论文标题
重新研究中微子振荡的平面波模型
Plane-wave model of neutrino oscillations revisited
论文作者
论文摘要
大规模中微子的现象学 - 轻质扇形中的风味混合，导致不同中微子类型之间的振荡沿其在真空中的宏观距离上的传播沿其传播之间的振荡 - 旨在将可观察到的数量（振荡频率（等效地，振动长度）与中微子属性相关联）与中微子的质量及其混合体：$ seprino properies $：} $：} $ $ s-s $ sous $ sij> suj c yj ij ij ij ij ij { $Δm_{ij}^2 $。 计算给定中微子类型的概率要么生存或突变为另一种类型，作为动量$ p $和行进距离$ l $的函数，适当地基于具有变化复杂性的波动模型。近似忽略了诸如变形之类的微妙效果导致标准振荡公式的术语与$ \ sin^2（Δm_{ij}^2 l / 4 p）$成正比。 如大多数教科书所示，也可以通过简单的平面波模型得出相同的结果。但是，这些方法依赖于非物理A-priory假设：在不同质量特征态的阶段中，“相等能量”或“相等的速度”或“相等动量” - 在其他地方被驳斥。此外，有些人默认地假设干扰发生在时间$ t = l $。 这项研究重新检查了平面波模型。得出标准公式无需非物理假设：启发式方法仅依赖于在时间$ t = l /β$时仔细定义干扰，并且通过基于波动式的定性方式的连贯参数证明是合理的。
The phenomenology of massive neutrinos -- flavour mixing in the lepton sector causing oscillations between different neutrino-types along their propagation over macroscopic distances in vacuum -- aims at relating observable quantities (oscillation frequency or, equivalently, oscillation length) to the neutrino properties: mixing angles $θ_{ij}$ and mass-squared differences $Δm_{ij}^2$. Calculation of the probabilities for a given neutrino-type either to survive or to mutate into another type, as functions of momentum $p$ and travelling distance $L$, are properly based on wave-packet models of varying complexity. Approximations neglecting subtle effects like decoherence result in the standard oscillation formulae with terms proportional to $\sin^2(Δm_{ij}^2 L / 4 p)$. The same result may also be derived by a simple plane-wave model as shown in most textbooks. However, those approaches rely on unphysical a-priory assumptions: either "equal energy" or "equal velocity" or "equal momentum" in the phases of different mass eigenstates -- which are refuted elsewhere. In addition, some assume tacitly that interference occurs at time $t = L$. This study re-examines the plane-wave model. No unphysical assumption is necessary for deriving the standard formulae: a heuristic approach relies only on carefully defining interference at time $t = L / β$, and is justified by coherence arguments based in a qualitative way on wave-packets.
