Introduction

As we have constantly stressed, the great achievement of the SM model is the unification of the weak and electromagnetic interactions into a single gauge theory SU(2)L × U(1). The strong interaction gauge theory, the SU(3)C of QCD, is totally separate, and the totality of weak, electromagnetic and strong interactions has been treated as the juxtaposition SU(2)L × U(1) × SU(3)C. There are many attempts to unify all these forces into larger schemes such as a grand unification theory (GUT), i.e. to look for a single semi-simple Lie group to describe all the interactions, and which would contain SU(2)L × U(1) × SU(3)C as a subgroup.

There were early attempts to establish a ‘baryon–lepton’ (B–L) symmetry (Gamba, Marshak and Okubo, 1959). In more recent years, the outpouring of theoretical papers on grand unification theories, supersymmetric theories, supergravity theories and the boom of superstring theories is, perhaps, only exceeded by the frustration caused by the lack of any experimental indication that any one of these attempts is relevant to nature. The present limit of > 1032 years on the proton lifetime has ruled out the so-called minimal SU(5) (see Section 28.4) but this seems to be the only concrete assertion to emerge. It is very difficult at this time to imagine, for instance, that measurements of the proton lifetime will be able to discriminate among the various models. The rate of background due to cosmic rays will make it hard to detect proton decay if τp > 1033 years.