Thermodynamics of
Quark Gluon Plasma
ns =
Over 14 billion years ago, our universe began
with the Big Bang.
1
e
( ε s − μ ) / kT
±1
Professor Jamie Nagle
Department of Physics
The Big Bang was very hot, and the universe
has been cooling off ever since.
10 trillion degrees Fahrenheit.
10 million degrees Fahrenheit.
10,000,000,000,000
Temperature a fraction of a second after the Big Bang!
Temperature of the Sun.
What happens at temperatures like these?
As we heat things up, we break down larger
scale structures into more fundamental ones.
By comparison, this is quite cool.
Start with the Basics
Atoms are the basic building blocks.
They are made from a positively charged
nucleus with neutrons and protons and
negatively charged electrons in orbit.
Helium Atom
Oxygen Nucleus
1
What if we want to break down the structure even
more with higher energy reactions?
Six Flavors of Quarks
Over 30 years ago we discovered that even protons
and neutrons are made of smaller particles called
quarks.
Proton (charge = +1)
2 up quarks (+2/3 charge)
1 down quark ((-1/3 charge)
Neutron (charge = 0)
1 up quarks (+2/3 charge)
2 down quark ((-1/3 charge)
We always seem to find these quarks
in groups. We call this confinement.
No one has ever seen a free quark.
QCD is a “confining” gauge theory,
with an effective potential:
V =−
Gluons
4 αs
+ kr
3 r
“Coulomb”
“Confining”
V(r)
Quarks
r
Melting the Hadrons
Can we melt the hadrons and liberate these quark
and gluon degrees of freedom?
ε=g
π2
30
T
4
The Quark Gluon Plasma
Calculations predict a transition to a Quark Gluon Plasma.
ε=g
Energy density for “g” massless d.o.f.
π2
30
T4
14.0
Transition values:
ε = 3⋅
π2
30
T4
Hadronic Matter: quarks and gluons confined
For T ~ 200 MeV, 3 pions with spin=0
2
7
⎧
⎫π
ε = ⎨ 2 ⋅ 8 g + ⋅ 2 s ⋅ 2 a ⋅ 2 f ⋅ 3c ⎬ T 4
8
⎩
⎭ 30
ε = 37 ⋅
π2
30
T4
Non-Interacting Gas Limit
ε/T4 16.0
37 !
Quark Gluon Matter:
8 gluons;
2 quark flavors, antiquarks,
2 spins, 3 colors
εSB/T4
ε/T4
12.0
10.0
8.0
T = 170 MeV = 10 trillion deg
ε = 0.8 GeV/fm3
6.0
3 flavour
2+1 flavour
2 flavour
4.0
2.0
hadrons ⇒quark/gluon
0.0
1.0
Assumes thermal system.
1.5
2.0
2.5
3.0
T/Tc
3.5
4.0
T/Tc
System of quarks and gluons where the long range confining
potential is screened.
2
Pressure is the Key
Pπ = 3
π2
90
PQGP = g
T
π2
90
4
Phase Diagrams
‘ Pressure of “pure” pion gas at temperature T
T 4 - B, g = 37
‘ Pressure in plasma phase with
“Bag constant” B ~ 0.2 GeV / fm3
Select system with higher pressure
0.5
Pion Phase
QGP Phase
PQGP
Î Phase transition at T ~ 140 MeV
with latent heat ~0.8 GeV / fm3
0.25
Pπ
Pressure
(GeV / fm 3)
0
0
100
200
Temperature (MeV)
Compare to best estimates (Karsch, QM01)
from lattice calculations:
T ~ 150-170 MeV
latent heat ~ 0.7±0.3 GeV / fm3
-0.25
Quick Review
Very early in the universe, quarks and gluons were
free in a plasma state.
Pulling apart
Temperature
How to do it
Molecules
~ 1000 0F
Use a flame
Atoms
~10,000 0F
Nuclei
Protons to
Quarks and
Gluons
Use an arc-torch
~10 billion
0F
Nuclear weapon
~10 trillion
0F
New Universe
Or we can build a giant particle accelerator!
As the universe cooled, they were confined
and have remained that way since.
Freeing the Quarks and Gluons
Where is this?
If we collide nuclei at much higher energy than
ever before, we can break these springs and
create a plasma of quarks and gluons – just like in
the early universe !
However, these reactions cannot chain react.
No $$$, but probably a good thing.
This research is for purely scientific interest.
There are no classified results.
3
Brookhaven National Laboratory
Gold + Gold Collisions
Picture of the Reaction
We accelerate Gold nuclei up to 99.995% the
speed of light.
Then we collide two beams to convert the
massive kinetic energy into heat to create a
small quark gluon plasma.
Time Evolution
Equilibrium Question
We start out with a system completely out of equilibrium and
lots of kinetic energy.
Particle Yields are well described
by two parameters. In general
Boltzmann statistics are fine.
Ni ∝ giV ∫
d3p
( 2π )
1
3
e(
p 2 + m2 − μ B ) / T
±1
Is there enough time for equilibrium to be achieved before
the system falls apart?
If so, we can use the Grand Canonical Ensemble to
calculate the abundances of all the final measured particles.
ns =
1
e
( ε s − μ ) / kT
Fermions or Bosons
±1
Depends on Temperature and Chemical Potential.
4
Where is the Bath?
Grand Canonical Ensemble
In our collisions, there is no real infinite bath of energy and
particle number. Why not use microcanonical then?
Each collisions has fluctuations in the amount of kinetic
energy and quantum numbers transferred from the incident
nuclei to the system created.
We assume a mean energy of the system and upgrade to the
canonical or grand canonical ensemble. This is a good
approximation for average quantities, but of course not for
fluctuations on those quantities.
My system.
Infinite heat bath with which
my system can exchange
energy and particles, hence
we have a temperature and
chemical potential.
Shifted Spectra
Black Body Radiation
Central (head-on) PHOBOS Au+Au 200 GeV
Expanding universe, galaxies are
moving away from us:
Red-shift
z
“Hubble
Plot”
r
Image from SDSS web site
Blue-Shift
Near-Perfect Liquid
RHIC Data & Calculations by U. Heinz / P. Kolb
βΤ=.6c
In RHIC collisions, hadrons expand
towards the detectors
Blue-shift
Teff = T0 + mβT2
Hydrodynamic calculations work!
Explain “push” w/ large energy density!
N i ∝ giV ∫
d3 p
( 2π )
1
3
e(
p2 + m2 − μB ) / T
±1
5
6