Minimal spontaneous <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>-violating GUT and predictions for leptonic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> phases
Ketan M. Patel
Abstract
A nonsupersymmetric renormalizable $SO(10)$ model, with $CP$ invariant Yukawa sector consisting of Lorentz scalars in 10 and $\overline{126}$ dimensional representations, is proposed. The elemental Yukawa couplings are real due to $CP$ symmetry. The latter is broken in the low energy effective theory through the standard model Higgs which is a complex linear combination of electroweak doublets residing in 10 and $\overline{126}$ scalars. As a result, the mass matrices in the quark and lepton sectors, including those of heavy and light neutrinos, depend only on three phases which in turn determine $CP$ violation in both sectors. The model is comprehensively analyzed for its viability and predictions including the possibility to generate baryon asymmetry through thermal leptogenesis. It predicts relatively small values for $CP$ phases in the lepton sector. Successful leptogenesis further restricts the ranges to $\ensuremath{-}0.4\ensuremath{\le}\mathrm{sin}\ensuremath{\delta}\ensuremath{\le}0.4$ for the Dirac phase and $\ensuremath{-}0.3\ensuremath{\le}\mathrm{sin}{\ensuremath{\eta}}_{1}\ensuremath{\le}0.2$, $\ensuremath{-}0.5\ensuremath{\le}\mathrm{sin}{\ensuremath{\eta}}_{2}\ensuremath{\le}0.5$ for the Majorana phases.