Tribimaximal Mixing in the $SU(5)\times {\mathcal{T}}_{13}$ Texture

Abstract

We extend the recently proposed $SU(5)\times {\mathcal{T}}_{13}$ model for the asymmetric texture to the up-type quark and seesaw sectors. The hierarchical up-type quark masses are generated from higher-dimensional operators involving family-singlet Higgses, gauge-singlet familons, and vectorlike messengers. The complex-tribimaximal (TBM) seesaw mixing arises from the vacuum structure of a minimal number of familons, resulting in an alignment between the Yukawa and Majorana matrices of the seesaw formula. Introducing four right-handed neutrinos, normal ordering of the light neutrino masses is obtained, with $m_{{\nu }_1}=27.6\mathrm{meV}$, $m_{{\nu }_2}=28.9\mathrm{meV}$ and $m_{{\nu }_3}=57.8\mathrm{meV}$. Their sum almost saturates Planck's cosmological upper bound ($120$ $\text{meV}$). The right-handed neutrino masses are expressed in terms of two parameters for a particular choice of familon vacuum alignment. We predict the $\require{cancel}\cancel{CP}$ Jarlskog-Greenberg invariant to be $|\mathcal{J}|=0.028$, consistent with the current PDG estimate, and Majorana invariants $|{\mathcal{I}}_1|=0.106$ and $|{\mathcal{I}}_2|=0.011$. A sign ambiguity in the model parameters leads to two possibilities for the invariant mass parameter $|m_{\beta \beta }|$: $13.02$ or $25.21$ $\text{meV}$, both within an order of magnitude of the most rigorous experimental upper limit ($61$--$165$ $\text{meV}$).

36 pages, 2 figures, minor changes to match with the published version