We study the time evolution of lepton family number for neutrino which forms SU(2) doublet with charged lepton. The lepton family number is defined through a weak basis of SU(2) doublet in which the charged lepton mass matrix is a real and diagonal one. The lepton family number carried by the neutrino is defined with a left-handed current of the neutrino family. We study the time evolution of the lepton family number operator for Majorana neutrino. To be definite, we introduce the mass term at $t=0$ and study the time evolution of the lepton family number for the later time. Since the operator in flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for flavor eigenstates are related to those of mass eigenstates. The total lepton number of the Majorana neutrino is conserved. By choosing a specific flavor eigenstate of neutrino as an initial state, we compute the time evolution of all lepton family numbers. They are sensitive to Majorana and Dirac phases and also are sensitive to the absolute mass and mass hierarchy of neutrinos.

中文翻译：

---

统一框架中的轻子数违规

我们研究了与带电轻子形成 SU(2) 双峰的中微子轻子族数的时间演化。轻子族数是通过 SU(2) doublet 的弱基定义的，其中带电的轻子质量矩阵是实数和对角线矩阵。中微子携带的轻子族数由中微子族的左手流定义。我们研究了 Majorana 中微子的轻子族数算子的时间演化。为明确起见，我们在 $t=0$ 处引入质量项，并研究以后轻子族数的时间演化。由于风味本征态的算符与质量本征态的算符连续相连，因此风味本征态的创生和湮灭算符与质量本征态的算符有关。Majorana 中微子的总轻子数是守恒的。通过选择中微子的特定风味本征态作为初始状态，我们计算了所有轻子族数的时间演化。它们对马约拉纳相和狄拉克相很敏感，并且对中微子的绝对质量和质量等级也很敏感。