Extending the Standard Model Using Charge Quantisation Rules

We examine extensions of the Standard Model (SM), basing our assumptions on what has already been observed; we don't consider anything fundamentally different, such as grand unification or supersymmetry, which is not directly suggested by the SM itself. We concentrate on the possibility of additional low mass fermions (relative to the Planck mass) and search for combinations of representations which don't produce any gauge anomalies. Generalisations of the SM weak hypercharge quantisation rule are used to specify the weak hypercharge, modulo 2, for any given representation of the non-abelian part of the gauge group. Strong experimental constraints are put on our models, by using the renormalisation group equations to obtain upper limits on fermion masses and to check that there is no U(1) Landau pole below the Planck scale. Our most promising model contains a fourth generation of quarks without leptons and can soon be tested experimentally.