Right-handed Neutrino Mass Matrix Research Articles

A simplest seesaw model of the TM1 and μ-τ reflection symmetries for the neutrino masses and leptogenesis

In this paper, following the Occam’s razor principle, we have put forward a very simple form of the Dirac neutrino mass matrix in the minimal seesaw model with the right-handed neutrino mass matrix being diagonal ; it has one texture zero and only contains three real parameters, whose values can be determined from the neutrino oscillation experimental results. Such a model leads to a neutrino mass matrix that obeys the TM1 and μ-τ reflection symmetries simultaneously. In this way all the lepton flavor mixing parameters except for are predicted; the value of is predicted by the TM1 symmetry, while those of , δ, ρ and σ by the μ-τ reflection symmetry. And the neutrino masses are predicted to be of the NO case with , for which all three light neutrino masses will be pinned down with the help of the experimental results for the neutrino mass squared differences. For these results, the effective Majorana neutrino mass that controls the rate of the neutrinoless double beta decay is predicted to be 1.6 or 3.8 meV in the case of σ = 0 or π/2. We have also studied the implications of the model for leptogenesis. It turns out that only in the two-flavor leptogenesis regime (which holds in the temperature range 109–1012 GeV) can leptogenesis have a chance to be successful. And a successful leptogenesis can be achieved at GeV in the case of σ = π/2, but not in the case of σ = 0.

Gauged U(1)Lμ−Lτ symmetry and two-zero textures of inverse neutrino mass matrix in light of muon (g − 2)

In the framework of anomaly free [Formula: see text] model, singlet scalar field with nonzero [Formula: see text] charge gives rise to massive gauge boson [Formula: see text] through spontaneous symmetry breaking. [Formula: see text] leads to one loop contribution to the muon anomalous magnetic moment. These scalar fields may, also, appear in the structure of right-handed neutrino mass matrix, thus, connecting the possible explanation of muon [Formula: see text] and low-energy neutrino phenomenology through vevs associated with the scalar fields. In this work, we consider textures of inverse neutrino mass matrix [Formula: see text] wherein any two elements of the mass matrix are zero. In this ansatz, with Dirac neutrino mass matrix diagonal, the zero(s) of right-handed Majorana neutrino mass matrix correspond to zero(s) in the low-energy effective neutrino mass matrix (within Type-I seesaw). We have realized two such textures of [Formula: see text] accommodating the muon [Formula: see text] and low-energy neutrino phenomenology. The requirement of successful explanation of muon [Formula: see text], further, constrains the allowed parameter space of the model and results in sharp correlations amongst neutrino mixing angles and CP invariants. The model explains muon [Formula: see text] for [Formula: see text] in the range (0.035–0.100 GeV) and [Formula: see text] which is found to be consistent with constraints coming from the current experiments CCFR, COHERENT, BABAR while being within sensitivities of future experiments such as NA62 and NA64.

Conditions of general Z2 symmetry and TM1,2 mixing for the minimal type-I seesaw mechanism in an arbitrary basis

In this paper, using a formula for the minimal type-I seesaw mechanism by LDLT (or generalized Cholesky) decomposition, conditions of general Z2-invariance for the neutrino mass matrix m are obtained in an arbitrary basis. The conditions are found to be (M22ai+−M12bi+)(M22aj−−M12bj−)=−det⁡Mbi+bj− for the Z2-symmetric and -antisymmetric part of a Yukawa matrix Yij±≡(Y±TY)ij/2≡(aj±,bj±) and the right-handed neutrino mass matrix Mij. In other words, the symmetric and antisymmetric part of bi must be proportional to those of the quantity a˜i≡ai−M12M22bi. They are equivalent to the condition that m is block diagonalized by eigenvectors of the generator T.These results are applied to three Z2 symmetries, the μ−τ symmetry, the TM1 mixing, and the magic symmetry which predicts the TM2 mixing. For the case of TM1,2, the symmetry conditions become M222a˜1TBMa˜2TBM=−det⁡Mb1TBMb2TBM and M222a˜1,2TBMa˜3TBM=−det⁡Mb1,2TBMb3TBM with components a˜iTBM and biTBM in the TBM basis v1,2,3. In particular, for the TM2 mixing, the magic (anti-)symmetric Yukawa matrix with S2Y=±Y is phenomenologically excluded because it predicts m2=0 or m1,m3=0. In the case where Yukawa is not (anti-)symmetric, the mass singular values are displayed without a root sign.

Two-loop renormalization group equations for right-handed neutrino masses and phenomenological implications

We calculate the two-loop beta functions of the right-handed neutrino mass matrix in the Standard Model extended with right-handed neutrinos. We show that two-loop quantum effects induced by the heavier right-handed neutrinos can induce sizable contributions (sometimes dominant) to the physical masses of the lighter right-handed neutrinos. These effects can significantly affect the masses of the active neutrinos in the seesaw mechanism and the low energy phenomenology.

Phenomenological study of texture zeros of neutrino mass matrix in minimal left-right symmetric model

We studied the phenomenological implications of texture zeros in the neutrino mass matrix of the minimal left-right symmetric model (LRSM). Since the possibility of maximum zeros reduces the maximum number of free parameters of the model making it more predictive, we considered only those cases with maximum possible texture zeros in light neutrino mass matrix Mv , Dirac neutrino mass matrix MD and heavy right-handed (RH) neutrino mass matrix MRR . We then computed the correlations among the different light neutrino parameters and then the new physics contributions to neutrinoless double beta decay(NDBD) for the different texture zero cases. We find that for RH neutrino masses above 1 GeV, the new physics contributions to NDBD can saturate the corresponding experimental bound.

A modular A4 symmetry realization of two-zero textures of the Majorana neutrino mass matrix

We show how to realize two-zero textures of the Majorana neutrino mass matrix Mν based on modular A4 invariant models without flavons. In these models, all matter fields are assigned to three inequivalent singlets, 1, 1′ and 1″, of the finite modular group Γ3≃A4. Considering tensor products of the A4 group, it is easy to make the charged lepton mass matrix Mℓ diagonal. Since not all modular forms of a specific weight and level 3 can be arranged into three inequivalent singlets of A4 simultaneously, we can always make some entries in Mν vanish by properly assigning the representations and modular weights for the matter fields. We consider two cases where neutrino masses originate from the Weinberg operator and the type-I seesaw mechanism, respectively. For the former case, all seven viable two-zero textures of Mν (A1,2, B1,2,3,4 and C) can be realized successfully. For the latter case, only five of them (namely A1,2, B3,4 and C) can be achieved due to the intrinsic structure of the right-handed neutrino mass matrix MR in our assumption for simplicity.

All fermion masses and mixings in an intersecting D-brane world

It is shown that neutrino mixing angles which are consistent with current experimental observations may be naturally obtained in a Pati-Salam model constructed from intersecting D6 branes on a T6/(Z2×Z2) orientifold. The Dirac mass matrices in the model are naturally the same as those which are obtained by imposing a Δ(27) flavor symmetry, which allows for near-tribimaximal mixing in the neutrino sector. In addition, it is possible to obtain the correct mass matrices for quarks and charged leptons, as well as nearly the correct CKM matrix. An RGE analysis of the neutrino mass parameters, including the seesaw mechanism assuming a specific form for the right-handed neutrino mass matrix is performed, and it is found that the neutrino mixing angles at the electroweak scale are θ12=35.0°, θ23=47.1°, and θ13=8.27°. In addition, the neutrino mass-squared differences are found to be Δm322=0.00252 eV2 and Δm212=0.0000739 eV2 with m1=0.0146 eV, m2=0.0170 eV, m3=0.0530 eV, and Σmi=0.0846 eV. These results depend slightly upon the scale at which the RGE running goes from being that of the MSSM to that of the SM, which we interpret to be the lightest stop mass. The best agreement with experimental data is for m˜t1≈4.28 TeV. This suggests that the superpartners which produce the strongest signal in a hadron collider are just out of reach at the LHC.

Seesaw mirroring between light and heavy Majorana neutrinos with the help of the S3 reflection symmetry

In the canonical seesaw mechanism we require the relevant neutrino mass terms to be invariant under the S3 charge-conjugation transformations of left- and right-handed neutrino fields. Then both the Dirac mass matrix MD and the right-handed neutrino mass matrix MR are well constrained, so is the effective light Majorana neutrino mass matrix Mν via the seesaw formula. We find that these mass matrices can be classified into 22 categories, among which some textures respect the well-known μ-τ permutation or reflection symmetry and flavor democracy. It is also found that there exist remarkable structural equalities or similarities between Mν and MR, reflecting a seesaw mirroring relationship between light and heavy Majorana neutrinos. We calculate the corresponding light neutrino masses and flavor mixing parameters as well as the CP-violating asymmetries in decays of the lightest heavy Majorana neutrino, and show that only the flavored leptogenesis mechanism is possible to work for three categories of MD and MR in the S3 reflection symmetry limit.

Mu-tau reflection symmetry with a high scale texture-zero

The μτ -reflection symmetric neutrino mass matrix can accommodate all known neutrino mixing angles, with maximal atmospheric angle fixed, and predicts all the unknown CP phases of the lepton sector but is unable to predict the absolute neutrino mass scale. Here we present a highly predictive scenario where μτ -reflection is combined with a discrete abelian symmetry to enforce a texture-zero in the mass matrix of the heavy right-handed neutrinos that generate the light neutrino masses. Such a restriction reduces the free parameters of the low energy theory to zero and the absolute neutrino mass scale is restricted to few discrete regions, three in the few meV range and one extending up to around 30 meV. The heavy neutrino sector is dependent only on two free parameters which are further restricted to small regions from the requirement of successful leptogenesis. Mass degenerate heavy neutrinos are possible in one case but there is no resonant enhancement of the CP asymmetry.

Same sign versus opposite sign dileptons as a probe of low scale seesaw mechanisms

We calculate the ratio $R_{\ell\ell}$ of same sign (SS) to opposite sign (OS) dileptons in type I and generalized inverse seesaw models and show that it can be anywhere between 0 and 1 depending on the detailed texture of the right-handed neutrino mass matrix. Measurement of $R_{\ell\ell}$ in hadron colliders can therefore provide a way to probe the nature of seesaw mechanism and also to distinguish between the two types of seesaw mechanisms. We work within the framework of left-right symmetric model as an example. We emphasize that coherence of the final states in the $W_R$ decay is crucial for this discussion and it requires the right-handed neutrinos to be highly degenerate. We isolate the range of parameters in the model where this effect is observable at the LHC and future colliders.

Structure of right-handed neutrino mass matrix

Recently, Nishiura and the author have proposed a unified quark-lepton mass matrix model under a family symmetry U(3)$\times$U(3)$'$. The model can give excellent parameter-fitting to the observed quark and neutrino data. The model has a reasonable basis as far as the quark sector, but the form of the right-handed neutrino mass matrix $M_R$ does not have a theoretical grand, that is, it was nothing but a phenomenological assumption. In this paper, it is pointed out that the form of $M_R$ is originated in structure of neutrino mass matrix for $(\nu_i, N_\alpha)$ where $\nu_i$ ($i=1,2,3$) and $N_\alpha$ ($\alpha=1,2,3$) are U(3)-family and U(3)$'$-family triplets, respectively.

Analysis of the right-handed Majorana neutrino mass in an SU(4)×SU(2)L×SU(2)R Pati-Salam model with democratic texture

In this paper, we attempt to build an unified model with democratic texture, that have some unification between $Y_{\nu}$ and $Y_{u}$. Since the $S_{3L} \times S_{3R}$ flavor symmetry is chiral, the unified gauge group is assumed to be Pati-Salam type $SU(4)_{c} \times SU(2)_{L} \times SU(2)_{R}$. The flavor symmetry breaking scheme is considered to be $S_{3L} \times S_{3R} \to S_{2L} \times S_{2R} \to 0$. In this picture, the four-zero texture is desirable for realistic mass and mixings. This texture is realized by a specific representation for the second breaking of the $S_{3L} \times S_{3R}$ flavor symmetry. Assuming only renormalizable Yukawa interactions, type-I seesaw mechanism, and neglecting $CP$ phases for simplicity, the right-handed neutrino mass matrix $M_{R}$ can be reconstructed from low energy input values. Numerical analysis shows that the texture of $M_{R}$ basically behaves like the "waterfall texture". Since $M_{R}$ tends to be the "cascade texture" in the democratic texture approach, a model with type-I seesaw and up-type Yukawa unification $Y_{\nu} \simeq Y_{u}$ basically requires fine-tunings between parameters. Therefore, it seems to be more realistic to consider universal waterfall textures for both $Y_{f}$ and $M_{R}$, e.g., by the radiative mass generation or the Froggatt--Nielsen mechanism. Moreover, analysis of eigenvalues shows that the lightest mass eigenvalue $M_{R1}$ is too light to achieve successful thermal leptogenesis. Although the resonant leptogenesis might be possible, it also requires fine-tunings of parameters.

A4-based seesaw model for realistic neutrino masses and mixing

We present an $A4$-based model where neutrino masses arise from a combination of see-saw mechanisms. The model is motivated by several small mixing and mass parameters indicated by the data. These are $\theta_{13}$, the solar mass splitting, and the small deviation of $\theta_{23}$ from maximal mixing (= $\pi/4$). We take the above as indications that at some level the small quantities are well-approximated by zero. In particular the mixing angles, to a zero order, should be either 0 or $\pi/4$. Accordingly, in this model the Type-II see-saw dominates and generates the larger atmospheric mass splitting and sets $\theta_{23} = \pi/4$. The other mixing angles are vanishing as is the solar splitting. We show how the $A4$ assignment for the lepton doublets leads to this form. We also specify the $A4$ properties of the right-handed neutrinos which result in a smaller Type-I see-saw contribution that acts as a perturbation and shifts the angles $\theta_{12}$ and $\theta_{13}$ into the correct range and the desired value of $\Delta m^2_{solar}$ is produced. The $A4$ symmetry results in relationships between these quantities as well as with a small deviation of $\theta_{23}$ from $\pi/4$. If the right-handed neutrino mass matrix, $M_R$, is chosen real then there is no leptonic CP-violation and only Normal Ordering is admissible. If $M_R$ is complex then Inverted Ordering is also allowed with the proviso that the CP-phase, $\delta$, is large, i.e., $\sim \pi/2$ or $-\pi/2$. The preliminary results from NO$\nu$A favouring Normal Ordering and $\delta$ near $-\pi/2$ imply quasi-degenerate neutrino masses in this model.

Exotic see-saw mechanism for neutrinos and leptogenesis in a Pati-Salam model

We discuss non-perturbative corrections to the neutrino sector, in the context of a D-brane Pati-Salam-like model, that can be obtained as a simple alternative to $SO(10)$ GUT's in theories with open and unoriented strings. In such D-brane models, exotic stringy instantons can correct the right-handed neutrino mass matrix in a calculable way, thus affecting mass hierarchies and modifying the see-saw mechanism to what we name exotic see-saw. For a wide range of parameters, a compact spectrum of right-handed neutrino masses can occur that gives rise to a predictive scenario for low energy observables. This model also provides a viable mechanism for Baryon Asymmetry in the Universe (BAU) through leptogenesis. Finally, a Majorana mass for the neutron is naturally predicted in the model, leading to potentially testable neutron-antineutron oscillations. Combined measurements in neutrino and neutron-antineutron sectors could provide precious informations on physics at the quantum gravity scale.

Leptonic CP violation phases, quark–lepton similarity and seesaw mechanism

We explore generic features of the leptonic CP violation in the framework of the seesaw type I mechanism with similarity of the Dirac lepton and quarks mass matrices mD. For this, we elaborate on the standard parametrization conditions which allow to simultaneously obtain the Dirac and Majorana phases. If the only origin of CP violation is the left-handed (LH) transformation which diagonalizes mD (similar to quarks), the leptonic CP violation is suppressed and the Dirac phase is close to π or to 0 with sinδCP≈(sinθ13q/sinθ13)cosθ23sinδq∼λ2sinδq. Here λ∼θC, is the Cabibbo mixing angle, and θ13q and θ13 are the 1–3 mixing angles of quarks and leptons respectively. The Majorana phases β1 and β2 are suppressed as λ3sinδq. For Majorana neutrinos implied by seesaw, the right-handed (RH) transformations are important. We explore the simplest extension inspired by Left–Right (L–R) symmetry with small CKM-type CP violation. In this case, seesaw enhancement of the CP violation occurs due to strong hierarchy of the eigenvalues of mD leading to δCP∼1. The enhancement is absent under the phase factorization conditions which require certain relations between parameters of the Majorana mass matrix of RH neutrinos.

Gauged Flavor Symmetries

Augmenting the Standard Model by three right-handed neutrinos allows for an anomaly-free gauge group extension Gmax=U(1)B−L×U(1)Le−Lμ×U(1)Lμ−Lτ. Simple U(1) subgroups of Gmax can be used to impose structure on the righthanded neutrino mass matrix, which then propagates to the active neutrino mass matrix via the seesaw mechanism. We show how this framework can be used to gauge the approximate lepton-number symmetries behind the normal, inverted, and quasidegenerate neutrino mass spectrum, and also how to generate texture-zeros and vanishing minors in the neutrino mass matrix, leading to testable relations among mixing parameters.

TeV scale horizontal gauge symmetry and its implications inBphysics

We propose a gauged $U(1)_{H}$ horizontal symmetry around TeV scale that is a subgroup of a $SU(3)_{H}$ horizontal gauge symmetry broken at ${\cal O}(10^{14}) \GeV$. The breaking generates right-handed Majorana neutrino masses through a $SU(3)_H$ sextet scalar. A particular Majorana right-handed neutrino mass matrix explicitly determines the remnant $U(1)_{H}$ at low energy which only couples to $b-s$ and $\mu-\tau$ in the gauge eigenstate. The dangerous $K-\bar{K}$, $D-\bar{D}$ mixing and $B_s \rightarrow \mu^+ \mu^-$ are kept to be safe because the relevant couplings are suppressed through high powers of small mixing angles in the fermion rotation matrix. Our analysis which applies to the general case shows that the Tevatron di-muon anomaly can be explained through the $B_{s}$ and $B_{d}$ mixing while keeping all the other experimental constraints within 90 \% C. L. For the $B$ meson decay, the $B_{s}\to \mu^{\pm}\tau^{\mp}$ is the leading leptonic decay channel which is several orders of magnitude below current experimental bound.

Direct link between neutrinoless double beta decay and leptogenesis in a seesaw model withS4symmetry

We study how leptogenesis can be implemented in a seesaw model with $S_4$ flavor symmetry, which leads to the neutrino tri-bimaximal mixing matrix and degenerate right-handed (RH) neutrino spectrum. Introducing a tiny soft $S_4$ symmetry breaking term in the RH neutrino mass matrix, we show that the flavored resonant leptogenesis can be successfully realized, which can lower the seesaw scale much so as to make it possible to probe in colliders. Even though such a tiny soft breaking term is essential for leptogenesis, it does not significantly affect the low energy observables. We also investigate how the effective light neutrino mass $|<m_{ee}> |$ associated with neutrinoless double beta decay can be predicted along with the neutrino mass hierarchies by imposing experimental data of low-energy observables. We find a direct link between leptogenesis and neutrinoless double beta decay characterized by $|<m_{ee}>|$ through a high energy CP phase $\phi$, which is correlated with low energy Majorana CP phases. It is shown that our predictions of $|<m_{ee}>|$ for some fixed parameters of high energy physics can be constrained by the current observation of baryon asymmetry.

Type I seesaw mechanism for quasi-degenerate neutrinos

We discuss symmetries and scenarios leading to quasi-degenerate neutrinos in type I seesaw models. The existence of degeneracy in the present approach is not linked to any specific structure for the Dirac neutrino Yukawa coupling matrix yD and holds in general. Basic input is the application of the minimal flavour violation principle to the leptonic sector. Generalizing this principle, we assume that the structure of the right-handed neutrino mass matrix is determined by yD and the charged lepton Yukawa coupling matrix yl in an effective theory invariant under specific groups GF contained in the full symmetry group of the kinetic energy terms. GF invariance also leads to specific structure for the departure from degeneracy. The neutrino mass matrix (with degenerate mass m0) resulting after seesaw mechanism has a simple form Mν≈m0(I−pylylT) in one particular scenario based on supersymmetry. This form is shown to lead to correct description of neutrino masses and mixing angles. The thermal leptogenesis after inclusion of flavour effects can account for the observed baryon asymmetry of the universe within the present scenario. Rates for lepton flavour violating processes can occur at observable levels in the supersymmetric version of the scenario.

CORRECTIONS TO TRIBIMAXIMAL MIXING FROM NONDEGENERATE PHASES

We propose a seesaw scenario that possible corrections to the tribimaximal pattern of lepton mixing are due to the small phase splitting of the right-handed neutrino mass matrix. We show that the small deviations can be expressed analytically in terms of two splitting parameters (δ1 and δ2) in the leading order. The solar mixing angle θ12 favors a relatively smaller value compared to zero order value (35.3°), and the Dirac type CP phase δ chooses a nearly maximal one. The two Majorana type CP phases ρ and σ turn out to be a nearly linear dependence. Also a normal hierarchy neutrino mass spectrum is favored due to the stability of perturbation calculations.