双模块化$S_4$和$SU(5)$ GUT
Twin Modular $S_4$ with $SU(5)$ GUT
摘要：
本文讨论了具有多重模对称的味模型的$SU(5)$大统一推广。所提出的模型涉及两个模块$S_4$组，一个作用于带电费米子扇区，与剩余$Z_3^T$对称性的模场值$τ_T$相关联，一个作用于右手中微子扇区，与剩余$Z_2^{SU}$对称性的另一个模场值$τ_{SU}$相关联。夸克和轻子的质量等级是在重子的帮助下自然产生的，重子是SM单态场，它们的非零模权扮演着Froggatt-Nielsen荷的角色。该模型预测TM $_1$轻子混合，和中微子双β衰变的速度接近目前和未来的实验的灵敏度，正常和倒置的顺序，抑制修正带电轻子混合由于三角形的汤川矩阵。
英文摘要：
We discuss the $SU(5)$ grand unified extension of flavour models with multiple modular symmetries. The proposed model involves two modular $S_4$ groups, one acting in the charged fermion sector, associated with a modulus field value $τ_T$ with residual $Z_3^T$ symmetry, and one acting in the right-handed neutrino sector, associated with another modulus field value $τ_{SU}$ 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 TM$_1$ 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.
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