We study the phenomenology of two-zero textures of $M_{\nu }^{4\times 4}$ neutrino mass matrices in the minimal extended seesaw (MES) mechanism. $M_{\nu }^{4\times 4}$ involves $3\times 3$ Dirac neutrino mass matrix ($M_D$), $3\times 3$ right-handed Majorana neutrino mass matrix $M_R$ and $1\times 3$ matrix $M_S$ that couples the singlet field ‘S’ with the right-handed neutrinos. We consider the phenomenologically predictive cases (5+3) and (6+2) schemes for zero textures of $M_D$ and $M_R$ of $3\times 3$ active sector of $M_{\nu }^{4\times 4}$ along with admissible one or two-zero textures of $M_S$. Although there is a large number of combinations of $M_D,M_R$ and $M_S$ leading to the desired two-zero textures, $S_3$ group transformations between the different zero textures of $M_D,M_R$ and $M_S$ reduce them to a small number of basic combinations. In MES, $M_{\nu }^{4\times 4}$ should be a matrix of rank 3, so we have 12 two-zero textures of neutrino mass matrices of rank 3 out of total 15 two-zero textures of neutrino mass matrices. In realization of the two-zero textures in (5+3) scheme we have obtained a number of correlations among the neutrino mass matrix elements $m_{ij}$, while none of the two-zero textures could be realized in the (6+2) scheme. The viability of each of the realizable textures is checked by plotting the scatter plots of their respective correlations under the current neutrino oscillation data. We have analysed the role played by the Dirac and Majorana CP phases for each of the textures. For constrained ranges of CP phases we also draw scatter plots for Jarlskog invariant ($J_{CP}$) and effective electron neutrino mass $|m_{\beta \beta }|$. In our study the viable textures are finally realized by $Z_8$ Abelian group symmetry by extending the Standard Model to include few scalar fields.

我们研究了二零纹理的现象学 ${\mathrm{中号}}_{\nu }^{4\times 4}$ 最小延伸跷跷板（MES）机制中的中微子质量矩阵。 ${\mathrm{中号}}_{\nu }^{4\times 4}$ 涉及 $3\times 3$ 狄拉克中微子质量矩阵（${\mathrm{中号}}_d$）， $3\times 3$ 右手的马约拉纳中微子质量矩阵 ${\mathrm{中号}}_{\mathrm{[R}}$ 和 $\mathrm{1个}\times 3$ 矩阵 ${\mathrm{中号}}_{\mathrm{小号}}$将单重态场“ S”与右旋中微子耦合在一起。我们考虑零纹理的现象学预测情况（5 + 3）和（6 + 2）方案${\mathrm{中号}}_d$ 和 ${\mathrm{中号}}_{\mathrm{[R}}$ 的 $3\times 3$ 的活跃部门 ${\mathrm{中号}}_{\nu }^{4\times 4}$ 以及允许的一或二零纹理 ${\mathrm{中号}}_{\mathrm{小号}}$。虽然有很多组合${\mathrm{中号}}_d，{\mathrm{中号}}_{\mathrm{[R}}$ 和 ${\mathrm{中号}}_{\mathrm{小号}}$ 导致所需的零二纹理， ${\mathrm{小号}}_3$ 的不同零纹理之间的组变换 ${\mathrm{中号}}_d，{\mathrm{中号}}_{\mathrm{[R}}$ 和 ${\mathrm{中号}}_{\mathrm{小号}}$将它们减少为少量的基本组合。在MES中，${\mathrm{中号}}_{\nu }^{4\times 4}$应该是等级3的矩阵，因此在中微子质量矩阵的总共15个二零纹理中，我们有12个等级3的中微子质量矩阵的十二个零。在（5 + 3）方案中实现零零纹理时，我们获得了中微子质量矩阵元素之间的许多相关性${米}_{\mathrm{一世}Ĵ}$，而在（6 + 2）方案中无法实现两个零纹理。通过在当前中微子振荡数据下绘制它们各自相关性的散点图，可以检查每个可实现纹理的生存能力。我们分析了Dirac和Majorana CP阶段对于每种纹理的作用。对于CP相的受约束范围，我们还绘制了Jarlskog不变量（${Ĵ}_{CP}$）和有效电子中微子质量 $|{米}_{\beta \beta }|$。在我们的研究中，可行的纹理最终通过${ž}_8$ 通过扩展标准模型以包括几个标量场来实现阿贝尔群对称。