Finite and Gaug-Yukawa unified theories: theory and predictions (Q2758381)

All-loop Finite Unified Theories are very interesting \(N=1\) GUTs in which a complete reduction of couplings has been achieved. FUTs realize an old field theoretical dream and have remarkable predictive power. Reduction of dimensionless couplings in \(N=1\) GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exist RGI relations among dimensionless couplings that guarantee the vanishing of the beta-functions in certain \(N=1\) supersymmetric GUTs even to all orders. Recent developments in the soft supersymmetry breaking (SSB) sector of \(N=1\) GUTs and FUTs lead to exact RGI relations also in this sector of theories. Of particular interest is a RGI sum rule for the soft scalar masses holding to all orders. The characteristic features of SU(5) models that have been constructed based on the above tools are: a) the old agreement of the top quark predictions with the measured value remains unchanged. b) the lightest Higgs boson is predicted to be around 120 GeV c) the s-spectrum starts above several hundreds of GeV. Finally the relation of the present framework to the recently proposed 'anomaly mediated' supersymmetry breaking scenario is also discussed and is pointed out that the sum rule offers a natural way out to its fatal problem.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00035].