论文标题
自发的CP违反模量$τ$ in $ a_4 $ Lepton Flavors
Spontaneous CP violation by modulus $τ$ in $A_4$ model of lepton flavors
论文作者
论文摘要
我们讨论了模块化$ a_4 $ lepton的模型与广义CP对称性相结合。在我们的模型中，CP和模块化对称性都因模量$τ$的真空期望值而自发地破裂。 CP违规的来源是$ {\ rm re} [τ] $的非平地值，而模型的其他参数是真实的。 $τ$的允许区域非常狭窄，靠近固定点$τ= i $，对于正常的层次结构（NH）和中微子质量的倒置（IH）。违反DIRAC阶段$δ_{CP} $的CP明显以$ [98^\ circ，\，\，110^\ circ] $和$ [250^\ circ，\，\，262^\ circ] $ for $ 3 \，σ$信心级别。另一方面，$δ_{cp} $在$ [95^\ circ，100^\ circ] $和$ [260^\ circ，\，265^\ circ] $ for Ih的$ 5 \，σ$ pusitiver级别。预测的$ \ sum m_i $ in $ [82，\，102] $ MEV为NH和$ \ sum m_i = [134，\，\，180] $ MEV for IH。有效的质量$ \ langle m_ {ee} \ rangle $对于$0νβ$衰减的$ [12.5，\，20.5] $ MEV和$ [54，\，67] $ MEV的NH和IH。
We discuss the modular $A_4$ invariant model of leptons combining with the generalized CP symmetry. In our model, both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus $τ$. The source of the CP violation is a non-trivial value of ${\rm Re} [τ]$ while other parameters of the model are real. The allowed region of $τ$ is in very narrow one close to the fixed point $τ=i$ for both normal hierarchy (NH) and inverted ones (IH) of neutrino masses. The CP violating Dirac phase $δ_{CP}$ is predicted clearly in $[98^\circ,\,110^\circ]$ and $[250^\circ,\,262^\circ]$ for NH at $3\,σ$ confidence level. On the other hand, $δ_{CP}$ is in $[95^\circ,100^\circ]$ and $[260^\circ,\,265^\circ]$ for IH at $5\,σ$ confidence level. The predicted $\sum m_i$ is in $[82,\,102]$ meV for NH and $\sum m_i=[134,\,180]$ meV for IH. The effective mass $\langle m_{ee}\rangle$ for the $0νββ$ decay is predicted in $[12.5,\,20.5]$ meV and $[54,\,67]$ meV for NH and IH, respectively.
