Large|Ue3|and tribimaximal mixing

Abstract

We investigate in a model-independent way to what extent one can perturb tribimaximal mixing in order to generate a sizable value of $|{U}_{e3}|$, while at the same time keeping solar neutrino mixing near its measured value, which is close to ${sin}^{2}{\ensuremath{\theta}}_{12}=\frac{1}{3}$. Three straightforward breaking mechanisms to generate $|{U}_{e3}|\ensuremath{\simeq}0.1$ are considered. For charged lepton corrections, the suppression of a sizable contribution to ${sin}^{2}{\ensuremath{\theta}}_{12}$ can be achieved if $CP$ violation in neutrino oscillations is almost maximal. Generation of the indicated value of $|{U}_{e3}|\ensuremath{\simeq}0.1$ through renormalization group corrections requires the neutrinos to be quasidegenerate in mass. The consistency with the allowed range of ${sin}^{2}{\ensuremath{\theta}}_{12}$ together with large running of $|{U}_{e3}|$ forces one of the Majorana phases to be close to $\ensuremath{\pi}$. This implies large cancellations in the effective Majorana mass governing neutrinoless double beta ($(\ensuremath{\beta}\ensuremath{\beta}{)}_{0\ensuremath{\nu}}$) decay, constraining it to lie near its minimum allowed value of ${m}_{0}\mathrm{cos}2{\ensuremath{\theta}}_{12}$, where ${m}_{0}\ensuremath{\gtrsim}0.1\text{ }\text{ }\mathrm{eV}$. Finally, explicit breaking of the neutrino mass matrix in the inverted hierarchical and quasidegenerate neutrino mass spectrum cases is similarly correlated with the $(\ensuremath{\beta}\ensuremath{\beta}{)}_{0\ensuremath{\nu}}$-decay effective Majorana mass, although to a lesser extent. The implied values for the atmospheric neutrino mixing angle ${\ensuremath{\theta}}_{23}$ are given in all cases.