PoS - Proceedings of Science
Volume 405 - 7th Symposium on Prospects in the Physics of Discrete Symmetries, DISCRETE 2020-2021 (DISCRETE2020-2021) - Plenary session
Fermion mass hierarchies from residual modular symmetries
P. Novichkov, J. Penedo* and S. Petcov
Full text: pdf
Pre-published on: April 07, 2022
Published on: October 05, 2022
We discuss the approach to the flavour problem based on modular invariance. In modular-invariant models of flavour, hierarchical fermion mass matrices may arise without fine-tuning, solely due to the proximity of the modulus $\tau$ to a point of residual symmetry. This mechanism does not require flavon fields, and modular weights are not analogous to Froggatt-Nielsen charges. We show that hierarchies depend on the decomposition of field representations under the residual symmetry group. We systematically go through the possible fermion field representation choices which may yield hierarchical structures in the vicinity of symmetric points, for the four smallest finite modular groups, isomorphic to $S_3$, $A_4$, $S_4$, and $A_5$, as well as for their double covers. We find a restricted set of pairs of representations for which the discussed mechanism may produce viable fermion (charged-lepton and quark) mass hierarchies. After formulating the conditions for obtaining a viable lepton mixing matrix in the symmetric limit, we construct a model in which both the charged-lepton and neutrino sectors are free from fine-tuning.
DOI: https://doi.org/10.22323/1.405.0021
How to cite

Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.

Open Access
Creative Commons LicenseCopyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.