Abstract
We present a calculating method for the quark and lepton mixing angles. After a general discussion in field theoretic models, we present a working model from a string compactification through $Z_{12-I}$ orbifold compactification. It is beyond presenting just three families of the standard model but is the first example from string compactification successfully fitting to the observed data. Assuming that all Yukawa couplings from string compactification are real, we also comment on a relation between the CP phases in the Jarlskog determinants obtained from the CKM and PMNS matrices. The flipped SU(5) model leads to the doublet-triplet splitting and possible proton decay operators. It is shown that the vacuum expectation values can be tuned such that the proton lifetime is long enough.
Highlights
“How is the current allocation of flavors realized?” is the most urgent and interesting theoretical problem in the standard model (SM)
Gauge symmetries as family groups should satisfy the anomaly freedom, which can be achieved in extended grand unification (GUT) [3] and in models without anomaly [4]
Not to worry about the gauge anomalies, sometimes global symmetries are used for the family groups [5,6,7]
Summary
“How is the current allocation of flavors realized?” is the most urgent and interesting theoretical problem in the standard model (SM). Gauge symmetries as family groups should satisfy the anomaly freedom, which can be achieved in extended GUTs [3] and in models without anomaly [4]. Not to worry about the gauge anomalies, sometimes global symmetries are used for the family groups [5,6,7]. In [34], it was shown that acceptable model is O(1) out of Oð106Þ Even in this case, one has to check all elements of the CKM and PMNS matrices.
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