Dirac Neutrino Mass Matrix Research Articles

Up quark masses from down quark masses

The quark and charged lepton masses and the angles and phase of the CKM mixing matrix are nicely reproduced in a model which assumes SU ( 3 ) ⊗ SU ( 3 ) flavor symmetry broken by the v.e.v.'s of fields in its bi-fundamental representation. The relations among the quark mass eigenvalues, m u / m c ≈ m c / m t ≈ m d 2 / m s 2 ≈ m s 2 / m b 2 ≈ Λ GUT 2 / M Pl 2 , follow from the broken flavor symmetry. Large tan β is required which also provides the best fits to data for the obtained textures. Lepton–quark grandunification with a field that breaks both SU ( 5 ) and the flavor group correctly extends the predictions to the charged lepton masses. The seesaw extension of the model to the neutrino sector predicts a Majorana mass matrix quadratically hierarchical as compared to the neutrino Dirac mass matrix, naturally yielding large mixings and low mass hierarchy for neutrinos.

Bi-large Neutrino Mixing See-Saw Mass Matrix with Texture Zerosand Leptogenesis

We study constraints on neutrino properties for a class ofbi-large mixing See-Saw mass matrices with texture zeros and withthe related Dirac neutrino mass matrix to be proportional to adiagonal matrix of the form diag(ϵ,1,1). Texture zerosmay occur in the light (class a)) or in the heavy (class b))neutrino mass matrices. Each of these two classes has 5 differentforms which can produce non-trivial three generation mixing withat least one texture zero. We find that two types of texture zeromass matrices in both class a and class b can be consistent withpresent data on neutrino masses and mixing. None of the neutrinoscan have zero masses and the lightest of the light neutrinos has amass larger than about 0.046 eV for class a and 0.0027 eV forclass b. In these models although the CKM CP violating phasevanishes, the non-zero Majorana phases can exist and can play animportant role in producing the observed baryon asymmetry in ouruniverse through leptogenesis mechanism. The requirement ofproducing the observed baryon asymmetry can further distinguishdifferent models and also restrict the See-Saw scale to be in therange of 1012∼1015 GeV. We also discuss RG effects on V13.

Relation between CKM and MNS Matrices Induced by Bi-Maximal Rotations in the Seesaw Mechanism

It is found that the seesaw mechanism not only explains the smallness of neutrino masses but also accounts for the large mixing angles simultaneously, even if the unification of the neutrino Dirac mass matrix with that of up-type quark sector is realized. In this mechanism, we show that the mixing matrix of the Dirac-type mass matrix gets extra rotations from the diagonalization of Majorana mass matrix. Assuming that the mixing angles to diagonalize the Majorana mass matrix are extremely small, we find that the large mixing angles of leptonic sector found in atmospheric and long baseline reactor neutrino oscillation experiments can be explained by these extra rotations. We also find that provided the mixing angle around y-axis to diagonalize the Majorana mass matrix vanishes, we can derive the information about the absolute values of neutrino masses and Majorana mass responsible for the neutrinoless double beta decay experiment through the data set of neutrino experiments. In the simplified case that there is no CP phase, we find that the neutrino masses are decided as $m_1:m_2:m_3\approx 1:2:8$ and that there are no solution which satisfy $m_3<m_1<m_2$ (inverted mass spectrum). Then, including all CP phases, we reanalyze the absolute values of neutrino masses and Majorana mass responsible for the neutrinoless double beta decay experiment.

Leptogenesis in minimal left–right symmetric models

We analyze lepton asymmetry induced in the decay of right-handed neutrinos in a class of minimal left–right symmetric models. In these models, which assume low energy supersymmetry, the Dirac neutrino mass matrix is proportional to the charged lepton mass matrix. As a result, lepton asymmetry is calculable in terms of 9 parameters, all measurable in low energy neutrino experiments. By solving the Boltzmann equations numerically we show that adequate baryon asymmetry is generated in these models. This however places significant constraints on the light neutrino parameters. We find tan 2 θ 12 ≃ m 1 / m 2 and θ 13 = ( 0.01 – 0.07 ) for the neutrino oscillation angles, and β ≃ α + π / 2 for the Majorana phases.

S3× Bbb Z2model for neutrino mass matrices

We propose a model for lepton mass matrices based on the seesaw mechanism, a complex scalar gauge singlet and a horizontal symmetry $S_3 \times \mathbbm{Z}_2$. In a suitable weak basis, the charged-lepton mass matrix and the neutrino Dirac mass matrix are diagonal, but the vacuum expectation value of the scalar gauge singlet renders the Majorana mass matrix of the right-handed neutrinos non-diagonal, thereby generating lepton mixing. When the symmetry $S_3$ is not broken in the scalar potential, the effective light-neutrino Majorana mass matrix enjoys $\mu$--$\tau$ interchange symmetry, thus predicting maximal atmospheric neutrino mixing together with $U_{e3} = 0$. A partial and less predictive form of $\mu$--$\tau$ interchange symmetry is obtained when the symmetry $S_3$ is softly broken in the scalar potential. Enlarging the symmetry group $S_3 \times \mathbbm{Z}_2$ by an additional discrete electron-number symmetry $\mathbbm{Z}_2^{(e)}$, a more predicitive model is obtained, which is in practice indistinguishable from a previous one based on the group $D_4$.

Heavy neutrino mass hierarchy from leptogenesis in left–right symmetric models with spontaneous CP-violation

We consider left–right symmetric model with spontaneous CP-violation. The Lagrangian of this model is CP invariant and the Yukawa couplings are real. Due to spontaneous breaking of the gauge symmetry, some of the neutral Higgses acquire complex vacuum expectation values, which lead to CP-violation. In the model considered here, we identify the neutrino Dirac mass matrix with that of Fritzsch type charged lepton mass matrix. We assume a hierarchical spectrum of the right-handed neutrino masses and derive a bound on this hierarchy by assuming that the decay of the lightest right-handed neutrino produces the baryon asymmetry via the leptogenesis route. It is shown that the mass hierarchy we obtain is compatible with the current neutrino oscillation data.

Neutrino oscillations in a supersymmetric SO(10) model with type-III see-saw mechanism

The neutrino oscillations are studied in the framework of the minimal supersymmetric SO(10) model with Type-III see-saw mechanism by additionally introducing a number of SO(10) singlet neutrinos. The light Majorana neutrino mass matrix is given by a combination of those of the singlet neutrinos and the $SU(2)_L$ active neutrinos. The minimal SO(10) model gives an unambiguous Dirac neutrino mass matrix, which enables us to predict the masses and the other parameters for the singlet neutrinos. These predicted masses take the values accessible and testable by near future collider experiments under the reasonable assumptions. More comprehensive calculations on these parameters are also given.

Nontrivial correlation between the CKM and MNS matrices

We point out that the Cabibbo–Kobayashi–Maskawa (CKM) quark mixing matrix VCKM and the Maki–Nakagawa–Sakata (MNS) lepton mixing matrix VMNS can naturally be correlated in a class of seesaw models if the Dirac neutrino mass matrix and the up-type quark mass matrix are symmetric and identical, but the texture of their correlation matrix Fν is rather nontrivial. The bimaximal mixing pattern of Fν is disfavored by current data, and other special forms of Fν may suffer from fine-tuning of the free phase parameters in fitting the so-called quark–lepton complementarity relation. A straightforward calculation of Fν in terms of VCKM and VMNS reveals a striking feature of Fν: its (1,3) element cannot be zero or too small, no matter whether the (1,3) elements of VCKM and VMNS are vanishing or not. We also add some brief comments on possible radiative corrections to VCKM and VMNS.

Bounds on neutrino masses from leptogenesis in type-II seesaw models

The presence of the triplet ${\ensuremath{\Delta}}_{L}$ in left-right symmetric theories leads to type-II seesaw mechanism for the neutrino masses. In these models, assuming a normal mass hierarchy for the heavy Majorana neutrinos, we derive a lower bound on the mass of the lightest of heavy Majorana neutrinos from the leptogenesis constraint. From this bound we establish a consistent picture for the hierarchy of heavy Majorana neutrinos in a class of left-right symmetric models in which we identify the neutrino Dirac mass matrix with that of Fritzsch type charged lepton mass matrix. It is shown that these values are compatible with the current neutrino oscillation data.

BOUNDS FOR NEUTRINOLESS DOUBLE BETA DECAY IN SO(10) INSPIRED SEESAW MODELS

By requiring the lower limit for the lightest right-handed neutrino mass, obtained in the baryogenesis from leptogenesis scenario, and a Dirac neutrino mass matrix similar to the up-quark mass matrix, we predict small values for the νe mass and for the matrix element mee responsible of the neutrinoless double beta decay, mνe around 5×10-3 eV and mee smaller than 10-3 eV , respectively. The allowed range for the mass of the heaviest right-handed neutrino is centered around the value of the scale of B–L breaking in the SO (10) gauge theory with Pati–Salam intermediate symmetry.

Seesaw Realization of Bi-Large Mixing and Leptogenesis

The seesaw realization of the bi-large mixing is presented based on the texture zeros of the neutrino mass matrix. By using the obtained Dirac neutrino mass matrix, the leptogenesis is discussed. In the framework of the texture zeros, SO (10)-like model is investigated by focusing on the neutrino masses and mixings.

Leptogenesis in seesaw models with a two-fold-degenerate neutrino Dirac mass matrix

We study leptogenesis in two seesaw models where maximal atmospheric neutrino mixing and Ue3 = 0 result from symmetries. Salient features of those models are the existence of three Higgs doublets and a two-fold degeneracy of the neutrino Dirac mass matrix. We find that in those models both leptogenesis and neutrinoless double beta decay depend on the same unique Majorana phase. Leptogenesis can produce a baryon asymmetry of the universe of the right size provided the mass of the heavy neutrino whose decays generate the lepton asymmetry is in the range 1011–1012 GeV. Moreover, in these models, leptogenesis precludes an inverted neutrino mass spectrum since it requires the mass of the lightest neutrino to be in the range 10−3–10−2 eV.

Symmetric Mass Matrix with Two Zeros in SUSY SO(10) GUT, Lepton Flavor Violations and Leptogenesis

We study the symmetric 2-zero texture of the neutrino mass matrix, which is obtained from the symmetric Dirac neutrino mass matrix with 2-zeros and right-handed Majorana neutrino mass matrix with the general form via the see-saw mechanism, for the SUSY SO(10) GUT model including the Pati-Salam symmetry. We show that the only one texture in our model, having degenerate mass spectrum for the 1st and 2nd generation of right-handed Majorana neutrino, can simultaneously explain the current neutrino experimental data, lepton flavor violating processes and baryon asymmetry of the Universe. Within such a framework, the predicted values of the light and heavy Majorana neutrino masses, together with $|U_{e3}|$, $J_{{\rm CP}}$ and $|< M_{ee} >|$, are almost uniquely determined.

Seesaw enhancement of bi-large mixing in two-zero textures

The seesaw enhancement of the bi-large mixings are discussed for the two-zero textures of the neutrino mass matrix. There are no large mixings in both Dirac neutrino mass matrix mD and right-handed Majorana neutrino mass matrix MR, however, the bi-large mixing is realized via the seesaw mechanism. We present twelve sets of mD and MR for the seesaw enhancement and discuss the related phenomena, the μ→e+γ process and the leptogenesis. The decay rate of μ→e+γ is enough suppressed due to zeros in the Dirac neutrino mass matrix. Six mD lead to the lepton asymmetry, which can explain the baryon number in the universe. Other six mD are the real matrices, which give no CP asymmetry. Modified Dirac neutrino mass matrices are also discussed.

New type of seesaw mechanism for neutrino masses.

In a wide class of unified models there is an additional (and possibly dominant) term in the neutrino mass formula that under the simplest assumption takes the form M(nu)=(M(N)+M(T)(N))u/M(G), where M(N) is the neutrino Dirac mass matrix, and u=O(M(W)). This makes possible highly predictive models. A generalization of this form yields realistic neutrino masses and mixings more readily than the usual seesaw formula in some models. The conditions for resonant enhancement of leptogenesis can occur naturally in such models.

On the connection of leptogenesis with low energyCPviolation and lepton flavor violating charged lepton decays

Assuming only a hierarchical structure of the heavy Majorana neutrino masses and of the neutrino Dirac mass matrix m_D of the see-saw mechanism, we find that in order to produce the observed baryon asymmetry of the Universe via leptogenesis, the scale of m_D should be given by the up-quark masses. Lepton flavor violating decays \mu \to e + \gamma, \tau \to \mu + \gamma and \tau \to e + \gamma are considered and a characteristic relation between their decay rates is predicted. The effective Majorana mass in neutrinoless double beta decay depends on the CP violating phase controlling the leptogenesis if one of the heavy Majorana neutrinos is much heavier than the other two. Successful leptogenesis requires a rather mild mass hierarchy between the latter. The compatibility of this hierarchical see-saw model with the low energy neutrino mixing phenomenology requires that the mixing angle limited by the CHOOZ and Palo Verde experiments should be relatively large, \sin^2\theta_3 \gtap 0.01. The CP violation effects in neutrino oscillations can be observable. In general, there is no direct connection between the latter and the CP violation in leptogenesis. If the CP violating phases of the see-saw model satisfy certain relations, the baryon asymmetry of the Universe and the rephasing invariant J_{CP} which determines the magnitude of the CP violation effects in neutrino oscillations, depend on the same CP violating phase and their signs are correlated.

Minimal seesaw mechanism

In the framework of the seesaw mechanism, and adopting a typical form for the Dirac neutrino mass matrix, we discuss the impact of minimal forms of the Majorana neutrino mass matrix. These matrices contain four or three texture zeros and only two parameters, a scale factor and a hierarchy parameter. Some forms are not compatible with large lepton mixing and are ruled out. Moreover, a normal mass hierarchy for neutrinos is predicted.

Bounds for the Mass of the Heaviest Right-Handed Neutrino in SO(10) Theories

By relating the Dirac neutrino mass matrix to the mass of the charged fermions and assuming that the product of the masses of the two lightest left-handed neutrinos is of the order of [Formula: see text], we derive, within a leptogenesis scenario, a range of values for the mass of the heaviest right-handed neutrino, centered around the scale of B–L symmetry breaking in the SO(10) theory with Pati–Salam intermediate symmetry.

Inverting the seesaw formula

By inverting the seesaw formula we determine the heavy neutrino mass matrix. The impact on the baryogenesis via leptogenesis and the radiative lepton decays in supersymmetric models is described. Links to neutrinoless double beta decay are also briefly discussed. The analysis leads to two distinct matrix models. One has small mixings while the other has one maximal mixing. Both cannot give a sufficient amount of baryon asymmetry. Then we also comment on a different form of the Dirac neutrino mass matrix, which does provide sufficient baryon asymmetry. In a supersymmetric scenario the branching ratios of radiative lepton decays are enhanced for this model.

Leptogenesis in neutrino textures with two zeros

The leptogenesis is studied in the neutrino textures with two zeros, which reduce the number of independent phases of the CP violation. The phenomenological favored neutrino textures with two zeros are decomposed into the Dirac neutrino mass matrix and the right-handed Majorana one in the see-saw mechanism. Putting the condition to suppress the $\mu \to e\gamma$ decay enough, the texture zeros of the Dirac neutrino mass matrix are fixed in the framework of the MSSM with right-handed neutrinos. These textures have only one CP violatig phase. The magnitude of each entry of the Dirac mass matrix is determined in order to explain the baryon asymmetry of the universe by solving the Boltzman equations. The relation between the leptogenesis and the low energy CP violation is presented in these textures.