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9.5: Color Symmetry

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  • The \(\Delta^{++}\) 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 \(\Delta^{++}\), see Fig. [fig:D++], which consists of three \(u\) quarks with identical spin and flavour (isospin) and symmetric spatial wavefunction, \[\psi_{\rm total} = \psi_{\rm space} \times \psi_{\rm spin} \times \psi_{\rm flavour}.\] 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: \[\psi_{\rm total} = \psi_{\rm space} \times \psi_{\rm spin} \times \psi_{\rm flavour} \times \psi_{\rm colour}\] We assume that quarks come in three colours. This naturally leads to yet another \(SU(3)\) 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.