论文标题
基于$ A_4 $对称和扰动方法的特殊两个零纹理
The special Two zeros texture based on $A_4$ symmetry and perturbation method
论文作者
论文摘要
当前的研究旨在研究基于$ a_4 $对称性的主要中微子质量矩阵中两个零的特殊情况，那里充电的Lepton Mass Matrix是对角线的。带有$（μ，μ）$和$（τ，τ）$m_ν^{s_7} $的纹理$m_ν^{s_7} $，$（τ，τ）$消失的质量矩阵的消失元素具有魔术和$μ-τ$对称性，带有trimimaximal形式的混合矩阵形式，它会导致$θ_{13} = 0 $不允许使用实验数据，并且似乎不允许使用实验数据。 Since $θ_{13}$ is small compared to other neutrino mixing angles, we show that $θ_{13}$, and $δ$ could be obtained by using a complex symmetrical perturbation in the mass basis and also could be shown that $δm^2\equiv~m_2^2-m^2_1\neq0$ affecting the atmospheric mixing angle. 我们发现，对于复杂的扰动质量矩阵，只有案例i的结果，$Δ<0 $和$ \ textit {re}（α）<0 $，与实验数据一致。此外，发现我们的参数空间的允许范围和扰动的复杂元素，从而从$ 45^\ circ $中找到了$θ_{23} $的偏差，其中此偏差与指示我们模型及其结果的准确性相符的实验数据一致。我们的预测是在案例I中倒数的。
The current study aimed to investigate the special case of two zeros in a Majorana neutrino mass matrix based on $A_4$ symmetry, where charged lepton mass matrix is diagonal. The texture $M_ν^{S_7}$ with $(μ, μ)$ and $(τ,τ)$ vanishing element of mass matrix has magic and $μ-τ$ symmetry, with a tribimaximal form of the mixing matrix which leads to $θ_{13}=0$ that it is not consistent with experimental data and does not seem to be allowed. Since $θ_{13}$ is small compared to other neutrino mixing angles, we show that $θ_{13}$, and $δ$ could be obtained by using a complex symmetrical perturbation in the mass basis and also could be shown that $δm^2\equiv~m_2^2-m^2_1\neq0$ affecting the atmospheric mixing angle. We find that for the complex perturbation mass matrix, only the results of the case I, $Δ<0$ and $\textit{Re}(α)<0$, are consistent with experimental data. Furthermore, the allowed range of our parameter space and complex element of perturbation are found which led to finding the deviation of $θ_{23}$ from $45^\circ$ where this deviation is in line with the experimental data which indicate the accuracy of our model and its results. Our prediction is inverted mass ordering in the Case I. The results of the case II, $Δ>0$ and $\textit{Re}(α)>0$, are ruled out.
