Viability of bi-maximal solution of the Zee mass matrix

We know $L_e-L_{\mu }-L_{\tau }$ symmetry gives $m_1^2=m_2^2>>m_3^2$ pattern in Zee model. $\mathrm{\Delta }{m}_{\odot }^2$ emerges from a small breaking of this symmetry. Because this symmetry is broken very weakly ${\theta }_{\odot }$ does not deviate much 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 exactly maximal. We confront this property of Zee mass matrix by phenomenologically analyzing recent results from solar and atmospheric neutrino oscillation experiments at various confidence levels. We conclude that LOW type solution is compatible with the Zee mass matrix at 99% confidence level when atmospheric neutrino deficit is explained by maximal ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ oscillation. Thus the minimal version of the Zee model even though disfavored by the LMA type or VO type solutions, is compatible with LOW type solution of solar neutrino problem.