The overall characteristics of the solar and atmospheric neutrino oscillations are approximately consistent with a tribimaximal form of the mixing matrix U of the lepton sector. Exact tribimaximal mixing leads to ${\theta }_{13}=0$. However, the results from the Daya Bay and RENO experiments have established, such that in comparison to the other neutrino mixing angles, ${\theta }_{13}$ is small. Moreover, the atmospheric and solar mass splitting differ by two orders of magnitude. These significant differences constitutes the great enthusiasm and main motivation for our research herein reported. Keeping the behavior of U as tribimaximal, we would make a response to the following questions: at some level, whether or not the small parameters such as the solar neutrino mass splitting and $U_{e3}$, which vanish in a new framework, can be interpreted as a modified FL neutrino mass model? Subsequently, a minimal single perturbation leads to nonzero values for both of them? Our minimal perturbation matrix is constructed solely from computing the third mass eigenstate, using the rules of perturbation theory. Let us point out that, unlike other investigations, this matrix is not adopted on an ad hoc basis, but is created following a series of steps that we will describe. Also in compared to the original FL neutrino mass model which generalize it by inserting phase factors, our work is more accurate. Subsequently, we produce the following results that add new contributions to the literature: (a) we obtain a realistic neutrino mixing matrix with $\delta \ne 0$ and ${\theta }_{23}={45}^{\circ }$; (b) the solar mass splitting term is dominated by an imaginary term, which could induce the existence of Majorana neutrinos, along with explaining a large CP violation in nature; (c) the ordering of the neutrino masses is normal; however, at the end of the allowed range, it becomes more degenerate ($97\%$); (d) we also obtain the allowed range of the mass parameters, which not only are in accordance with the experimental data but also allow falsifiable predictions for the masses of the neutrinos and the CP violating phases which none of these results has been achieved in the original FL neutrino mass model. Finally, let us emphasize that the results obtained by our framework here are much more efficient compared to those obtained in previous works in terms of currently available experimental data (namely, the best fit column).

中文翻译：

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从修正的 Fridberg-Lee 模型生成 CP 违例

太阳和大气中微子振荡的总体特征与轻子扇区混合矩阵U的三极大形式大致一致。精确的三极大混合导致${\theta }_{13}=0$. 然而，大亚湾和 RENO 实验的结果已经确定，因此与其他中微子混合角度相比，${\theta }_{13}$是小。此外，大气和太阳质量分裂相差两个数量级。这些显着差异构成了我们在此报道的研究的巨大热情和主要动机。保持 U 的行为为三极大，我们将对以下问题做出回应：在某种程度上，诸如太阳中微子质量分裂和${ü}_{e3}$，在新的框架中消失，可以解释为修改后的 FL 中微子质量模型？随后，最小的单个扰动导致它们两者的非零值？我们的最小微扰矩阵仅由计算第三质量本征态构成，使用微扰理论规则。让我们指出，与其他调查不同，该矩阵不是临时采用的，而是按照我们将描述的一系列步骤创建的。此外，与通过插入相位因子对其进行概括的原始 FL 中微子质量模型相比，我们的工作更加准确。随后，我们产生了以下结果，为文献增添了新的贡献：（a）我们获得了一个现实的中微子混合矩阵$\delta \ne 0$和${\theta }_{23}={45}^{\circ }$; (b) 太阳质量分裂项由一个虚项支配，这可能导致马约拉纳中微子的存在，同时解释了自然界中的大 CP 破坏；(c) 中微子质量的排序是正常的；但是，在允许范围的末尾，它变得更加退化（$97\%$); (d) 我们还获得了质量参数的允许范围，这不仅与实验数据一致，而且还可以对中微子和 CP 破坏相的质量进行可证伪的预测，而这些结果在原始的 FL 中微子质量模型。最后，让我们强调一下，就当前可用的实验数据（即最佳拟合列）而言，我们的框架在此处获得的结果与以前的工作中获得的结果相比要高效得多。