Abstract
We study the problem of modulus stabilisation in the framework of the modular symmetry approach to the flavour problem. By analysing simple UV-motivated CP-invariant potentials for the modulus τ we find that a class of these potentials has (non-fine-tuned) CP-breaking minima in the vicinity of the point of \( {\mathrm{\mathbb{Z}}}_3^{ST} \) residual symmetry, τ ≃ e2πi/3. Stabilising the modulus at these novel minima breaks spontaneously the CP symmetry and can naturally explain the mass hierarchies of charged leptons and possibly of quarks.
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Novichkov, P.P., Penedo, J.T. & Petcov, S.T. Modular flavour symmetries and modulus stabilisation. J. High Energ. Phys. 2022, 149 (2022). https://doi.org/10.1007/JHEP03(2022)149
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DOI: https://doi.org/10.1007/JHEP03(2022)149