AI 中文总结
研究基于非全纯\(A_4\)模对称性的I型跷跷板框架，用多调和马阿斯形式构建相关矩阵实现共振轻子生成。通过引入复标量场扩展模型，解决宇宙学畴壁问题并产生可间接探测RHN质量尺度的引力波信号。
AI 中文摘要
我们研究了基于非全纯\(A_4\)模对称性的I型跷跷板框架，其中多调和马阿斯形式构建了汤川耦合和右手中微子（RHN）马约拉纳质量矩阵。使用非全纯模形式产生了高度受限的中性轻子质量矩阵，具有更严格的轻子扇区结构，并自然地产生了准简并的RHN质谱，能够在中间尺度上实现共振轻子生成，RHN质量为\(\mathcal{O}(10^3)\) TeV，而无需特设的质量简并。我们通过引入一个在\(\mathbb{Z}_3\)对称下带电的复标量场\((\Phi)\)进一步扩展了该模型。与\(\Phi\)相关的相变后离散对称性的自发破缺导致畴壁（DW）形成。与RHN扇区相关的辐射诱导偏置项触发DW湮灭，解决了宇宙学DW问题，并产生了一个随机引力波（GW）信号，间接探测了RHN质量尺度。伴随的一阶相变产生了第二个GW峰值，产生了一个特征性的双峰谱，频率相差几个数量级，未来的互补GW探测器可能会观测到。
英文摘要
We study a type-I seesaw framework based on non-holomorphic $A_4$ modular symmetry, where polyharmonic Maaß forms construct the Yukawa couplings and right-handed neutrino (RHN) Majorana mass matrix. The use of non-holomorphic modular forms yields highly constrained neutral lepton mass matrices with a more restrictive lepton-sector structure and naturally generates a quasi-degenerate RHN mass spectrum, enabling resonant leptogenesis at an intermediate scale with RHN masses of $\mathcal{O}(10^3)$ TeV without requiring an ad hoc mass degeneracy. We further extend the model by introducing a complex scalar field $(Φ)$ charged under $\mathbb{Z}_3$ symmetry. The spontaneous breaking of the discrete symmetry after the phase transition associated with $Φ$ leads to domain-wall (DW) formation. A radiatively induced bias term associated with the RHN sector triggers DW annihilation, resolving the cosmological DW problem, and producing a stochastic gravitational wave (GW) signal that indirectly probes the RHN mass scale. The accompanying first-order phase transition produces a second GW peak, yielding a characteristic double-peaked spectrum with frequencies separated by several orders of magnitude and potentially observable by complementary future GW detectors.
Comments43 pages including references, 12 figures, 4 tables
