Abstract
We propose a realistic A4 extension of the Standard Model involving a particular quark–lepton mass relation, namely that the ratio of the third family mass to the geometric mean of the first and second family masses are equal for down-type quarks and charged leptons. This relation, which is approximately renormalization group invariant, is usually regarded as arising from the Georgi–Jarlskog relations, but in the present model there is no unification group or supersymmetry. In the neutrino sector we propose a simple modification of the so-called Zee–Wolfenstein mass matrix pattern which allows an acceptable reactor angle along with a deviation of the atmospheric and solar angles from their bi-maximal values. Quark masses, mixing angles and CP violation are well described by a numerical fit.
Highlights
Supersymmetric Grand Unified Theories (SUSY GUTs) are very attractive from the theoretical point of view as they allow to obtain the Standard Model (SM) from a single unified gauge group [1,2]
Several GUT models have been studied in the literature, having as prediction a mass relation between down-quark masses and the charged leptons
Which is in good agreement with data to first approximation, assuming that holds at the GUT scale, and taking into account renormalization group running to low energies, with suitable SUSY threshold effects
Summary
Supersymmetric Grand Unified Theories (SUSY GUTs) are very attractive from the theoretical point of view as they allow to obtain the SM from a single unified gauge group [1,2]. Apart from predicting for instance the quantization of electric charge, they reduce the number of free parameters They give the right value for the electroweak mixing angle and may provide a good framework for the understanding of the flavor problem. Which is in good agreement with data to first approximation, assuming that holds at the GUT scale, and taking into account renormalization group running to low energies, with suitable SUSY threshold effects. Such mass relations are very welcome since, by itself, the Standard Model sheds no light on the flavor problem.
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