Introduction to QCD. adopted from Peter G. Jones. THE UNIVERSITY OF BIRMINGHAM. Layout. Phase transitions in the earlier universe The sequence of events t = 10 43 10 5 s after the Big Bang Phase transitions in the early universe The QCD phase transition is the most recent of these
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Proton (uud)
Neutron (udd)
Gluon
W±,Z0
Photon
Graviton ?
u
5 MeV
c
1500 MeV
t
180000 MeV
Quarks
Gauge
bosons
d
10 MeV
s
150 MeV
b
5000 MeV
m
e
t
Leptons
n
n
n
m
e
t
Table of “bare” quark masses, leptons and gauge bosons
The universe is a hot plasma of fundamental particles … quarks, leptons, force particles (and other particles ?)
1043 s Planck scale (quantum gravity ?) 1019 GeV
1035 s Grand unification scale (strong and electroweak) 1015 GeV
Inflationary period 10351033 s
1011 s Electroweak unification scale 200 GeV
105 s QCD scale  protons and neutrons form 200 MeV
3 mins Primordial nucleosynthesis 5 MeV
3105 yrs Radiation and matter decouple  atoms form 1 eV
1 bill yrs Protogalaxies and the first stars
3 bill yrs Quasars and galaxy spheroids
5 bill yrs Galaxy disks
Today Life !
Important features of QCD
Charges electric (2) colour (3)
Gauge boson g (1) g (8)
Charged no yes
Strength
q1
q2
Confinementa) QED or QCD (r < 1 fm)
r
q1
q2
b) QCD (r > 1 fm)
+
dielectric
+


+


+
q
q

+


+
+
d ~ molecular spacing
where a = a(Q2 0) = e2/4p= 1/137
which decreases at large Q2 provided nf < 16.
em em
Q2»m2
Q2 = q2
“Superdense Matter: Neutrons or Asymptotically Free Quarks”
J.C. Collins and M.J. Perry, Phys. Rev. Lett. 34 (1975) 1353
and rD is the Debye screening radius.
an electric insulator becomes conducting.
nucleons (hadrons) cease to exist.
a) d > rD
b) d < rD
V(r)
V(r)
d
r
V(r)
V(r)
d
Unbound electron(s)
r
1. Compression.
2. Heating = creation of pions.
1. Quarks and gluons become deconfined.
2. Chiral symmetry may be (partially) restored.
Note: a phase transition is not expected in binary nucleonnucleon collisions.
chiral symmetry is broken (or hidden).
chiral symmetry is (partially) restored
Below the Curie temperature the underlying rotational symmetry is hidden.
Above the Curie temperature the rotational symmetry is restored.
a) blue’s velocity > red’s
b) red’s velocity > blue’s
Red’s rest frame
Lab frame
Blue’s handedness changes depending on red’s velocity
Lab frame
Red’s rest frame
1. Phenomenological models
2. Lattice QCD calculations
where qV= 1 inside the bag and 0 outside the bag.
and satisfies a linear boundary condition at the bag surface.
Temperature
Tc
QuarkGluon
Plasma
Hadronic
matter
Nuclear matter
Density
rc
e.g. nucleon ground state is
3 quarks in 1s1/2 level
e.g. allow quark interactions
T. deGrand et al, Phys. Rev. D 12 (1975) 2060
where m is the quark chemical potential, mq =  mq and b = 1/T.
1. High temperature, low net baryon density (T > 0, mB = 0).
2. Low temperature, high net baryon density (T = 0, mB > 0).
natural units
mB = 3 mq
B
Estimates of the critical parametersMIT bag model
~ 28 times normal nuclear matter density
given pFermi ~ 250 MeV and r ~ 2m3/3p2
Taking B1/4 ≈ 235 MeV
Tc (m=0) ≈ 170 MeV
Solves the problem of divergences in pQCD calculations (which arise due to loop diagrams)
The lattice provides a natural momentum cutoff
Recover the continuum limit by letting a 0
Lattice QCDpure gauge = gluons only