Due to finite masses and mixing, for neutrinos propagation in space-time, there is a chiral oscillation between left- and right- chiral neutrinos, besides the usual oscillation between different generations. The probability of chiral oscillation is suppressed by a factor of making the effect small for relativistic neutrinos. However, for non-relativistic neutrinos, this effect can be significant. In matter, the equation of motion is modified. When neutrinos produced in weak interaction pass through the matter, the eigen-energies are split into two different ones depending on the helicity of the neutrino. This results in different oscillation behavior for neutrinos with different helicity, in particular there is a new resonant effect related to the helicity state of neutrino different than the usual MSW effect. For Majorana neutrinos, chiral oscillation also depends on Majorana phases.

中文翻译：

---

中微子手性振荡中的马约拉纳相位和物质效应


由于质量有限和混合，中微子在时空传播时，除了通常的不同代中微子之间的振荡外，还存在左手性中微子和右手性中微子之间的手性振荡。手征振荡的概率通过减小相对论性中微子的影响的因素来抑制。然而，对于非相对论性中微子，这种影响可能很显着。实质上，运动方程被修改。当弱相互作用产生的中微子穿过物质时，根据中微子的螺旋度，本征能量被分成两种不同的能量。这导致具有不同螺旋度的中微子的不同振荡行为，特别是与通常的MSW效应不同的与中微子螺旋度状态相关的新共振效应。对于马约拉纳中微子，手性振荡也取决于马约拉纳相位。