Seesaw Mass Matrix Research Articles

On Quark–Lepton Mixing and the Leptonic CP Violation

In the absence of a Grand Unified Theory framework, connecting the values of the mixing parameters in the quark-and-lepton sector is a difficult task, unless one introduces ad hoc relations among the matrices that diagonalize such different kinds of fermions. In this paper, we discuss in detail the possibility that the PMNS matrix is given by the product UPMNS=VCKM★T★, where T comes from the diagonalization of a see-saw like mass matrix that can be of a Bimaximal (BM), Tri-Bimaximal (TBM) and Golden Ratio (GR) form, and identify the leading corrections to such patterns that allow for a good fit to the leptonic mixing matrix as well as to the CP phase. We also show that the modified versions of BM, TBM and GR can easily accommodate the solar and atmospheric mass differences.

NANOGrav meets Hot New Early Dark Energy and the origin of neutrino mass

It has recently been speculated that the NANOGrav observations point towards a first-order phase transition in the dark sector at the GeV scale [1]. Here, we show that such a phase transition might already have been predicted in the Hot New Early Dark Energy model (Hot NEDE) [2,3]. There, it was argued that two dark sector phase transitions are the signature of neutrino mass generation through the inverse seesaw mechanism. In particular, an IR phase transition serves a double purpose by resolving the Hubble tension through an energy injection and generating the Majorana mass entry in the inverse seesaw mixing matrix. This usual NEDE phase transition is then accompanied by a UV counterpart, which generates the heavy Dirac mass entry in the inverse seesaw mass matrix of a right-handed neutrino. Here, we investigate if the UV phase transition of the Hot NEDE model can occur at the GeV scale in view of the recent NANOGrav observations.

$$\text {TM}_1$$ neutrino mixing with $$\sin \theta _{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}$$

We construct a neutrino model using the flavour group \(S_4\times C_4 \times C_3{ \times C_2}\) under the type 1 seesaw mechanism. The vacuum alignments of the flavons in the model lead to \(\text {TM}_1\) mixing with \(\sin \theta _{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}\). The mixing also exhibits \(\mu \text {-}\tau \) reflection symmetry. By fitting the eigenvalues of the effective seesaw mass matrix with the observed neutrino mass-squared differences, we predict the individual light neutrino masses. The vacuum alignment of the \(S_4\) triplet appearing in the Majorana mass term plays a key role in obtaining the aforementioned \(\text {TM}_1\) scenario. Since the symmetries of the flavour group are not sufficient to define this alignment, we apply the recently proposed framework of the auxiliary group in our model. Using this framework, the \(S_4\) triplet is obtained by coupling together several irreducible multiplets that transform under an expanded flavour group consisting of the original flavour group as well as an auxiliary group. The vacuum alignment of each of these multiplets is uniquely defined in terms of its residual symmetries under the expanded flavour group. As a result, the \(S_4\) triplet constructed from these multiplets also becomes uniquely defined.

Linear seesaw for Dirac neutrinos with A4 flavour symmetry

We propose a linear seesaw model to realise light Dirac neutrinos within the framework of A4 discrete flavour symmetry. The additional fields and their transformations under the flavour symmetries are chosen in such a way that naturally predicts the hierarchies of different elements of the seesaw mass matrix and also keeps the unwanted terms away. For generic choices of flavon alignments, the model predicts normal hierarchical light neutrino masses with the atmospheric mixing angle in the lower octant. Apart from predicting interesting correlations between different neutrino parameters as well as between neutrino and model parameters, the model also predicts the leptonic Dirac CP phase to lie in a specific range −π/2≲δ≲−π/5 and π/5≲δ≲π/2 that includes the currently preferred maximal value. The predictions for the absolute neutrino masses in one specific version of the model can also saturate the cosmological upper bound on sum of absolute neutrino masses.

Ameliorating the popular lepton mixings with A4 symmetry: A seesaw model for realistic neutrino masses and mixing

A model for neutrino masses and mixing is devised appointing the see-saw mechanism. The proffered model is fabricated with a combination of Type -I and Type-II see-saw contributions of which the latter dominates. The scalars and the leptons in the model are assigned $A4$ charges conducive to obtain the mass matrices viable for the scheme. The Type -II see-saw mass matrix accommodates atmospheric mass splitting and maximal mixing in the atmospheric sector ($\theta_{23}=\pi/4$). It is characterized by vanishing solar mass splitting and $\theta_{13}$ whereas the third neutrino mixing angle is free to acquire any value of $\theta_{12}^0$. Particular alternatives of $\theta_{12}^0$ corresponding to the popular lepton mixings viz. $\theta_{12}^0=35.3^\circ$ (tribimaximal), $45.0^\circ$ (bimaximal), $31.7^\circ$ (golden ratio) are accounted for. Another choice of $\theta_{12}^0=0^\circ$ (no solar mixing) is reckoned. The subdominant Type-I see-saw constituent of the model propels all the neutrino oscillation parameters into the ranges allowed by the data which in its turn get interrelated owing to their common origin. This makes the model testable in the light of future experimental data. As an example, $\theta_{23}$ emerges in the first (second) octant for normal (inverted) ordering. CP-violation is governed by phases present in the right-handed Majorana neutrino mass matrix, $M_{\nu R}$. Only normal ordering is allowed if these phases are absent. If $M_{\nu R}$ is complex the Dirac CP-violating phase $\delta$, is capable of being large, i.e., $\sim \pm \pi/2$, and inverted ordering of neutrino masses is also permitted. T2K and NOVA preliminary data favouring normal ordering and $\delta \sim -\pi/2$ predicts lightest neutrino mass to be 0.05 eV or more within the framework of this model.

Radiative neutrino masses from order-4 CP symmetry

Generalized CP symmetry of order 4 (CP4) is surprisingly powerful in shaping scalar and quark sectors of multi-Higgs models. Here, we extend this framework to the neutrino sector. We build two simple Majorana neutrino mass models with unbroken CP4, which are analogous to Ma’s scotogenic model. Both models use three Higgs doublets and two or three right-handed (RH) neutrinos. The minimal CP4 symmetric scotogenic model uses only two RH neutrinos, leads to three non-zero light neutrino masses, and contains a built-in mechanism to further suppress them via phase alignment. With three RH neutrinos, one generates a type I seesaw mass matrix of rank 1, which is then corrected by the same scotogenic mechanism, naturally leading to two neutrino mass scales with mild hierarchy. These minimal CP4-based constructions emerge as a primer for introducing additional symmetry structures and exploring their phenomenological consequences.

Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures

In the standard model extended with a seesaw mass matrix, we study the production of sterile neutrinos from the decay of vector bosons at $T\simeq M_{W,Z}$. We derive a general quantum kinetic equation for the production of sterile neutrinos and their effective mixing angles valid in a wide range of temperature, to all orders in interactions of the standard model, and to leading order mixing angle $\theta \ll 1$. Production rates and effective mixing angles depend sensitively on helicity. Positive helicity states interact more weakly with the medium and their effective mixing angle is not modified significantly whereas the mixing angle for negative helicity is strongly suppressed by the medium. If $M_s \lesssim 8.35\,\mathrm{MeV}$, there are fewer states with negative helicity produced than those with positive helicity. There is an MSW resonance in the absence of lepton asymmetry, but is screened by the damping rate, without production enhancement. Negative helicity states freeze-out at $T^-_f\simeq 5\,\mathrm{GeV}$ and positive helicity states freeze-out at $T^+_f \simeq 8\,\mathrm{GeV}$, both distributions are far from thermal. Negative helicity states feature a broader momentum distribution than that for those with positive helicity. Sterile neutrinos produced via vector boson decay do not satisfy the abundance, lifetime and cosmological constraints to be the sole dark matter component in the universe but might solve the $^{7}Li$ problem, albeit at the very edge of the possible parameter space. A heavy sterile neutrino with a mass of a few MeV could decay into light sterile neutrinos, of a few keV in mass, that contribute to warm dark matter. We argue that heavy sterile neutrinos with lifetime $\leq 1/H_0$ reach local thermodynamic equilibrium.

Discriminating Majorana neutrino phases in the light of lepton flavor violation and leptogenesis in type I+II seesaw models

We study the effects of Majorana neutrino phases in lepton flavor violation and the origin of matter–antimatter asymmetry through the mechanism of leptogenesis within the framework of a model where both type I and type II seesaw mechanisms can contribute to tiny neutrino masses. We parametrize the type I seesaw mass matrix by assuming it to give rise to a tri-bimaximal (TBM) type neutrino mixing which predicts [Formula: see text]. The type II seesaw mass matrix is then constructed in such a way that the necessary deviation from TBM mixing and the best fit values of neutrino parameters can be obtained when both type I and type II seesaw contributions are taken into account. Considering both subleading as well as equally dominating type II seesaw term, we first constrain the Majorana CP phases from the requirement of producing correct baryon asymmetry through leptogenesis and then incorporating the experimental bounds on lepton flavor violating decays [Formula: see text] and [Formula: see text].

Connecting leptonic CP violation, lightest neutrino mass and baryon asymmetry through type II seesaw

We study the possibility of connecting leptonic Dirac CP phase δ, lightest neutrino mass and baryon asymmetry of the universe within the framework of a model where both type I and type II seesaw mechanisms contribute to neutrino mass. Type I seesaw gives rise to Tri-Bimaximal (TBM) type neutrino mixing whereas type II seesaw acts as a correction in order to generate nonzero θ13. We derive the most general form of type II seesaw mass matrix which cannot only give rise to correct neutrino mixing angles but also can generate nontrivial value of δ. Considering both the cases where type II seesaw is subleading and is equally dominant compared to type I seesaw, we correlate the type II seesaw term with δ and lightest neutrino mass. We further constrain the Dirac CP phase δ and hence the type II seesaw mass matrix from the requirement of producing the observed baryon asymmetry through the mechanism of leptogenesis.

Perturbations to theμ−τsymmetry, leptogenesis, and lepton flavor violation with the type II seesaw mechanism

We study the possibility of generating non-zero reactor mixing angle $\theta_{13}$ by perturbing the $\mu-\tau$ symmetric neutrino mass matrix. The leading order $\mu-\tau$ symmetric neutrino mass matrix originates from type I seesaw mechanism whereas the perturbations to $\mu-\tau$ symmetry originate from type II seesaw term. We consider four different realizations of $\mu-\tau$ symmetry: Bimaximal Mixing(BM), Tri-bimaximal Mixing (TBM), Hexagonal Mixing (HM) and Golden Ratio Mixing (GRM) all giving rise to $\theta_{13} = 0, \theta_{23} = \frac{\pi}{4}$ but different non-zero values of solar mixing angle $\theta_{12}$. We assume a minimal $\mu-\tau$ symmetry breaking type II seesaw mass matrix as a perturbation and calculate the neutrino oscillation parameters as a function of type II seesaw strength. We then consider the origin of non-trivial leptonic CP phase in the charged lepton sector and calculate the lepton asymmetry arising from the lightest right handed neutrino decay by incorporating the presence of both type I and type II seesaw. We constrain the type II seesaw strength as well as leptonic CP phase (and hence the charged lepton sector) by comparing our results with experimental neutrino oscillation parameters as well as Planck bound on baryon to photon ratio. Finally, we extend our analysis on lepton flavour violating decays like $\mu \to e \gamma$ and $\mu \to eee$ due to exchange of TeV scale Higgs triplet scalar within the low scale type II seesaw framework. The branching ratios for these lepton flavour processes are examined with the small type II perturbation term $\omega$ and the estimated values are very close to the experimental bound coming from current search experiments.

Unsterile-Active Neutrino Mixing

We consider a sterile neutrino to be an unparticle, namely an "unsterile" neutrino, and study its mixing with a canonical active neutrino via a see-saw mass matrix. There is no unitary transformation that diagonalizes the mixed propagator and a field redefinition is required. The unsterile-like propagating mode features a resonance for anomalous dimension between 0 and 1/3, but the complex pole disappears when the anomalous dimension is larger than 1/3. The active-like propagating mode is described by a stable pole, but inherits a non-vanishing spectral density above the unparticle threshold. We also find that the radiative decay width of the unsterile neutrino into the active neutrino (and a photon) via charged current loops is suppressed, and this suppression weakens the bound from the X-ray or soft gamma-ray background when one considers the unsterile neutrino to be a dark matter candidate.

Double seesaw mechanism in a left-right symmetric model with TeV neutrinos

A left-right symmetric model is discussed with new mirror fermions and a Higgs sector with two doublets and neutral scalar singlets. The seesaw mechanism is generalized, including not only neutrino masses but also charged fermion masses. The spectrum of heavy neutrinos presents a second seesaw mass matrix and has neutrinos masses naturally in the TeV region. The model has very clear signatures for the new neutral vector gauge bosons. Two classes of models are discussed. New mirror neutrinos can be very light and a new ${Z}^{\ensuremath{'}}$ can be discriminated from other models by a very high invisible branching fraction. The other possibility is that mirror neutrinos can have masses naturally in the TeV region and can be produced through ${Z}^{\ensuremath{'}}$ decays into heavy neutrino pairs. Signatures and production processes for the model at the LHC energy are also presented.

Sterile neutrinos produced near the electroweak scale: Mixing angles, MSW resonances, and production rates

We study the production of sterile neutrinos in the region $T\ensuremath{\sim}{M}_{W}$ in an extension beyond the standard model with the seesaw mass matrix originating in Yukawa couplings to Higgs-like scalars with masses and vev's of the order of the electroweak scale. Sterile neutrinos are produced by the decay of scalars and standard model vector bosons. We obtain the index of refraction, dispersion relations, mixing angles in the medium and production rates including those for right-handed sterile neutrinos, from the standard model and beyond the standard model self-energies. For $1\ensuremath{\lesssim}{M}_{W}/T\ensuremath{\lesssim}3$ we find narrow MSW resonances with $k\ensuremath{\lesssim}T$ for both left- and right-handed neutrinos even in absence of a lepton asymmetry in the (active) neutrino sector, as well as very low energy ($k/T\ensuremath{\ll}|\ensuremath{\xi}|$) narrow MSW resonances in the presence of a lepton asymmetry consistent with the bounds from Wilkinson Microwave Anisotropy Probe and Big Bang Nucleosynthesis. For small vacuum mixing angle, consistent with observational bounds, the absorptive part of the self-energies lead to a strong damping regime very near the resonances resulting in the exact degeneracy of the propagating modes with a concomitant breakdown of adiabaticity. We argue that cosmological expansion sweeps through the resonances, resonant and nonresonant sterile neutrino production results in a highly nonthermal distribution function enhanced at small momentum $k<T$, with potentially important consequences for their free-streaming length and transfer function at small scales.

Unsterile-active neutrino mixing: Consequences on radiative decay and bounds from the x-ray background

We consider a sterile neutrino to be an unparticle, namely, an unsterile neutrino, with anomalous dimension $\ensuremath{\eta}$ and study its mixing with a canonical active neutrino via a seesaw mass matrix. We show that there is no unitary transformation that diagonalizes the mixed propagator and a field redefinition is required. The propagating or ``mass'' states correspond to an unsterilelike and activelike mode. The unsterile mode features a complex pole or resonance for $0\ensuremath{\le}\ensuremath{\eta}l1/3$ with an ``invisible width'' which is the result of the decay of the unsterile mode into the active mode and the massless particles of the hidden conformal sector. For $\ensuremath{\eta}\ensuremath{\ge}1/3$, the complex pole disappears, merging with the unparticle threshold. The active mode is described by a stable pole, but ``inherits'' a nonvanishing spectral density above the unparticle threshold as a consequence of the mixing. We find that the radiative decay width of the unsterile neutrino into the active neutrino (and a photon) via charged current loops, is suppressed by a factor $\ensuremath{\sim}[2{sin}^{2}({\ensuremath{\theta}}_{0})\frac{{M}^{2}}{{\ensuremath{\Lambda}}^{2}}{]}^{\ensuremath{\eta}/(1\ensuremath{-}\ensuremath{\eta})}$, where ${\ensuremath{\theta}}_{0}$ is the mixing angle for $\ensuremath{\eta}=0$, $M$ is approximately the mass of the unsterile neutrino, and $\ensuremath{\Lambda}\ensuremath{\gg}M$ is the unparticle scale. The suppression of the radiative (visible) decay width of the sterile neutrino weakens the bound on the mass and mixing angle from the x-ray or soft gamma-ray background.

Neutrino mixing based on mass matrices with a2↔3symmetry

Under an assumption that the 2{r_reversible}3 symmetry is broken only through phases, we give a systematic investigation of possible lepton mass matrix forms without referring to explicit parameter values. Two types of the 2{r_reversible}3 symmetry are investigated: one is that the left- and right-handed fields (f{sub L},f{sub R}) obey the symmetry, and another one is that only f{sub L} obeys the symmetry. In the latter case, in spite of no 2{r_reversible}3 symmetry in the Majorana mass matrix M{sub R} for {nu}{sub R}, the neutrino seesaw mass matrix still obeys the 2{r_reversible}3 symmetry. Possible phenomenology is discussed.

S3 symmetry and neutrino masses and mixings

Based on the universal seesaw mass matrix model with the three scalars φi, and by assuming S3 flavor symmetry for the Yukawa interactions, the lepton masses and mixings are investigated systematically. In order to understand the observed neutrino mixing, the charged leptons (e,μ,τ) are regarded as the three objects (e1,e2,e3) of S3, while the neutrino mass eigenstates are regarded as the irreducible representation (νη,νσ,νπ) of S3, where (νπ,νη) and νσ are a doublet and a singlet, respectively, which are composed of the three objects (ν1,ν2,ν3) of S3.

Seesaw mass matrix model of quarks and leptons with flavor-triplet Higgs scalars

In a seesaw mass matrix model $M_f = m_L M_F^{-1} m_R^\dagger$ with a universal structure of $m_L \propto{m}_R$ , as the origin of mL (mR) for quarks and leptons, flavor-triplet Higgs scalars whose vacuum expectation values vi are proportional to the square roots of the charged lepton masses mei, i.e. $v_i\propto\sqrt{m_{ei}}$ , are assumed. Then, it is investigated whether such a model can explain the observed neutrino masses and mixings (and also quark masses and mixings) or not.

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.

SO(10)×SO(10)universal seesaw model and its intermediate mass scales

On the basis of the universal seesaw mass matrix model, which is a promising model for a unified description of the quark and lepton mass matrices, the behavior of the gauge coupling constants and intermediate energy scales in the $\mathrm{SO}{(10)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SO}{(10)}_{R}$ model is investigated related to the neutrino mass generation scenarios. The non-SUSY model cannot give favorable values of the intermediate energy scales to explain the smallness of the neutrino masses, while the SUSY model can give plausible values if the number ${n}_{\ensuremath{\varphi}}$ of the weak doublet Higgs scalars is ${n}_{\ensuremath{\varphi}}>~3$.

Universal seesaw mass-matrix model and SO(10) $\times$ SO(10) unification

On the universal seesaw mass matrix model, which is a promising model of the unified description of the quark and lepton mass matrices, the behaviors of the gauge coupling constants and intermediate energy scales in the SO(10)_L\times SO(10)_R model are investigated related to the neutrino mass generation scenarios. The unification of the gauge coupling constants in the framework of the non-SUSY model is possible if the SO(10) symmetry is broken via Pati-Salam type symmetries.