Colour symmetry

9.5 Colour symmetry

Delta++

Figure 9.10: The

Δ^{+ +}

in the quark model.

So why don’t we see fractional charges in nature? This is an important point! In so-called deep inelastic scattering we see pips inside the nucleon – these have been identiﬁed as the quarks. We do not see any direct signature of individual quarks. Furthermore, if quarks are fermions, as they are spin $1 ∕ 2$ particles, what about antisymmetry of their wavefunction? Let us investigate the $Δ^{+ +}$ , see Fig. 9.10, which consists of three $u$ quarks with identical spin and ﬂavour (isospin) and symmetric spatial wavefunction,

ψ_{t o t a l} = ψ_{s p a c e} \times ψ_{s p i n} \times ψ_{f l a v o u r} .

(9.15)

This would be symmetric under interchange, which is unacceptable. Actually there is a simple solution. We “just” assume that there is an additional quantity called colour, and take the colour wave function to be antisymmetric:

ψ_{t o t a l} = ψ_{s p a c e} \times ψ_{s p i n} \times ψ_{f l a v o u r} \times ψ_{c o l o u r}

(9.16)

We assume that quarks come in three colours. This naturally leads to yet another $S U (3)$ symmetry, which is actually related to the gauge symmetry of strong interactions, QCD. So we have shifted the question to: why can’t we see coloured particles?

This is a deep and very interesting problem. The only particles that have been seen are colour neutral (“white”) ones. This leads to the assumption of conﬁnement – We cannot liberate coloured particles at “low” energies and temperatures! The question whether they are free at higher energies is an interesting question, and is currently under experimental consideration.

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