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Register a new userDirac CP phase in the neutrino mixing matrix and the Froggatt-Nielsen mechanism with ${rm bf det} bf [M_ u]=0$
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We discuss the Dirac CP violating phase $delta_{CP}$ in the Froggatt-Nielsen model for a neutrino mass matrix $M_ u$ imposing a condition ${rm det} [M_ u]=0$. This additional condition restricts the CP violating phase $delta_{CP}$ drastically. We find that the phase $delta_{CP}$ is predicted in the region of $pm (0.4- 2.9)$ radian, which is consistent with the recent T2K and NO$ u$A data. There is a remarkable correlation between $delta_{CP}$ and $sin^2theta_{23}$. The phase $delta_{CP}$ converges on $sim pm pi/2$ if $sin^2theta_{23}$ is larger than $0.5$. Thus, accurate measurements of $sin^2theta_{23}$ are important for a test of our model. The effective mass $m_{ee}$ for the neutrinoless double beta decay is predicted in the rage of $3.3-4.0$ meV.
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We present a doubly parametric extension of the standard Froggatt--Nielsen (FN) mechanism. As is well known, mass matrices of the up- and down-type quark sectors and the charged lepton sector in the standard model can be parametrized well by a parameter $lambda$ which is usually taken to be the sine of the Cabibbo angle ($lambda = sintheta_text{C} simeq 0.225$). However, in the neutrino sector, there is still room to realize the two neutrino mass squared differences $Delta m_text{sol}^2$ and $Delta m_text{atm}^2$, two large mixing angles $theta _{12}$ and $theta _{23}$, and non-zero $theta _{13}$. Then we consider an extension with an additional parameter $rho$ in addition to $lambda$. Taking the relevant FN charges for a power of $lambda~(=0.225)$ and additional FN charges for a power of $rho$, which we assume to be less than one, we can reproduce the ratio of the two neutrino mass squared differences and three mixing angles. In the normal neutrino mass hierarchy, we show several patterns for taking relevant FN charges and the magnitude of $rho$. We find that if $sin theta_{23}$ is measured more precisely, we can distinguish each pattern. This is testable in the near future, for example in neutrino oscillation experiments. In addition, we predict the Dirac CP-violating phase for each pattern.
The extensions of the Standard Model based on the $SU(3)_ctimes SU(3)_Ltimes U(1)_X$ gauge group (331-models) have been advocated to explain the number of fermion families in nature. It has been recently shown that the Froggatt-Nielsen mechanism, a popular way to explain the mass hierarchy of the charged fermions, can be incorporated into the 331-setting in an economical fashion (FN331). In this work we extend the FN331-model to include three right-handed neutrino singlets. We show that the seesaw mechanism is realized in this model. The scale of the seesaw mechanism is near the $SU(3)_Ltimes U(1)_X$-breaking scale. The model we present here simultaneously explains the mass hierarchy of all the fermions, including neutrinos, and the number of families.
We study how to incorporate CP violation in the Froggatt--Nielsen (FN) mechanism. To this end, we introduce non-renormalizable interactions with a flavor democratic structure to the fermion mass generation sector. It is found that at least two iso-singlet scalar fields with imposed a discrete symmetry are necessary to generate CP violation due to the appearance of the relative phase between their vacuum expectation values. In the simplest model, ratios of quark masses and the Cabibbo-Kobayashi-Maskawa (CKM) matrix including the CP violating phase are determined by the CKM element |V_{us}| and the ratio of two vacuum expectation values R=|R|e^{i*alpha} (a magnitude and a phase). It is demonstrated how the angles phi_i (i=1--3) of the unitarity triangle and the CKM off-diagonal elements |V_{ub}| and |V_{cb}| are predicted as a function of |V_{us}|, |R| and alpha. Although the predicted value of the CP violating phase does not agree with the experimental data within the simplest model, the basic idea of our scenario would be promising to construct a more realistic model of flavor and CP violation.
The latest experimental progress have established three kinds of neutrino oscillations with three mixing angles measured to rather high precision. There is still one parameter, i.e., the CP violating phase, missing in the neutrino mixing matrix. It is shown that a replay between different parametrizations of the mixing matrix can determine the full neutrino mixing matrix together with the CP violating phase. From the maximal CP violation observed in the original Kobayashi-Maskawa (KM) scheme of quark mixing matrix, we make an Ansatz of maximal CP violation in the neutrino mixing matrix. This leads to the prediction of all nine elements of the neutrino mixing matrix and also a remarkable prediction of the CP violating phase $delta_{rm CK}=(85.48^{+4.67(+12.87)}_{-1.80(-4.90)})^circ$ within $1sigma (3sigma)$ range from available experimental information. We also predict the three angles of the unitarity triangle corresponding to the quark sector for confronting with the CP-violation related measurements.
In the model of gauge mediation of SUSY breaking in the presence of tree-level mediation, the Froggatt-Nielsen mechanism provides a different hierarchy of sparticle masses. We study the spectra and show the results to be like those in an effective supersymmetric model.
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