Low-energy N=1 supergravity and N=2 supersymmetry models
Firstly, scalar quark mass matrices are calculated for a non-minimal SU5 N=l supergravity theory with realistic fermion masses. The squark mixing matrices, analogues of the Kobayashi-Maskawa matrices for quarks, are also calculated and have significant off-diagonal entries. Thus, there are non-zero flavour-changing gaugino interactions between 'up' quarks and 'up' squarks in the non-minimal model. This is in contrast to the case for minimal SU5 . It is shown that in the non-minimal model flavour-changing gluino interactions contribute to the proton decay modes p → μ+K0, ῡμK+ at about the same rate as the mode p → ῡμK+ mediated by Wino exchange. Contributions to the KL-KS mass difference from flavour-changing gluino and wino interactions are small. Secondly, for a finite N=2 globally supersymmetric theory it is shown that the set of finiteness-preserving soft operators previously derived by Parkes and West is incomplete. The complete set of 1-loop finite operators is derived by a graphical analysis, and it is shown that most of these preserve finiteness to all orders. The low-energy N=2 model of Del Aguila et al. is reviewed, and it is shown that new constraints on the τ-neutrino mass require an unnaturally high scale of supersymmebry breaking in the model.