arXiv 2410.005652024-10-01hep-phhep-th

模自对偶点处的残余味（反）对称性及其对中微子质量与混合的约束

Residual flavour (anti)symmetries at the modular self-dual point and constraints on neutrino masses and mixing

Monal Kashav, Ketan M. Patel

备注：: 28 pages, 5 figures

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AI总结：

本文研究模不变理论中自对偶点τ=i处残余味（反）对称性对中微子质量与混合的约束，证明中微子具有唯一残余对称性或反对称性，并通过扫描有限模群导出混合角与CP相位的关联预言。

摘要：

我们探讨了在模不变理论中自对偶点 $τ=i$ 处保持不破缺的对称性所带来的影响。假设（a）三代轻子二重态作为有限模群 $Γ_N$ 的不可约表示进行变换，并且（b）轻中微子质量由 Weinberg 算符产生且为模形式，我们证明这一构造会根据模权重为中微子给出唯一的残余味对称性或反对称性。在反对称情形下，一个中微子始终无质量，而另外两个中微子若质量矩阵为实数则可以简并。这些发现与层级 $N$ 无关。如果带电轻子被安排为展现来自同一 $Γ_N$ 的适当残余对称性，它们将确定轻子混合矩阵的一列，从而给出混合角与 Dirac CP 相位之间的特定关联。残余（反）对称性的存在使得可以应用标准味对称性技术来推导这些预言，并且我们扫描了所有满足条件（a）的可能 $Γ_N$。大多数解在固定列中给出 ${\cal O}(1)$ 量级的矩阵元，倾向于相对较大的轻子混合。

英文摘要：

We explore the implications of symmetries that remain unbroken at the self-dual point $τ=i$ in modular invariant theories. Assuming that (a) the three generations of lepton doublets transform as an irreducible representation of a finite modular group $Γ_N$, and (b) the light neutrino masses arise from the Weinberg operator and are in modular form, we demonstrate that this setup yields a unique residual flavor symmetry or antisymmetry for the neutrinos, depending on the modular weight. In the antisymmetric case, one neutrino is always massless, and the other two can be degenerate if the mass matrix is real. These findings are independent of the level $N$. If the charged leptons are arranged to exhibit an appropriate residual symmetry from the same $Γ_N$, they determine a column of the leptonic mixing matrix, leading to specific correlations between the mixing angles and the Dirac CP phase. The presence of residual (anti)symmetries enables the application of standard flavor symmetry techniques to derive these predictions, and we scan all possible $Γ_N$ satisfying condition (a). Most solutions yield ${\cal O}(1)$ entries in the fixed column, favouring relatively large lepton mixing.

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