
exponentially with mass.
dN


~ exp M 
 TH 
dM
TH ~ 21012 oK
Broniowski, et.al. 2004
Prior to the 1970’s this was explained in several ways theoretically
Statistical Bootstrap Hadrons made of hadrons made of hadrons…
Regge Trajectories Stretchy rotators, first string theory
Hagedorn Limiting Temperature
Ordinary statistical mechanics
E~
 E i gi expE i /T ~

E
states i
dN
exp E /T dE
dE
For thermal hadron gas (somewhat crudely):
dN
dN
exp
M
/T
dM
now
add
in
~ exp M /TH 


 dM
dM
 1 1 
~  M expM  
 dM
 T TH 
E ~
M
Energy diverges as T --> TH
Maximum achievable temperature?
“…a veil, obscuring our view of the very
beginning.” Steven Weinberg, The First Three
Minutes (1977)
Rolf Hagedorn
German
Hadron bootstrap
model and limiting
temperature (1965)
What do I mean “Bjorken”?
Boost-invariant
Increasing E
y
y
dN/dy’
“Inside-out” & 1 dimensional
y’=y-ybeam
0
Impact of “Bjorken”
X
X
• dN/dy distribution is flat over a large region except
“near the target”.
• v2 is independent of y over a large region except
“near the target”. (2d-hydro.)
• pT(y) described by 1d or 2d-hydro.
• Usual HBT interpretation starts from a boostinvariant source.
• T(t) described by 1d-hydro.
• Simple energy density formula
Notations
We’ll be using the
x0
following notations:
proper time
  x02  x32
and rapidity
1 x0  x3
  ln
2 x0  x3
x3
Most General Boost Invariant Energy-Momentum Tensor
The most general boost-invariant energy-momentum tensor
for a high energy collision of two very large nuclei is (at x3 =0)
T 
which, due to
gives
  ( )

 0

0

 0

 T

0
p( )
0
0
0
0
p( )
0
0  xt 0

0  xx1
0 x
y
 2
p3 ( )  x
z3
0
x2
  p3
d

d

There are 3 extreme limits.
x3
x1
Limit I: “Free Streaming”
Free streaming is characterized by the following “2d”
energy-momentum tensor:
T 
~
  ( )

 0

0

 0

0
p( )
0
0
0
0  xt 0

0
0  x1
p( ) 0  xy2

0
0  xz3
1

such that
d


d

and
 The total energy E~ is conserved, as expected for
non-interacting particles.
Limit II: Bjorken Hydrodynamics
In the case of ideal hydrodynamics, the energy-momentum
tensor is symmetric in all three spatial directions (isotropization):
T 
  ( )

 0

0

 0

0
p( )
0
0
0
p( )
0
0
 tx0

 xx1
 yx
 2
p( )  zx3
0
0
0
Using the ideal gas equation of state,
~
1
 4/3
such that
d
p

d

, yields
 3p
Bjorken, ‘83
 The total energy E~  is not conserved, while the total entropy S is conserved.
Most General Boost Invariant Energy-Momentum Tensor
 getsp3
d , one

d

p3  0then, as
If
~
1

1 
~
 1 
1
 ~scaling of energy density,

Deviations from the
like
.
1
,
aredue
0 to longitudinal pressure
p3 , which does work
longitudinal direction
pin 3thedV
modifying the energy density scaling with tau.
 Non-zero positive longitudinal
pressure and isotropization
↔ deviations from
 ~
1

Limit III: Color Glass at Early Times
 ~ log
In CGC at very early times
such that, since
  p3
d

d

1

,(Lappi, ’06)
QS  1
we get, at the leading log level,
Energy-momentum tensor is
T 
2
0
0
0 
  ( )


 ( ) 0
0 
 0

0
0
 ( )
0 


 0

0
0


(

)


tx0
xx1
yx2
zx3
Replace Hadrons
(messy and
numerous)
by Quarks and
Gluons (simple
and few)
“In 1972 the early universe seemed
hopelessly opaque…conditions of
ultrahigh temperatures…produce a
theoretically intractable mess. But
asymptotic freedom renders
ultrahigh temperatures friendly…”
Frank Wilczek, Nobel Lecture
(RMP 05)
D. Gross
H.D. Politzer
F. Wilczek
American
QCD Asymptotic
Freedom (1973)
/T4
 g*S
Thermal QCD
”QGP”
Hadron gas
QCD to the rescue!
(Lattice)
Karsch, Redlich, Tawfik,
Eur.Phys.J.C29:549-556,2003
Nobel prize for Physics 2005
e+e- Annihilation
Nucleosynthesis
Mesons
freeze out
QCD Transition
g*S
Heavy quarks and
bosons freeze out
Thermal QCD -- i.e.
quarks and gluons -makes the very
early universe
tractable; but where
is the experimental
proof?
 Decoupling
“Before [QCD] we could not go back further than 200,000 years after the Big Bang.
Today…since QCD simplifies at high energy, we can extrapolate to very early times
when nucleons melted…to form a quark-gluon plasma.” David Gross, Nobel
Lecture (RMP 05)
Kolb & Turner, “The Early Universe”
The main features of Quantum Chromodynamics
•
•
•
Confinement
– At large distances the effective coupling between quarks is large, resulting
in confinement.
– Free quarks are not observed in nature.
Asymptotic freedom
– At short distances the effective coupling between quarks decreases
logarithmically.
– Under such conditions quarks and gluons appear to be quasi-free.
(Hidden) chiral symmetry
– Connected with the quark masses
– When confined quarks have a large dynamical mass - constituent mass
– In the small coupling limit (some) quarks have small mass - current mass
Quarks and Gluons
Basic Building Blocks ala Halzen and Martin
Quark properties ala Wong
What do we know about quark masses ?
Why are quark current masses so
different ?
Can there be stable (dark) matter
based on heavy quarks ?
Elementary Particle Generations
Some particle properties
Elemenary particles summary
Comparing QCD with QED (Halzen & Martin)
Quark and Gluon Field Theory == QCD (I)
Quark and Gluon Field Theory == QCD (II)
Quark and Gluon Field Theory == QCD (III)
• Boson mediating the q-qbar interaction is the gluon.
• Why 8 and not 9 combinations ? (analogy to flavor
octet of mesons)
–
–
–
–
R-Bbar, R-Gbar, B-Gbar, B-Rbar, G-Rbar, G-BBar
1/sqrt(2) (R-Rbar - B-Bbar)
1/sqrt(6) (R-Rbar + B-Bbar – 2G-Gbar)
Not: 1/sqrt(3) (R-Rbar + G-Gbar + B-Bbar) (not net color)
Hadrons
QCD – a non-Abelian Gauge Theory
Particle Classifications
Quarks
Theoretical and computational (lattice) QCD
In vacuum:
- asymptotically free quarks have current mass
- confined quarks have constituent mass
- baryonic mass is sum of valence quark constituent masses
Masses can be computed as a function of the evolving coupling
Strength or the ‘level of asymptotic freedom’, i.e. dynamic masses.
But the universe was not a vacuum at the time of hadronization, it was likely a plasma
of quarks and gluons. Is the mass generation mechanism the same ?
Confinement Represented by Bag Model
Bag Model of Hadrons
Comments on Bag Model
Still open questions in the Standard Model
Why RHIC Physics ?
Why RHIC Physics ?