Extending the Symmetries of the Standard Model

Abstract

We discuss the possibilities for determining the parameters of the Standard Model by extending its symmetries. Supersymmetry combined with a stage of unification is capable of determining the magnitude of the gauge couplings and explaining the pattern of spontaneous breaking. We consider how further family symmetries may determine the qualitative struc­ ture of the fermion masses and mixing angles. Finally we explore the possibility that the dynamics of the low-energy theory may determine the magnitude of the Yukawa couplings via its fixed point structure and hence give a complete theory of the fermion masses. With the advent of precision measurements of the parameters of the Standard Model we have been able to test quantitatively the possibility of supersymmetric unifi­ cation in several areas. In particular the couplings are found to come together at a scale 0(10 1 6 GeV) the values corresponding to the SU(5) normalisation of the U(l) coupling with sin 2 (0w) = 3/8 (this is not the case in the Standard Model where the couplings are some six standard deviations apart). The idea the soft SUSY breaking terms unify may be tested too because the Higgs mass as well as the squark and slepton mass are unified and deviate at low energy only through calculable radiative corrections. The exciting thing about soft mass unification is that it gives a reason why the pattern of symmetry breaking in the Standard Model is the way it is. Due to the large top mass and associated Yukawa coupling the RG equations drive the Higgs mass squared neg­ ative, triggering electroweak breaking. Due to the QCD radiative corrections the top squark masses which also feel the top Yukawa coupling are not driven negative giving a simple explanation for the observed pattern of symmetry breakdown. Such unification predictions encourage us in the belief there is some extension of the symmetries of the Standard Model. However there still remains much to explain. In particular the pattern of fermion masses and mixing angles suggests the need for further symmetries and indeed simple relationships do appear· at high scales. The measured values of the bottom quark and the T lepton masses are consistent with their equality at the unification scale. l), 2 ) Indeed this simplicity might extend to the top quark sector for it is a viable possibility that the top, bottom and tau Yukawa couplings are all equal and governed by the infra-red structure of the theory. 3 ) However the pattern of light masses and mixing angles appears at first sight to be too complicated to be explained by such simple unification ideas. In this talk I wish to show that this is not the case and that a very simple extension of the Standard Model is capable of generating both the qualitative and quantitative structure of the full set of fermion masses and mixing