Finite unified theories and their predicitions
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inite Unified Theories and Their Predicitions1 S. Heinemeyera, M. Mondragónb, and G. Zoupanosc a
Institute de Física de Cantabria (CSICUC) E39005 Santander, Spain Institute de Física Universidad National Autónoma de México Apdo. Postal 20364, México 01000 cMaxPlanckInstitut für Physik (WernerHeisenbergInstitut) Föhringer Ring 6 80805 München and ArnoldSommerfeldCenter für Theoretische Physik Department fur Physik, LudwigMaximiliansUniversität München Theresienstrasse 37, 80333 München, Germany
b
Abstract—Allloop Finite Unified Theories (FUTs) are very interesting N = 1 supersymmetric Grand Uni fied Theories (GUTs) realising an old field theory dream, and moreover have a remarkable predictive power due to the required reduction of couplings. The reduction of the 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 dimensional couplings that guarantee the vanishing of all betafunctions in certain N = 1 GUTs even to all orders. Additional devel opments in the soft supersymmetry breaking sector of N = 1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in this dimensionful sector of the theory, too. Based on the above theoretical frame work phenomenologically consistent FUTs have been constructed. Here we review two FUT models based on the SU(5) gauge group. Confronting their predictions with the top and bottom quark masses and other experimental constraints a light Higgsboson mass in the range MH ~ 121–126 GeV has been predicted, in striking agreement with the recent experimental results from ATLAS and CMS. Furthermore naturally a rel atively heavy sspectrum emerged with coloured supersymmetric particles above ~1.5 TeV in agreement with the nonobservation of those particles at the LHC. Restricting further the parameter space of the best version of the SU(5) FUT according to the reported accuracy of the Higgs boson mass and Bphysics observables we find predictions for the rest of the Higgs masses and the sspectrum. DOI: 10.1134/S1063779613020159 1
1. INTRODUCTION
A large and sustained effort has been done in the recent years aiming to achieve a unified description of all interactions. Out of this endeavor two main direc tions have emerged as the most promising to attack the problem, namely, the superstring theories and non commutative geometry. The two approaches, although at a different stage of development, have common uni fication targets and share similar hopes for exhibiting improved renormalization properties in the ultraviolet (UV) as compared to ordinary field theories. Moreover the two frameworks came closer by the observation that a natural realization of noncommutativity of space appears in the string theory context of Dbranes in the presence of a constant background antisymmet ric field [1]. Among the numerous important develop ments in both frameworks, it is worth noting two
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