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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, [email protected]
GRADERS: none
TEXT: No required text. The following could be useful: R.L Vogt Ultrarelativistic Heavy Ion CollisionsC.Y. Wong Introduction to High-Energy Heavy-Ion CollisionsL.P. Csernai Introduction to Relativistic Heavy Ion CollisionsJ. 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.
PHYSICS 224C
Nuclear Physics III - Experimental High Energy
Course OutlineI. Overview and Historical Perspective
a. Hagedorn Bootstrap Modelb. Bjorken energy densityc. Basic Kinematics
I. Quantum Chromodynamicsa. Asymptotic freedomb. Confinementc. Chiralityd. Drell-yan
II. Initial Conditions and First Collisionsa. Glauber Model --- pre-collision and initial geometry (impact parameter)b. Color-Glass Condensatec. Parton Cascade ---
I. Quark-Gluon Plasma Formation and Evolutiona. Lattice QCDb. Hydrodynamicsc. Elliptic flow
II. Probes of the Dense Partonic Phasea. J/y Suppression and open charmb. Upsilon c. Jetsd. Direct Photonse. Di-Leptons
I. HadronizationI. Recombination vs. FragmentationII. Chemical Equilibrium, Chemical freeze-outIII. Strangeness enhancement
• Thermal Freeze-outI. Pion production/EntropyII. Radial FlowIII. HBT
• ImplicationsI. Big Bang CosmologyII. BBNIII. SupernovaeIV. Neutron, Strange, and Quark Stars
Broad Historic Developments
04/18/23 3Physics 224C – Lecture 1 -- Cebra
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/ (Ricther, Ting)1977 Discovered and bottom inferred (Lederman)1980 First Quark Matter meeting (Darmstadt, Germany)1983 W and Z discovered (Rubbia)1983 Isabelle cancelled1984 RHIC Proposal1986 Heavy-ion operations at the AGS and SPS1992 Au beams at the AGS and Pb beams at the SPS1995 Top quark observed (Fermilab)2000 Au+Au operations at RHIC2009?Pb+Pb operations at the LHC
A brief history of relativistic heavy-ion facilities
04/18/23 4Physics 224C – Lecture 1 -- Cebra
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); NA52WA85/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]STARPHENIXPhobosBRAHMSpp2pp
CERN – LHC (2009?)[Pb+Pb]ALICECMSATLAS
Quark-Gluon Plasma
04/18/23 5Physics 224C – Lecture 1 -- Cebra
Motivation for Relativistic Heavy Ion Collisions
Two big connections: cosmology and QCD
The phase diagram of QCDT
em
per
atu
re
baryon density
Neutron stars
Early universe
nucleinucleon gas
hadron gascolour
superconductor
quark-gluon plasmaTc
0
critical point ?
vacuum
CFL
Evolution of Forces in Nature
Age Energy Matter in universe
0 1019 GeV grand unified theory of all forces
10-35 s 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(strong:hadrons + electro:g + weak: l,n)
3 min. 0.1 MeV nuclei
6*105 years 0.3 eV atoms
Now (1.5*109 years) 3*10-4 eV = 3 K
Going back in time…
RHIC, LHC & FAIRRIA & FAIR
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 CPT-symmetry 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, chargeThe basic parameters: mass, charge
dE TdS PdV
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 = 0Isentropic Adiabatic
Hot
Hot
Hot
Hot
Cool
Basic Thermodynamics
Nuclear Equation of State
Nuclear Equation of State
Golden Rule 1: Entropy per co-moving volume is conserved
Golden Rule 3: All chemical potentials are negligible
Golden Rule 2: All entropy is in relativistic speciesExpansion covers many decades in T, so typically either T>>m (relativistic) or T<<m (frozen out)
Entropy S in co - moving volume 3preserved
Relativistic gas S
Vs sParticle Type
Particle Type
2 2
45
T 3
Particle Type
2 2
45
gS T 3
gS effective number of relativistic species
Entropy density S
V S
3
1
a3 2 2
45gS T 3
T gS 1
31
aGolden Rule 4:
g*S1 Billion oK 1 Trillion oK
Start with light particles, no strong nuclear force
g*S1 Billion oK 1 Trillion oK
Previous Plot
Now add hadrons = feel strong nuclear force
g*S1 Billion oK 1 Trillion oK
Previous Plots
Keep adding more hadrons….
Density of hadron mass states dN/dM increases exponentially with mass.
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
dN
dM~ exp M
TH
Broniowski, et.al. 2004TH ~ 21012 oK
How many hadrons?
Rolf Hagedorn GermanHadron bootstrap model and limiting temperature (1965)
E ~ E i gi
states i
exp E i /T ~ EdN
dE exp E /T dE
E ~ MdN
dM exp M /T dM now add in
dN
dM~ exp M /TH
~ M exp M1
T 1
TH
dM
Ordinary statistical mechanics
For thermal hadron gas (somewhat crudely):
Energy diverges as T --> TH
Maximum achievable temperature?
“…a veil, obscuring our view of the very beginning.” Steven Weinberg, The First Three Minutes (1977)
Hagedorn Limiting Temperature
What do I mean “Bjorken”?
y y
Increasing E
y’=y-ybeam
0
dN/dy’
“Inside-out” & 1 dimensional
Boost-invariant
Impact of “Bjorken”
• 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 boost-
invariant source.• T(t) described by 1d-hydro.• Simple energy density formula
X
X
Notations
We’ll be using the
following notations:
proper time
and rapidity
23
20 xx
30
30ln2
1
xx
xx
0x
3x
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)
z
y
x
t
p
p
pT
)(000
0)(00
00)(0
000)(
3
which, due to 0 T
gives
3p
d
d
There are 3 extreme limits.
0x
1x
2x
3x
3x
2x
1x
Limit I: “Free Streaming”
1
~
Free streaming is characterized by the following “2d”
energy-momentum tensor:
z
y
x
t
p
pT
0000
0)(00
00)(0
000)(
d
d
such that
and
The total energy E~ is conserved, as expected for
non-interacting particles.
0x
1x
2x
3x
Limit II: Bjorken Hydrodynamics
3/4
1~
In the case of ideal hydrodynamics, the energy-momentum
tensor is symmetric in all three spatial directions (isotropization):
z
y
x
t
p
p
pT
)(000
0)(00
00)(0
000)(
p
d
d
such that
Using the ideal gas equation of state, , yields p3
Bjorken, ‘83
The total energy E~ is not conserved, while the total entropy S is
conserved.
0x
1x
2x
3x
Most General Boost Invariant Energy-Momentum Tensor
Deviations from the scaling of energy density,
like are due to longitudinal pressure
, which does work in the longitudinal direction
modifying the energy density scaling with tau.
1
~
3p0,
1~
1
dVp3
Non-zero positive longitudinal
pressure and isotropization 1
~
3p
d
d If then, as , one gets .03 p 1
1~
↔ deviations from
Limit III: Color Glass at Early Times1,
1log~ 2 SQ
In CGC at very early times
z
y
x
t
T
)(000
0)(00
00)(0
000)(
3p
d
d such that, since
0x
1x
2x
3x
we get, at the leading log level,
Energy-momentum tensor is
(Lappi, ’06)
Karsch, Redlich, Tawfik, Eur.Phys.J.C29:549-556,2003
/T4
g*S
D. GrossH.D. PolitzerF. Wilczek
American
QCD Asymptotic Freedom (1973)
“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)
QCD to the rescue!
Replace Hadrons (messy and numerous)
by Quarks and Gluons (simple
and few)
Ha
dro
n g
as
Thermal QCD ”QGP” (Lattice)
Nobel prize for Physics 2005
Kolb & Turner, “The Early Universe”
QC
D T
rans
ition
e+e- A
nnih
ilatio
n
Nuc
leos
ynth
esis
D
ecou
plin
g
Mes
ons
free
ze o
ut
Hea
vy q
uark
s an
d bo
sons
free
ze o
ut
“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)
Thermal QCD -- i.e. quarks and gluons -- makes the very early
universe tractable; but where is the experimental
proof?
g*S
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) QCDIn 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 ?