SUSY breaking constraints on modular flavor S3 invariant SU(5) GUT model

Abstract

Modular flavor symmetry can be used to explain the quark and lepton flavor structures. The SUSY partners of quarks and leptons, which share the same superpotential with the quarks and leptons, will also be constrained by the modular flavor structure and show a different flavor(mixing) pattern at the GUT scale. So, in realistic modular flavor models with SUSY completion, constraints from the collider and DM constraints can also be used to constrain the possible values of the modulus parameter. In the first part of this work, we discuss the possibility that the S3 modular symmetry can be preserved by the fixed points of T2/ZN orbifold, especially from T2/Z2. To illustrate the additional constraints from collider etc on modular flavor symmetry models, we take the simplest UV SUSY-completion S3 modular invariance SU(5) GUT model as an example with generalized gravity mediation SUSY breaking mechanism. We find that such constraints can indeed be useful to rule out a large portion of the modulus parameters. Our numerical results show that the UV-completed model can account for both the SM (plus neutrino) flavor structure and the collider, DM constraints. Such discussions can also be applied straightforwardly to other modular flavor symmetry models, such as A4 or S4 models.

Fermion mass hierarchies, large lepton mixing and residual modular symmetries

“…After the first studies, the interest in the approach grew significantly and models based on the groups Γ 4 S 4 [19][20][21][22][23][24][25][26], Γ 5 A 5 [26][27][28], Γ 3 A 4 [23,, Γ 2 S 3 [51,52] and Γ 7 PSL(2, Z 7 ) [53] have been constructed and extensively studied. Similarly, attempts have been made to construct viable models of quark flavour [54] and of quark-lepton unification [55][56][57][58][59][60][61][62][63]. The formalism of the interplay of modular and gCP symmetries has been developed and first applications made in [14].…”

SU(5) GUTs with A4 modular symmetry

“…Indeed, modular symmetry in the context of SU(5) GUTs was first studied in an (Γ 3 A 4 ) × SU(5) model in [14]. Other modular GUT models were subsequently constructed based on (Γ 2 S 3 ) × SU(5) [10,63], and (Γ 4 S 4 ) × SU(5) [64].…”

Twin modular S4 with SU(5) GUT

“…It was pointed out that the role of the FN flavon may be played by a singlet under both the gauge symmetry and the finite modular symmetry which carries a non-zero modular weight, called the weighton [65], leading to natural quark and lepton mass hierarchies. 2 The question of quark and lepton mass and mixing is necessarily simultaneously addressed in GUTs, and various SU(5) models have been proposed [45,49,[87][88][89] which include finite modular symmetries which act as family symmetries. Modular symmetry in the context of SU(5) GUTs was first studied in an (Γ 3 A 4 ) × SU(5) model in [49], then (Γ 2 S 3 ) × SU(5) [45,87], and (Γ 4 S 4 ) × SU(5) [88].…”