We know $L_e-L_\mu-L_\tau$ symmetry gives $m^2_1= m^2_2 >> m^2_3$ pattern inZee model. $\Delta m^2_\odot$ emerges from a small breaking of this symmetry.Because this symmetry is broken very weakly $\theta_\odot$ does not deviatemuch from $\tan^2 \theta_\odot=1$ which is its value in the symmetric limit.This gives a mismatch with LMA solution where mixing is large but not exactlymaximal. We confront this property of Zee mass matrix by phenomenologicallyanalyzing recent results from solar and atmospheric neutrino oscillationexperiments at various confidence levels. We conclude that LOW type solution iscompatible with the Zee mass matrix at 99% confidence level when atmosphericneutrino deficit is explained by maximal $\nu_\mu \leftrightarrow \nu_\tau$oscillation. Thus the minimal version of the Zee model even though disfavoredby the LMA type or VO type solutions, is compatible with LOW type solution ofsolar neutrino problem.
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机译：我们知道$ L_e-L_ \ mu-L_ \ tau $对称性会给Zee模型提供$ m ^ 2_1 = m ^ 2_2 >> m ^ 2_3 $模式。 $ \ Delta m ^ 2_ \ odot $通过这种对称性的微小破坏而出现，因为这种对称性非常弱地被破坏了，因此$ \ theta_ \ odot $不会与$ \ tan ^ 2 \ theta_ \ odot = 1 $产生偏差该值与LMA解决方案不匹配，在LMA解决方案中混合很大但不是完全最大。我们通过现象学分析太阳和大气中微子振荡实验在不同置信度下的最新结果来面对Zee质量矩阵的这一特性。我们得出的结论是，当大气中微子缺陷由最大$ \ nu_ \ mu \ leftrightarrow \ nu_ \ tau $ oscillation解释时，LOW型解与Zee质量矩阵在99％置信度下兼容。因此，即使不适合LMA型或VO型解决方案，Zee模型的最小版本也与太阳能中微子问题的LOW型解决方案兼容。
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