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arXiv · 2101.08718

Modular Invariant Dynamics and Fermion Mass Hierarchies around $τ= i$

Ferruccio Feruglio·Valerio Gherardi·Andrea Romanino·Arsenii Titov
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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 $Z_4$ invariance. In this region the breaking of $Z_4$ can be fully described by the spurion $ε\approx τ- i$, that flips its sign under $Z_4$. Degeneracies or vanishing eigenvalues of fermion mass matrices, forced by the $Z_4$ 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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Ferruccio Feruglio, Valerio Gherardi, Andrea Romanino, Arsenii Titov. 2021-05-26. Modular Invariant Dynamics and Fermion Mass Hierarchies around $τ= i$. https://doi.org/10.1007/jhep05(2021)242

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