14 - Higher symmetries

Summary

Grand unification

We first recall some facts which emerge from the studies and analysis described in the preceding chapters concerning the properties of quarks and leptons. Both quarks and leptons

1. (i) have spin ½;

2. (ii) obey the Pauli principle;

3. (iii) exhibit no internal structure (at the present limit ∼ 10^-18 m), i.e. they act as point particles;

4. (iv) are left-handed in respect of weak processes;

5. (v) fall into the same kind of doublets for weak processes;

6. (vi) obey similar gauge theories and interact by exchange of spin 1 bosons.

The only difference we recognise between quarks and leptons is that the quarks carry colour while the leptons do not.

These similarities and the successful unification of the weak and electromagnetic interactions naturally lead to intensive efforts to unify the electro–weak with the strong interactions. Such unification implies the existence of a larger group encompassing

In such a group, the couplings for the different processes would not be independent, so that, for instance, the Weinberg angle θ_W linking the weak and electromagnetic couplings would be predicted by the theory. All the interactions are then described in terms of a single coupling to which the other couplings can be related once the grand unified group is recognised. Such grand unified theories are frequently referred to by the abbreviation ‘GUTS’.

We recall that the strong coupling decreases as a result of the logarithmic screening term (section 13.3) while the electromagnetic coupling increases due to the screening effect, as a function of momentum transfer.