We use perturbation theory to obtain neutrino oscillation probabilities, including the standard mass-mixing paradigm and non-standard neutrino interactions (NSI). The perturbation is made on the standard parameters and sin²(θ ₁₃) and on the non-diagonal NSI parameters, but keeps diagonal NSI parameters non-perturbated. We perform the calculation for the channels ν _μ → ν _e and ν _μ → ν _μ . The resulting oscillation formulas are compact and present functional structure similar to the standard oscillation (SO) case. They apply to a wide range in the allowed NSI space of parameters and include the previous results from perturbative approaches as limit cases. Also, we use the compact formulas we found to explain the origin of the degeneracies in the neutrino probabilities in terms of the invariance of amplitude and phase of oscillations. Then we determine analytically the multiple sets of combinations of SO and NSI parameters that result in oscillation probabilities identical to the SO case.

我们使用微扰理论来获得中微子振荡概率，包括标准的质量混合范式和非标准的中微子相互作用（NSI）。扰动是在标准参数进行和sin ²（θ ₁₃）和非对角NSI参数，但保持对角NSI参数的非的扰动。我们执行计算用于通道ν _μ →交通ν _Ë和ν _μ →交通ν _μ 。产生的振荡公式很紧凑，并且具有类似于标准振荡（SO）情况的功能结构。它们适用于参数允许的NSI空间中的广泛范围，并且包括摄动方法的先前结果作为极限情况。此外，我们使用发现的紧凑公式来解释中微子概率的简并性的起源，即振幅和相位的不变性。然后，我们通过分析确定SO和NSI参数的多组组合，从而得出与SO情况相同的振荡概率。