Twin modular S4 with SU(5) GUT

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 $$ {Z}_3^T $$ Z 3 T symmetry, and one acting in the right-handed neutrino sector, associated with another modulus field value τSU with residual $$ {Z}_2^{SU} $$ 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.

Completing the eclectic flavor scheme of the ℤ2 orbifold

“…We performed a detailed analysis of the modular symmetries of the T 2 /Z 2 orbifold which (among others) might be relevant for the (discrete) flavor symmetries of string compactifications with an elliptic fibration. The T 2 /Z 2 case has two unconstrained moduli with JHEP06(2021)110 SL(2, Z) T × SL(2, Z) U modular symmetry and allows contact with previous bottom-up constructions that have more than one modulus [16,17,[35][36][37]. In the present paper, we completed the discussion of our earlier work [1] now including the automorphy factors of modular symmetry.…”

Modular origin of mass hierarchy: Froggatt-Nielsen like mechanism

“…The Yukawa coupling itself is also controlled by the modular weights of the fermion fields, since the modular forms are classified by modular weights. This FN-like mechanism based on modular symmetry has been recently considered to explain the large mass hierarchy in [28,[47][48][49]. 2 We note that while in the previous model the mass hierarchy originates from powers of the weighton vev, the resulting quark mass matrices do not fully simulate the FN-like structure, so that the relationship between two origins of mass hierarchy and the small mixing angles becomes more subtle than that of the FN model.…”

A radiative seesaw model in a supersymmetric modular $A_4$ group

“…[48][49][50][51][52][53], S 4 in refs. [54][55][56][57][58][59][60][61][62][63][64][65][66], A 5 in refs. [59,67,68], double covering of A 4 in refs.…”