论文标题
Lepton风味型号具有模块化$ A_4 $对称性的大容量限制
Lepton flavor model with modular $A_4$ symmetry in large volume limit
论文作者
论文摘要
我们将与额外尺寸的压实相关的模块化对称性作为Lepton部门的风味对称性。尤其是，我们提出了一个基于模块化$ A_4 $对称的模型，其中包括三个右手中微子和一个量规单程希格斯，该模型在所谓的额外尺寸的所谓大容量限制中，即$ \ mbox {im}τ\ to modulus $τ$。引入了右撇子中微子，以实现振荡实验中观察到的微小中微子质量的Seesaw机制。 Singlet Higgs的真空期望值为右撇子中微子提供了主要群众和Higgs领域的$μ$ - $ $ $。该模型可以成功地解释中微子的观测质量和混合角度。我们发现其中一个混合角应在$ \ sin^2θ_{23} \ ge 0.58 $中。重要的是，在两个受限制区域中预测了违反中微子的CP阶段。一个是，狄拉克相为$δ_{\ rm cp} \ simeq -0.5π$，主要阶段为$α__{21} \ simeq 0 $和$α_{31}} \simeqπ$。另一个是$δ_ {\ rm cp} \ simeq +0.5π$，$α_{21} \ simeq2π$和$α__{31} \simeqπ$。中微子双β衰减中的有效中微子质量被发现为$ m _ {\ rm eff} = 0.037 $ -0.047 ev。这些预测将在未来的中微子实验中进行测试。
We consider the modular symmetry associated with the compactification of extra dimensions as the flavor symmetry on lepton sector. Especially, we propose a model based on the modular $A_4$ symmetry with three right-handed neutrinos and a gauge singlet Higgs, which works well in the so-called large volume limit of the extra dimensions, i.e., $\mbox{Im}τ\to \infty$ for a modulus $τ$. The right-handed neutrinos are introduced to realize the seesaw mechanism for tiny neutrino masses observed in oscillation experiments. The vacuum expectation value of the singlet Higgs gives the Majorana masses for right-handed neutrinos and the $μ$-term for Higgs fields. The model can explain the observed masses and mixing angles of neutrinos successfully. We find that one of the mixing angles should be in the range $\sin^2 θ_{23} \ge 0.58$. Importantly, the CP violating phases of neutrinos are predicted in the two restricted regions. One is that the Dirac phase is $δ_{\rm CP} \simeq - 0.5 π$ and the Majorana phases are $α_{21} \simeq 0$ and $α_{31} \simeq π$. The other is $δ_{\rm CP} \simeq + 0.5 π$, $α_{21} \simeq 2 π$ and $α_{31} \simeq π$. The effective neutrino mass in the neutrinoless double beta decay is found to be $m_{\rm eff} = 0.037$--0.047 eV. These predictions will be tested in the future neutrino experiments.
