104 8 Quarks, Gluons, and the Strong Interaction
Including the colour property, a kind of quark charge, the Pauli princi-
ple may be salvaged. The quantum number colour can assume three values,
which may be called red, blue and green. Accordingly, antiquarks carry the
anticolours anti-red, anti-blue,andanti-green. Now the three u-quarks may
be distinguished. Thus, a colour wave function antisymmetric under particle
interchange can be constructed, and we so have antisymmetry for the total
wave function. The quantum number colour was introduced for theoretical
reasons; yet, experimental clues indicate that this hypothesis is correct, as
will be discussed in Sect. 9.3.
Gluons. The interaction binding quarks into hadrons is called the strong
interaction. Such a fundamental interaction is, in our current understanding,
always connected with a particle exchange. For the strong interaction, gluons
are the exchange particles that couple to the colour charge. This is analogous
to the electromagnetic interaction in which photons are exchanged between
electrically charged particles.
The experimental findings of Sect. 8.1 led to the development of a field
theory called quantum chromodynamics (QCD). As its name implies, QCD
is modelled upon quantum electrodynamics (QED). In both, the interaction
is mediated by exchange of a massless field particle with J
P
=1
−
(a vector
boson).
The gluons carry simultaneously colour and anticolour. According to
group theory, the 3 × 3 colour combinations form two multiplets of states: a
singlet and an octet. The octet states form a basis from which all other colour
states may be constructed. They correspond to an octet of gluons. The way
in which these eight states are constructed from colours and anticolours is a
matter of convention. One possible choice is:
r¯g, r
¯
b, g
¯
b, g¯r, b¯r, b¯g,
1/2(r¯r − g¯g),
1/6(r¯r+g¯g − 2b
¯
b) .
The colour singlet:
1/3(r¯r+g¯g+b
¯
b),
which is symmetrically constructed from the three colours and the three
anticolours is invariant with respect to a re-definition of the colour names
(rotation in colour space). It therefore has no effect in colour space and cannot
be exchanged between colour charges.
By their exchange the eight gluons mediate the interaction between par-
ticles carrying colour charge, i.e., not only the quarks but also the gluons
themselves. This is an important difference to the electromagnetic interac-
tion, where the photon field quanta have no charge, and therefore cannot
couple with each other.
In analogy to the elementary processes of QED (emission and absorption
of photons, pair production and annihilation); emission and absorption of
gluons (Fig. 8.3a) take place in QCD, as do production and annihilation of
quark–antiquark pairs (Fig. 8.3b). In addition, however, three or four gluons
can couple to each other in QCD (Fig. 8.3c,d).