Physics 357 :
1998 Lecture 23

Quantum
Chromodynamics

Quantum ChromoDynamics (QCD) is an
SU(3) gauge theory based on 3 colour charges, needing 8 gauge
bosons to mediate the transformations between the 3 colours. There
are 6 explicitly coloured gluons

and two antisymmetric colour-anticolour
gluons from the 3 colour-anticolour possibilities:

(One can choose any two colour-anticolour
combinations, e.g.

and

,
as long as they are orthogonal to each
other and to the symmetric combination

which is not a gluon.)

The most important difference between
gluons and photons is that gluons carry colour charge, but photons
do not carry electric charge.

SU(3)colour
is thought to be an exact symmetry, but there only experimental
limits on a gluon mass are crude estimates of about 10 MeV.

QCD is **not**
the only possible SU(3)colour based gauge theory.
SU(3)colour allows additional
interactions which violate P and T symmetries.
There is no theoretical reason for such interactions to be absent,
but current experimental limits on P and T violations in strong
interactions tell us that any SU(3)colour P and T violation interactions
are at least 8 orders of magnitude weaker then the P and T conserving
QCD interactions. Various theoretical explanations of the absence
of P and T violations (e.g. axions) have not been confirmed experimentally.

At low energies the
coupling constant of QCD, as,
is of order unity, so perturbation theory is not valid and it
is almost impossible to calculate anything. QCD gets weaker with
increasing energy, however, (see
F&H equation 14.58) so at
high energies QCD is similar to QED, and experimental tests are
possible.

The observed potential for heavy quark-antiquark
systems can be approximately fit to

(see
F&H equations 14.59 and Section 15.8)

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#### Copyright 1998 David Bailey, University of Toronto