Solving the Strong CP Problem with Discrete Symmetries and the Right Unitarity Triangle

Abstract

We present a solution to the strong CP problem based on spontaneous CP violation and discrete family symmetries. The model predicts in a natural way the almost right-angled quark unitarity triangle angle ($\alpha \simeq 90^{\circ }$) by making the entries of the quark mass matrices either real or imaginary. By this choice the determinants of the mass matrices are rendered real and hence the strong CP phase vanishes. We present a toy model for the quark sector that demonstrates the viability of our approach.

20 pages, 4 figures; v2: references added, minor changes, version published in NPB

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• Generalised CP and $\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons
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• Lepton Mixing Parameters from $\Delta (48)$ Family Symmetry and Generalised CP
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• Modular invariance and the QCD angle
• Accidental Peccei-Quinn Symmetry from Discrete Flavour Symmetry and Pati-Salam
• An $S_4\times SU(5)$ SUSY GUT of flavour in 6d
• Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries
• Consequences of vector-like quarks of Nelson-Barr type
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• Flavor constraints for a Vector-like quark of Nelson-Barr type
• $A_4\times U(1{)}_{PQ}$ Model for the Lepton Flavor Structure and the Strong $CP$ Problem
• Predicting ${\delta }^{\text{PMNS}}$, ${\theta }_{23}^{\text{PMNS}}$ and fermion mass ratios from flavour GUTs with CSD2
• Yukawa ratio predictions in non-renormalizable $\mathrm{SO}(10)$ GUT models
• A bottom-up approach to the strong CP problem
• Implications of the Zero 1-3 Flavour Mixing Hypothesis: Predictions for ${\theta }_{23}^{\mathrm{PMNS}}$ and ${\delta }^{\mathrm{PMNS}}$
• The Strong CP Problem and Discrete Symmetries
• Effective description of Nelson-Barr models and the theta parameter