The Phase Diagram of
Nuclear Matter
Oumarou Njoya
Outline

Motivations for studying QCD phase transitions

Introduction to QCD

Mapping the phase diagram

Experimental considerations

Summary
Motivations

The Big bang Theory

Neutron stars

Discovery of strong force
Forces and structures in Nature
Gravity
one “charge” (mass)
force decreases with distance
m1
m2
Electromagnetism
two “charges” (+ / -)
Atom
force decreases with distance
+
-
+
+
Atomic nuclei and the “nuclear” force
Nuclei composed of:
quark
protons (+ electric charge)
neutrons (no electric charge)
neutron
Do not fly apart!?  “nuclear force”
overcomes electrical repulsion
determines nuclear reactions
(stellar burning, bombs…)
arises from fundamental strong force (#3)
acts on color charge of quarks
proton
What is QCD?

Quantum chromo-dynamics

A theory of the strong (or nuclear, or color) force.


Closely modeled on QED but with three conserved
color charges:

Quarks: r, g, b

Anti quarks: anti-red, anti-green, anti-blue.
Quarks scatter by exchanging gluons, which carry color
and anticolor.
More QCD

Only colour singlet states can exist as free particles.
Hadrons are colour singlet.

Mesons:

Baryons:

Confinement (r ~ 1fm)

Chiral symmetry


Having to do with quark masses
Asymptotic freedom (r → 0)

Strong interaction becomes weaker at high energy

Relativistic hot gas
Confinement
to study structure of an atom…
electron
nucleus
neutral atom
Confinement: fundamental & crucial (but not well understood!) feature of strong
force
- colored objects (quarks)
have  energy
quark-antiquark
pair in normal vacuum… QCD
created from vacuum
quark
“white” proton
(confined quarks)
Strong color field
“white” 0
“white”
proton
Energy
grows
with separation
(confined quarks)
!!!
QCD Thermodynamics


Relativistic kinematics of free gas.
Partition function:
bosons
fermions
A simple model

Ideal gas of massless pions. Stefan-Boltzmann
From hadrons to quarks and gluons


Chiral symmetry argument

Massless u and d implies chirally
symmetric Lagrangian. Spontaneous
symmetry breaking in ground state.

Symmetry conserved at high T.

Expect phase transition. (akin to Curie
point in a ferromagnet).

Pisarski-Wilzeck: 1st order transition
Tricritical point

Evidence suggests 1st order at high T
and low μB

At low T: nuclear matter
Crossover and critical point

Crossover for μB = 0. (Lattice QCD)

Critical point

Coexisting phases along 1st order line, similar to that of liquid in condensed matter
physics

Low-T high- μB: ordered quark phases exist
Locating the critical point

Theoretically simple (singularity of partition
function).

Importance sampling and sign problem.

Lattice QCD.
Lattice QCD
• There are two order parameters

Quarks and gluons are studied on a discrete space-time
lattice
1. The Polyakov Loop
2. The Chiral Condensate


Solves the problem of divergences in pQCD
calculations (which arise due to loop diagrams)
L ~ Fq
 ~ mq
The lattice provides a natural momentum cut-off
pure gauge = gluons only
pmax  ,
a

pmin 
Ns  a
Recover the continuum limit by letting a  0
  1  2s
Order Parameters



Deconfinement measure:
Palyokov loop
Effective quark mass
Energy density є at
deconfinement
The phase diagram of QCD
Early universe
Temperature
critical point ?
quark-gluon plasma
Tc
hadron gas
nucleon gas
nuclei
0
vacuum
baryon density
Neutron stars
Generating a deconfined state
Present understanding of Quantum Chromodynamics (QCD)
heating
compression
 deconfined color matter
Hadronic
Nuclear
Matter
Matter
Quark
Gluon
Plasma
(confined)!
deconfined
Relativistic Heavy Ion Collider (RHIC)
PHOBOS
PHENIX
1 km
RHIC
BRAHMS
STAR
v = 0.99995c = 186,000 miles/sec
AGS
TANDEMS
A few methods

Hadron radiation

Electromagnetic radiation


Dissipation of a passing quarkonyum beam
(fancy for Debye screening in nuclear matter)
Energy loss of a passing jet.
Hadron radiation



Formed at the transition surface between hot matter and
physical vacuum.
At Tc local hadronization occurs. Mostly pions, kaons,
nucleons and anti-nucleons.
Study of relative abundances gives us information about
hadronization temperature.
Electromagnetic radiation


Spectra of photons and leptons provide
information about the state of the medium at the
time they were formed.
Consider for illustration μ+μ- formation
Summary




Mapping the QCD phase diagram is important for
understanding the early evolution of the universe and the
physics of neutron star.
QCD thermodynamics suggests a well-defined transition
from hadronic matter to a plasma of deconfined quarks and
gluons.
The nature and the origin of the transition at high needs to
be clarified further.
The properties of the QGP can be explored through hard
probes. Certainly, lots of new physics await discovery.
Bibliography

M. Stephanov, [arXiv:hep-lat/0701002v1]

Helmut Satz, [arXiv:0903.2778v1 [hep-ph]]


Peter G Jones, Introduction to QCD,
rhic.physics.wayne.edu/~bellwied/classes/phy707
0/QCD-lecture.ppt
Slides 5,8,17,18 were borrowed from Gang Wang
(UCLA).
Thank you!