Abstract
We formulate general conditions under which the strong CP problem is solved by spontaneous CP violation. Quark-mass matrix elements are polynomials in the CP-breaking order parameters, engineered such that their determinant is a real constant. This scheme permits only a limited number of textures. These conditions can be realized in supersymmetric theories with CP as an anomaly-free local flavor symmetry, suggesting a unified solution to the strong CP problem and the flavor puzzle. Our solution can be implemented using either modular invariance or a local U(1) symmetry. We present modular-invariant realizations where matter fields are assigned small modular weights ±2 (±1), utilising higher levels N = 2 (N = 3). Heavy quarks are in general not required, but their presence allows for models where colored particles fill non-singlet representations of the flavor group.
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Acknowledgments
F.F., M.P. and A.T. are grateful to the Mainz Institute for Theoretical Physics (MITP) of the Cluster of Excellence PRISMA+ (Project ID 390831469), for its hospitality and partial support during the completion of this work.
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Feruglio, F., Parriciatu, M., Strumia, A. et al. Solving the strong CP problem without axions. J. High Energ. Phys. 2024, 214 (2024). https://doi.org/10.1007/JHEP08(2024)214
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DOI: https://doi.org/10.1007/JHEP08(2024)214