Bi-pair Neutrino Mixing

with Teruyuki Kitabayashi, published in Phys. Lett. B 696, No. 5 (2011) 478-481 (Received date: November, 2010).

arXiv:1101.2073

$A new type of neutrino mixing named bi-pair neutrino mixing is proposed to describe the current neutrino mixing pattern with a vanishing reactor mixing angle and is determined by a mixing matrix with two pairs of identical magnitudes of matrix elements. As a result, we predict \sin^2\theta_{12}=1-1/\sqrt{2}\left(\approx 0.293\right) for the solar neutrino mixing and either \sin^2\theta_{23}=\tan^2\theta_{12} or \cos^2\theta_{23}=\tan^2\theta_{12} for the atmospheric neutrino mixing. We determine flavor structure of a mass matrix M, leading to diagonal masses of m_{1,2,3}, and find that \left| M_{\mu \mu } - M_{ee}/t_{12}^2 \right|:\left| {{M_{\mu \tau }}} \right|:\left| M_{\tau \tau } - M_{ee}/t_{12}^2 \right|=t^2_{23}:\left| t_{23} \right|:1 for the normal mass hierarchy if m_1=0, where t_{ij}=\tan\theta_{ij} (i,j=1,2,3) and M_{ij} (i,j=e,\mu,\tau) stand for flavor neutrino masses. For the inverted mass hierarchy, the bi-pair mixing scheme turns out to satisfy the strong scaling ansatz requiring that \left| {{M_{\mu \mu }}} \right|:\left| {{M_{\mu \tau }}} \right|:\left| {{M_{\tau \tau }}} \right| = 1:\left|t_{23}\right|:t_{23}^2 if m_3=0.$

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