Abstract
We discuss the SU(5) grand unified extension of flavour models with multiple modular symmetries. The proposed model involves two modular S4 groups, one acting in the charged fermion sector, associated with a modulus field value τT with residual {Z}_3^T symmetry, and one acting in the right-handed neutrino sector, associated with another modulus field value τSU with residual {Z}_2^{SU} symmetry. Quark and lepton mass hierarchies are naturally generated with the help of weightons, which are SM singlet fields, where their non-zero modular weights play the role of Froggatt-Nielsen charges. The model predicts TM1 lepton mixing, and neutrinoless double beta decay at rates close to the sensitivity of current and future experiments, for both normal and inverted orderings, with suppressed corrections from charged lepton mixing due to the triangular form of its Yukawa matrix.
Highlights
JHEP04(2021)291 atmospheric and solar neutrino experiments, and later by long baseline oscillation experiments, continue to take the tri-bimaximal form
There is a phenomenological preference for the first case, called TM1 mixing [12, 13], in which follows from S4 where T associated with a Z3T subgroup preserved in the charged lepton sector, as usual, while the product SU associated with Z2SU controlling the neutrino sector
Despite the motivation from neutrino physics for introducing a discrete non-Abelian family symmetry such as S4, this raises the question of the origin of such symmetry, and the nature of its spontaneous breaking, with particular subgroups preserved in different sectors of the theory, all of which seems to require a large number of flavon fields whose vaccuum alignment requires further driving fields, plus ad hoc shaping symmetries [12, 13]
Summary
We review the approach of using multiple finite modular symmetries to explain flavour mixing, with Γ4 S4 as the representative in the following discussion. The Majorana mass matrix for right-handed neutrinos is straightforwardly obtained from the singlet, doublet and triplet modular forms M1, M2 = (M2,1, M2,2)T and M3 = (M3,1, M3,2, M3,3)T , i.e., M1 0 0. This stabiliser is invariant under the action of SU. The mass matrix in eq (3.14) further constrains coefficients for the third and fourth mass matrix patterns on the right hand side with the ratio − 2/3 This is a feature different from classical flavour models without modular symmetry, e.g., in [13], where all parameters in front of different patterns are arbitrary. We will check how large is the deviation from the TM1 mixing numerically
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