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” (+ / -)

force decreases with distance

+ -

+ +

Atom

Atomic nuclei and the “nuclear” force

Nuclei composed of:

protons (+ electric charge)

neutrons (no electric charge)

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

neutron

quark

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

Strong color field

Energy grows with

separation !!!

Confinementto study structure of an

atom…

“white” proton

nucleus

electron

quark

quark-antiquark pair

created from vacuum

“white” proton

(confined

quarks)

“white” 0

(confined

quarks)

Confinement: fundamental & crucial (but not well understood!) feature of strong

force

- colored objects (quarks) have energy in normal vacuum… QCD

neutral atom

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 Quarks and gluons are studied on a discrete space-

time lattice

Solves the problem of divergences in pQCD calculations (which arise due to loop diagrams)

The lattice provides a natural momentum cut-off

Recover the continuum limit by letting a 0

• There are two order parameters

aa

Ns3 N

pmax

a

, pmin

Ns a

1. The Polyakov Loop L ~ Fq2. The Chiral Condensate ~ mq

pure gauge = gluons only

1 s2

Order Parameters Deconfinement measure:

Palyokov loop

Effective quark mass

Energy density є at

deconfinement

The phase diagram of QCDT

em

per

atu

re

baryon density

Neutron stars

Early universe

nucleinucleon gas

hadron gas

quark-gluon plasma

Tc

0

critical point ?

vacuum

Generating a deconfined state

Nuclear Matter(confined)

Hadronic Matter(confined)

Quark Gluon Plasmadeconfined !

Present understanding of Quantum Chromodynamics (QCD)

heating

compression deconfined color matter

RHICBRAHMSPHOBOS

PHENIXSTAR

AGS

TANDEMS

Relativistic Heavy Ion Collider (RHIC)

1 km

v = 0.99995c = 186,000 miles/sec

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!