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 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 ?