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 ($61$--$165$ $\text{meV}$).
Highlights
In Ref. [1], three of us proposed a minimally asymmetric Yukawa texture for the down-type quark matrix, Yð−1=3Þ, and charged lepton matrix, Yð−1Þ, in the context of SUð5Þ gauge unification
II, we review the construction of the asymmetric texture, its key features, and how they are realized by a T 13 family symmetry
We proposed a phenomenologically successful framework—a diagonal Yð2=3Þ, asymmetric Yð−1=3Þ and Yð−1Þ related by SUð5Þ grand unification, and a complexTBM seesaw mixing—in Ref. [1]
Summary
In Ref. [1], three of us proposed a minimally asymmetric Yukawa texture for the down-type quark matrix, Yð−1=3Þ, and charged lepton matrix, Yð−1Þ, in the context of SUð5Þ gauge unification. 1 2 down-type quark and charged-lepton Yukawa matrices constructed from higher-dimensional operators in terms of gauge-singlet familons, family-singlet Higgses, and messengers with heavy vectorlike masses. Turning to the ΔIw 1⁄4 0 seesaw sector, we show how the complex-TBM seesaw mixing arises from the vacuum structure of a minimal number of familons, resulting from the T 13 Clebsch-Gordan coefficients.1 It requires an alignment between the Yukawa (Yð0Þ) and Majorana (M) matrices of the seesaw formula. We calculate the CP Dirac and Majorana phases [14] yielded by the asymmetric texture with complex-TBM seesaw mixing. The full symmetry of the unified model is SUð5Þ × T × Zn, successfully explaining the masses and mixings of both quarks and leptons. See [11] for other approaches to study neutrino mixing with TBM in relation to T 13 family symmetry as well as [12] for a recent review of neutrino flavor symmetries
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