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Flavor Neutrino Masses giving sinθ13=0

  • with Keisuke Yuda, published in Phys. Lett. B 693, No. 5 (2010) 571-574 (Received date: September, 2010).
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Among neutrino mixings, the reactor mixing angle, $\theta_{13}$, is observed to be almost vanishing and is consistent with $\theta_{13}=0$. We discuss how the condition of $\theta_{13}=0 $ constrains models of neutrino mixingsand show that, for  flavor neutrino masses given by $M_{ij}$ ($i,j$=$e,\mu,\tau$),two conditions of $M_{e\tau } =  - e^{2i\gamma }\tan\theta_{23}M_{e\mu }$ and$M_{\tau \tau } = e^{4i\gamma }M_{\mu \mu } + e^{2i\gamma }\left(2/\tan 2\theta_{23}\right)M_{\mu \tau }$lead to $\theta_{13}$=0, where $\theta_{23}$ is the atmospheric neutrino mixing angle and $\gamma$ is its associated phase.  The rephasing invariance can select two phases provided by $\alpha$ = arg($M_{e\mu }$) and $\beta$ = arg($M_{e\tau }$), giving $\gamma=(\beta-\alpha)/2$.


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