We construct a texture where the seesaw matrix is diagonalized by the tribimaximal (TBM) matrix with a phase. All angles of the Cabibbo-Kobayashi-Maskawa matrix and Pontecorvo-Maki-Nakagawa-Sakata matrix are consistent with particle data group values, and the mass relations of quarks and charged leptons extrapolated to the grand unified theory scale are satisfied, including the Gatto relation. The novel ingredient is the asymmetry of the down-quark and charged lepton Yukawa matrices. Explaining the reactor angle requires a CP phase in the TBM matrix, resulting in the Jarlskog-Greenberg invariant at jJj ¼ 0.028, albeit with an undetermined sign. While SOð10Þ restrains the right-handed neutrino Majorana matrix, the neutrino masses are left undetermined.
We extend the recently proposed SU (5) × 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 vector-like 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 ν1 = 27.6 meV, m ν2 = 28.9 meV and m ν3 = 57.8 meV. Their sum almost saturates Planck's cosmological upper bound (120 meV). The right-handed neutrino masses are expressed in terms of two parameters for a particular choice of familon vacuum alignment. We predict the¨CP Jarlskog-Greenberg invariant to be |J | = 0.028, consistent with the current PDG estimate, and Majorana invariants |I 1 | = 0.106 and |I 2 | = 0.011. A sign ambiguity in the model parameters leads to two possibilities for the invariant mass parameter |m ββ |: 13.02 meV or 25.21 meV, both within an order of magnitude of the most rigorous experimental upper limit (61-165 meV). *
We propose T13 = Z13 Z3 as the underlying non-Abelian discrete family symmetry of the asymmetric texture presented in [1]. Its mod 13 arithmetic distinguishes each Yukawa matrix element of the texture. We construct a model of effective interactions that singles out the asymmetry and equates, without finetuning, the products of down-quark and charged-lepton masses at a GUT-like scale. *
The four-point correlation function of primordial scalar perturbations has parity-even and parity-odd contributions and the parity-odd signal in cosmological observations is opening a novel window to look for new physics in the inflationary epoch. We study the distinct parity-odd and even prediction from the axion inflation model, in which the inflaton couples to a vector field via a Chern-Simons interaction, and the vector field is considered to be either approximately massless (mA ≪ Hubble scale H) or very massive (mA ∼ H). The parity-odd signal arises due to one transverse mode of the vector field being predominantly produced during inflation. We adopt the in-in formalism to evaluate the correlation functions. Considering the vector field mode function to be dominated by its real part up to a constant phase, we simplify the formulas for numerical computations. The numerical studies show that the massive and massless vector fields give significant parity-even signals, while the parity-odd contribution is about one to two orders of magnitude smaller.
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