Abstract
We discuss fermion mass hierarchies within modular invariant flavour models. We analyse the neighbourhood of the self-dual point τ = i, where modular invariant theories possess a residual Z4 invariance. In this region the breaking of Z4 can be fully described by the spurion ϵ ≈ τ − i, that flips its sign under Z4. Degeneracies or vanishing eigenvalues of fermion mass matrices, forced by the Z4 symmetry at τ = i, are removed by slightly deviating from the self-dual point. Relevant mass ratios are controlled by powers of |ϵ|. We present examples where this mechanism is a key ingredient to successfully implement an hierarchical spectrum in the lepton sector, even in the presence of a non-minimal Kähler potential.
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Feruglio, F., Gherardi, V., Romanino, A. et al. Modular invariant dynamics and fermion mass hierarchies around τ = i. J. High Energ. Phys. 2021, 242 (2021). https://doi.org/10.1007/JHEP05(2021)242
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DOI: https://doi.org/10.1007/JHEP05(2021)242