## QCD

### Why Colour?

There are several strong evidences why quarks should carry - besides the electric charge -
an additional internal degree of freedom: the colour charge.
__Quark Wave Function of Baryons__

Colour had been introduced as an internal degree of freedom to solve a conflict
between the quark model for baryons and the Pauli exclusion principle.

The Δ^{++} state in the quark model without colour has the following
decomposition in terms of space, flavour and spin, respectively:
Since the Δ is an excitation of the nucleon with respect to spin the relative
angular momentum of the three quarks is equal to zero. As a consequence, the space
state is symmetric under exchange of any pair of quarks.

The flavour state as well as the state are also symmetric under exchange of any pair
of quarks. Hence, the state is symmetric resulting in a violation of the Pauli
principle which requires an anti-symmetric state.

The Pauli principle can be rescued by introducing three colour charges 'red', 'blue'
and 'green'. A state consisting of equal weights in the three different colour
charges is a colour neutral state.

Free quarks have never been observed. As a consequence, there is the hypothesis that
all hadrons consisting of quarks are always colour neutral states.

The corresponding colour state is the colour singlet
which is a colour neutral state and antisymmetric under exchange of an arbitrary pair
of quarks.

In the full quark model the full Δ^{++} is described by
guaranteeing the Pauli exclusion principle.

__Electron Positron Annihilation into Hadrons__

__tau decays__

__pi0 decay__