Using Charge Quantisation Rules to Extend the Standard Model

Theoretical physics

Smith, Douglas James

University:University of Glasgow

关键词: Theoretical physics;   

Others  :  http://theses.gla.ac.uk/76303/1/13834035.pdf

来源: University of Glasgow

【 摘 要 】

We examine extensions of the Standard Model (SM), trying to base our assumptions on what has already been observed. We consider our models to be the most obvious extensions of the SM in the sense that we don't consider anything fundamentally different such as grand unification or supersymmetry which are not directly suggested by the SM itself. We use features of the SM to guide our extensions. This method has the advantage that all our models will be based (at least in part) on experimental observations. The disadvantage is that we cannot expect such models to give us any fundamentally new explanations. The main features we use from the SM are small representations and charge quantisation. By small representations we mean fundamental or singlet representations of each non-abelian group and weak hypercharges close to zero. We use generalisations of the weak hypercharge quantisation rule observed in the Standard Model to specify the weak hypercharge modulo 2 for any given representation of the non-Abelian part of the gauge group. When we combine these principles with the requirement, for a theoretically consistent model, that there are no anomalies, we are left with a very restricted choice of models. For most of this thesis we concentrate on the possibility of additional low mass fermions (relative to the Planck mass) and search for combinations of allowed representations which don't produce any gauge anomalies. We put strong experimental constraints on these models by using the renormalisation group equations to estimate fixed point masses for the new fermions in our models, and also to check that there is no U(l) Landau pole below the Planck scale. This is required since we are assuming a desert up to the Planck scale. In our most promising model we show that a fourth generation of quarks without leptons is possible and can soon be tested experimentally. In this model we replace the fourth generation of leptons (required in the SM to cancel anomalies) with a generation of 5f/(5)-"quarks" which are a generalisation of the SM quarks but coupling to a new SU(b) group instead of 5C/(3). We discuss how well this model agrees with experiment and give estimates for the masses of the new fermions. In the final chapter we examine a different model where we don't introduce any new low mass fermions. Instead we try to explain the mass structure of the SM in a natural way. The problem with the SM is that the masses require different fermions to have different Yukawa couplings to the SM Higgs boson. The smallest and largest couplings differ by a factor of about 10.