论文标题
带有$ a_4 $模块化风味对称性的Fliptiped Su（5）肠的夸克和叶子的风味结构
Flavor Structures of Quarks and Leptons from Flipped SU(5) GUT with $A_4$ Modular Flavor Symmetry
论文作者
论文摘要
我们建议用$ A_4 $模块化风味对称性产生标准模型的风味结构以及中微子的中微子。讨论了在模块化肠道方案中分配夸克和叶子不同模量值的可能方法。我们建议将多个模块对称性减少到具有适当边界条件的低能有效理论中的单个模块对称性。我们根据模块化$ a_4 $表示的物质超级场地的分配对本方案中的所有可能方案进行了分类，并在我们的方案上列出了Quark和Lepton质量矩阵的表达方式。在适当地为各种超级场所选择模块化权重之后，我们可以获得最佳拟合点，以相应的$χ^2 $值为样品subscenarios。我们发现，标准模型和中微子的风味结构可以完美地安装在具有单个或两个模量字段的$ A_4 $模块化风味肠道方案中。尤其是，即使仅采用了Quark和Lepton sectors的单个常见模量字段，即使仅使用单个常见的模量字段，否则我们的安装的$χ^2_ {total} $的样本$ {\ bf ix^\ prime} $也可以低至$ 1.558 $。最具预测性的方案$ {\ bf iii} $，其中所有超级场地都以$ a_4 $的三重态变化，可以使用两个独立的模量$τ_q，quark sector和lepton sector（$χ^2_ {2_ {2_ {2_ {2_左右）的情况，将其安装得更好。 282.4 $）。
We propose to generate the flavor structures of the Standard Model plus neutrinos from flipped SU(5) GUT with $A_4$ modular flavor symmetry. Possible way to assign different moduli values for quarks and leptons in modular GUT scheme is discussed. We propose to reduce the multiple modular symmetries to a single modular symmetry in the low energy effective theory with proper boundary conditions. We classify all possible scenarios in this scheme according to the assignments of the modular $A_4$ representations for matter superfields and give the expressions of the quark and lepton mass matrices predicted by our scheme at the GUT scale. After properly selecting the modular weights for various superfields that can lead to better fitting, we can obtain the best-fit points with the corresponding $χ^2$ values for the sample subscenarios. We find that the flavor structures of the Standard Model plus neutrinos can be fitted perfectly in such a $A_4$ modular flavor GUT scheme with single or two modulus fields. Especially, the $χ^2_{total}$ of our fitting can be as low as $1.558$ for sample ${\bf IX^\prime}$ of scenario ${\bf III}$ even if only a single common modulus field for both quark and lepton sectors is adopted. The most predictive scenario ${\bf III}$, in which all superfields transform as triplets of $A_4$, can be fitted much better with two independent moduli fields $τ_q,τ_l$ for quark sector and lepton sector ($χ^2_{total}\approx 95$) than that with the single modulus case ($χ^2_{total}\approx 282.4$).
