论文标题
半融合体重模块化形式和中微子质量模型的应用
Half-integral weight modular forms and application to neutrino mass models
论文作者
论文摘要
我们将模块化不变性方法推广到包括半融合重量模块化形式。因此，模块化组应扩展到其Meplectic覆盖组以保持一致性。我们介绍了一致性亚组$γ（4n）$的定义明确定义的半融合模块化表格，并表明它们可以分解为有限的Metaplectic $ \wideTildedγ_{4n} $的不可还原多重。我们以$γ（4）$至重量6的价格构建半集成/整体模块化表格的混凝土表达式，并将它们安排到$ \widetildedγ_4$的不可约表示中。我们提出了三个典型模型，其中包括$ \widetildeγ_4$用于中微子质量和混合的模块化对称性，每个模型的现象学预测进行数值分析。
We generalize the modular invariance approach to include the half-integral weight modular forms. Accordingly the modular group should be extended to its metaplectic covering group for consistency. We introduce the well-defined half-integral weight modular forms for congruence subgroup $Γ(4N)$ and show that they can be decomposed into the irreducible multiplets of finite metaplectic group $\widetildeΓ_{4N}$. We construct concrete expressions of the half-integral/integral modular forms for $Γ(4)$ up to weight 6 and arrange them into the irreducible representations of $\widetildeΓ_4$. We present three typical models with $\widetildeΓ_4$ modular symmetry for neutrino masses and mixing, and the phenomenological predictions of each model are analyzed numerically.
