We study the effect of sterile neutrino on some low scale processes in the framework of minimal extended seesaw (MES). MES is the extension of the seesaw mechanism with the addition of sterile neutrino of intermediate mass. The MES model in this work is based on $Δ(96)\times C_{2}\times C_{3}$ flavor symmetry. The structures of mass matrices in the framework lead to $TM_{1}$ mixing with $μ\text{-}τ$ symmetry. The model predicts maximal value of Dirac CP phase. We carry out our analysis to study the new physics contributions from the sterile neutrino to different charged lepton flavor violation (cLFV) processes involving muon and tau leptons as well as neutrinoless double beta decay (0$νββ$). The model predicts normal ordering (NO) of neutrino masses and we perform the numerical analysis considering normal ordering (NO) only. We find that sterile neutrino mass in GeV range can lead to cLFV processes that are within the reach of current and planned experiments. The GeV scale sterile neurtrino in our model is consistent with the current limits on the effective neutrino mass set by $0νββ$ experiments.
Renewed interest in GeV-scale sterile neutrinos capable of explaining active neutrino oscillations via see-saw type I mechanism has been expressed in several proposals of direct searches. Given this activity we estimate the minimal values of sterile-active mixing angles provided one, two, or three sterile neutrinos are lighter than D-meson.
In the framework of type II seesaw mechanism we discuss the number of sterile right-handed Majorana neutrinos being the warm dark matter (WDM). When the type II seesaw mass term $M_ν^{II}$ is far less than the type I seesaw mass term $M_ν^{I}$, only one of three sterile neutrinos may be the WDM particle. On the contrary, the WDM particles may contain all sterile neutrinos. If $M_ν^{II} \sim M_ν^{I}$, the allowed number is not more than $N - 1$ for $N$ sterile neutrinos. It is worthwhile to stress that three different types of neutrino mass spectrum are permitted when $M_ν^{II} \gg M_ν^{I}$ and…
Motivated by the recent observations on sterile neutrinos, we present a minimal extension of the canonical type-I seesaw by adding one extra singlet fermion. After the decoupling of right-handed neutrinos, an eV-scale mass eigenstate is obtained without the need of artificially inserting tiny mass scales or Yukawa couplings for sterile neutrinos. In particular, the active-sterile mixing is predicted to be of the order of 0.1. Moreover, we show a concrete flavor A_4 model, in which the required structures of the minimal extended seesaw are realized. We also comment on the feasibility of accommo…
The appearance of a $3.5$ keV photon line in the X-ray spectra of Andromeda galaxy and other galaxy clusters including the Perseus galaxy can be interpreted as the signal of a $7$ keV sterile neutrino dark matter candidate as one of the plausible explanations. We present here a novel framework of extended seesaw mechanism where the lightest sterile neutrino acts as a Dark Matter candidate and its decay into a photon and an ordinary neutrino accounts for the excess 3.5 keV X-ray line. For implementing the idea, we add two different types of neutral fermion singlets ($S_L$, $N_R$) to the SM ligh…
The inverse and linear seesaw scenarios are two typical extensions of the canonical seesaw mechanism, which contain much more sterile degrees of freedom but can naturally explain the smallness of three active neutrino masses at a sufficiently low energy scale (e.g., the TeV scale). To fully describe the mixing among three active neutrinos, three sterile neutrinos and three extra gauge-singlet neutral fermions in either of these two seesaw paradigms, we present the {\it first} full parametrization of the $9\times 9$ flavor mixing matrix in terms of 36 rotation angles and 36 CP-violating phases.…
The cosmological evolution of neutrino energy densities driven by cosmon-type field equations is introduced assuming that active and sterile neutrinos are intrinsically connected by cosmon fields through the {\em seesaw} mechanism. Interpreting sterile neutrinos as dark matter adiabatically coupled with dark energy results in a natural decoupling of (active) mass varying neutrino (MaVaN) equations. Identifying the dimensionless scale of the {\em seesaw} mechanism, $m/M$, with a power of the cosmological scale factor, $a$, allows for embedding the resulting masses into the generalized Chaplygin…
Assuming the existence of an eV or KeV scale sterile neutrino, we develop a 3+1 neutrino mass model using $A_4\times Z_4 \times Z_2$ symmetry group. Three Higgs $H, H^{\prime}$ and $H^{\prime\prime}$ are considered to give a desired neutrino mass matrix which generates non-zero $θ_{13}$. The model can give neutrino mixing parameters that are well within the experimental 3$σ$ bounds. We also calculate the $4\times 4$ active-sterile neutrino mixing matrix, and it is found to be consistent with experimental bounds.
We explore the possibility of a single generation of $keV$ scale sterile neutrino ($m_S$) as a dark matter candidate within the minimal extended seesaw (MES) framework and it's influence in neutrinoless double beta decay ($0νββ$) study. Three hierarchical right-handed neutrinos were considered to explain neutrino mass. We also address baryogenesis via the mechanism of thermal leptogenesis considering the decay of the lightest RH neutrino to a lepton and Higgs doublet. A generic model based on $A_4\times Z_4\times Z_3$ flavor symmetry is constructed to explain both normal and inverted hierarchy…
We show that a double seesaw framework for neutrino masses with $μ-τ$ exchange symmetry can lead to one of the righthanded seesaw partners of the light neutrinos being massless. This can play the role of a light sterile neutrino, giving a $3+1$ model that explains the LSND results. We get a very economical scheme, which makes it possible to predict the full $4\times 4$ neutrino mass matrix if CP is conserved. Once CP violation is included, effect of the LSND mass range sterile neutrino is to eliminate the lower bound on neutrinoless double beta decay rate which exists for the three neutrino ca…
Active-sterile neutrino mixing in the ISS(p,q) inverse seesaw models
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University（斯寇别尔钦核物理研究所，莫斯科国立罗蒙诺索夫大学）；Physics Department, Lomonosov Moscow State University（物理系，莫斯科国立罗蒙诺索夫大学）
We study a model of neutrino within the framework of the minimal extended seesaw (MES), which plays an important role in active and sterile neutrino phenomenology in (3+1) scheme. The $A_4$ flavor symmetry is augmented by an additional $Z_4\times Z_3$ symmetry to constraint the Yukawa Lagrangian of the model. We use non-trivial Dirac mass matrix, with broken $μ-τ$ symmetry, as the origin of leptonic mixing. Interestingly, such a structure of mixing naturally leads to the non-zero reactor mixing angle $θ_{13}$. Non-degenerate mass structure for right-handed neutrino $M_R$ is considered so that …
We consider an extension of the Standard Model (SM) augmented by two neutral singlet fermions per generation and a leptoquark. In order to generate the light neutrino masses and mixing, we incorporate inverse seesaw mechanism. The right handed neutrino production in this model is significantly larger than the conventional inverse seesaw scenario. We analyze the different collider signatures of this model and find that the final states associated with three or more leptons, multi jet and at least one b-tagged and (or) $τ$-tagged jet can probe larger RH neutrino mass scale. We have also proposed…
We consider seesaw type-I models including at least one (mostly-)sterile neutrino with mass at the eV scale. Three distinct situations are found, where the presence of light extra neutrinos is naturally justified by an approximately conserved lepton number symmetry. To analyse these scenarios consistently, it is crucial to employ an exact parametrisation of the full mixing matrix. We provide additional exact results, including generalised versions of the seesaw relation and of the Casas-Ibarra parametrisation, valid for every scale of seesaw. We find that the existence of a light sterile neutr…
We propose a simple model of the neutrino mass matrix which can explain the solar and atmospheric neutrino problems in a 3($ν_L + ν_R$) framework. Assuming that only two right-handed neutrinos are heavy and a Dirac mass matrix has a special texture, we construct a model with four light neutrinos. The favorable structure of flavor mixings and mass eigenvalues required by those neutrino deficits is realized as a result of the seesaw mechanism. Bi-maximal mixing structure might be obtainable in this scheme. Since it contains a light sterile neutrino, it has a chance to explain the LSND result suc…
The recent recomputation of the neutrino fluxes from nuclear reactors relaxes the tension between the LSND and MiniBooNE anomalies and disappearance data when interpreted in terms of sterile neutrino oscillations. The simplest extension of the Standard Model with such fermion singlets is the addition of right-handed sterile neutrinos with small Majorana masses. Even when introducing three right-handed neutrinos, this scenario has less free parameters than the 3+2 scenarios studied in the literature. This begs the question whether the best fit regions obtained can be reproduced by this simplest…
Motivated by the capability of the KATRIN experiment to explore the existence of KeV neutrinos in the $[1-18.5]$ KeV mass range, we explore the viability of minimal extensions of the Standard Model involving sterile neutrinos (namely the 3 + $N$ frameworks) and study their possible impact in both the beta energy spectrum and the neutrinoless double beta decay effective mass, for the two possible ordering cases for the light neutrino spectrum. We also explore how both observables can discriminate between motivated low-scale seesaw realizations involving KeV sterile neutrinos. Our study concerns…
Based on the "democratic" universal seesaw model, where mass matrices $M_f$ of quarks and leptons f_i (f=u,d,ν,e; i=1,2,3) are given by a seesaw form M_f\simeq -m_L M_F^{-1} m_R, and m_L and m_R are universal for all the fermion sectors, and the mass matrices M_F of hypothetical heavy fermions F_i have a democratic structure, a possible neutrino mass matrix is investigated. In the model, there are three sterile neutrinos ν_{iR} which mix with the active neutrinos ν_{iL} with θ\sim 10^{-2} and which are harmless for constraint from the bib bang nucleosynthesis. The atmospheric, solar and LSND n…
We study $S_{4}$ flavor symmetric inverse seesaw model which has the possibility of simultaneously addressing neutrino phenomenology, dark matter (DM) and baryon asymmetry of the universe (BAU) through leptogenesis. The model is the extension of the standard model by the addition of two right handed neutrinos and three sterile fermions leading to a keV scale sterile neutrino dark matter and two pairs of quasi-Dirac states. The CP violating decay of the lightest quasi- Dirac pair present in the model generates lepton asymmetry which then converts to baryon asymmetry of the universe. Thus this m…
A low-scale neutrino seesaw may be probed or even reconstructed at colliders provided that supersymmetry is at the weak scale and the LSP is a sterile sneutrino. Because the neutrino Yukawa couplings are small, the NLSP is typically long-lived and thus a significant fraction of colored or charged NLSPs may stop in the detector material before decaying to the LSP and a charged lepton, gauge boson, or Higgs. For two-body NLSP decays, the energy spectrum of the visible decay product exhibits a monochromatic line for each sterile sneutrino which can be used to extract the sterile sneutrino masses …
The presence of small neutrino masses and flavour mixings can be accounted for naturally in various models about extensions of the standard model, particularly in the seesaw mechanism models. In this work, we present a minimally extended seesaw framework with two right-handed neutrinos, where the active neutrino masses are derived in the radiative regime. Using the framework it can be shown that within certain mass limits, the light neutrino mass term can approach a form that is similar to its form under the type-I seesaw mechanism. Apart from this, we show that the decay width of right-handed…
A four-neutrino spectrum with a sterile neutrino without significant involvement in the atmospheric and solar neutrino oscillation experiments has been recently advocated as the correct picture to explain all existing experimental data. We propose a supersymmetric model in which this picture can be naturally implemented. In this model, the mass for the mainly active neutrino eigenstates is induced by the seesaw mechanism with a large intermediate scale $M_R$, whereas the mass for the mainly sterile neutrino state is closely related to supersymmetry breaking.
We make a comparative study of the neutrinoless double beta decay constraints on heavy sterile neutrinos versus other direct and indirect constraints from both lepton number conserving and violating processes, as a sensitive probe of the extent of lepton number violation and possible interference effects in the sterile sector. We introduce a phenomenological parametrisation of the simplified one-generation seesaw model with one active and two sterile neutrino states in terms of experimentally measurable quantities, such as active-sterile neutrino mixing angles, CP phases, masses and mass split…
We consider an extension of the Standard Model with three right-handed (RH) neutrinos and a Dirac pair of extra sterile neutrinos, odd under a discrete $Z_2$ symmetry, in order to have left-right symmetry in the neutrino content and obtain tiny neutrino masses from the latter ones only. Our working hypothesis is that the heavy RH neutrinos do not influence phenomenology at low energies. We use the usual high-scale seesaw to suppress all of the mass terms involving RH neutrinos and a low-scale minimal variant of the linear seesaw led by the Dirac mass of the extra sterile neutrinos to provide t…
We study the zero textures of the Yukawa matrices in the minimal extended type-I seesaw (MES) model which can give rise to $\sim$ eV scale sterile neutrinos. In this model, three right handed neutrinos and one extra singlet $S$ are added to generate a light sterile neutrino. The light neutrino mass matrix for the active neutrinos, $ m_ν$, depends on the Dirac neutrino mass matrix ($ M_{D} $), Majorana neutrino mass matrix ($ M_{R} $) and the mass matrix ($ M_{S} $) coupling the right handed neutrinos and the singlet. The model predicts one of the light neutrino masses to vanish. We systematica…
We consider an SU(3)'_c\times SU(2)'_L\times U(1)'_Y mirror sector where the field content and dimensionless couplings are a copy of the SU(3)_c\times SU(2)_L\times U(1)_Y ordinary sector. Our model also contains three gauge-singlet fermions with heavy Majorana masses and an [SU(2)_L\times SU(2)'_L]-bidoublet Higgs scalar with seesaw-suppressed vacuum expectation value. The mirror sterile neutrino masses will have a form of canonical seesaw while the ordinary active neutrino masses will have a form of double and linear seesaw. In this canonical and double-linear seesaw scenario, we can expect …
The seesaw mechanism is conceived on the basis that a mass scale, $ξ$, and a dimensionless scale, $s$, can be fine-tuned in order to control the dynamics of active and sterile neutrinos through cosmon-type equations of motion: the seesaw cosmon equations. This allows for sterile neutrinos to be a dark matter candidate. In this scenario, the dynamical masses and energy densities of active and sterile neutrinos can be consistently embedded into the generalized Chaplygin gas (GCG), the unified dark sector model. In addition, dark matter adiabatically coupled to dark energy allows for a natural de…
We study a model of neutrino and dark matter within the framework of a minimal extended seesaw. This model is based on $A_4$ flavour symmetry along with the discrete $Z_3\times Z_4$ symmetry to stabilize the dark matter and construct desired mass matrices for neutrino mass. Five-zero textures are imposed in the final $4\times4$ active-sterile mass matrix, which significantly reduces free parameter in the model. Three right-handed neutrinos were considered, two of them have nearly degenerate masses which help us to achieve baryogenesis via resonant leptogenesis. A singlet fermion (sterile neutr…
Ultraviolet Flavor Transmission to T-Violating Neutrino Oscillation Observables in a Seesaw Framework with Sterile Mixing and Planck-Suppressed Corrections
Department of Physics, Kirori Mal College, University of Delhi（德里大学科里尔马尔学院物理系）；Department of Physics, Chaudhary Charan Singh University（乔杜里·查兰·辛格大学物理系）
We propose that a hierarchical spectrum of sterile neutrinos (eV, keV, $10^{13-15}$ GeV) is considered to as the explanations for MiniBooNE and LSND oscillation anomalies, dark matter, and baryon asymmetry of the universe (BAU) respectively. The scenario can also realize the smallness of active neutrino masses by seesaw mechanism.
We study the impact of maximal zeros of the Dirac mass matrix on neutrino phenomenology and dark matter within the framework of an inverse seesaw ISS $(2,3)$. ISS $(2,3)$ is obtained by adding two right handed neutrinos and three gauge singlets sterile fermions to the standard model leading to an extra sterile state in the keV range. The model is more predictive because of the presence of fewer numbers of right handed neutrinos than the conventional inverse seesaw. Moreover, texture zeros in the structures of the mass matrices involved in the model can reduce the free parameters. We extensivel…
One of the main purposes of SHiP experiment is to shed light on neutrino mass generation mechanisms like the so-called seesaw. We consider a minimal type-I seesaw neutrino mass mechanism model with two heavy neutral leptons (right-handed or sterile neutrinos) with arbitrary masses. Extremely high active-sterile mixing angle requires a correlation between the phases of the Dirac neutrino couplings. Actual experimental limits on the half-life of neutrinoless double beta decay $0νββ$-rate on the active-sterile mixing angle are not significative for SHiP.
The recently proposed "mini-seesaw mechanism" combines naturally suppressed Dirac and Majorana masses to achieve light Standard Model neutrinos via a low-scale seesaw. A key feature of this approach is the presence of multiple light (order GeV) sterile-neutrinos that mix with the Standard Model. In this work we study the bounds on these light sterile-neutrinos from processes like μ---> e + γ, invisible Z-decays, and neutrinoless double beta-decay. We show that viable parameter space exists and that, interestingly, key observables can lie just below current experimental sensitivities. In partic…
Motivated by the short-baseline neutrino oscillation anomalies that suggest the existence of sterile neutrinos at the eV scale, we construct a scenario of a seesaw mechanism for 3+1 light neutrinos implemented by warped compactification of an extra dimension. As the seesaw mechanism necessitates at least two right-handed neutrinos at mass scales much larger than eV, incorporating an eV-scale sterile neutrino into a seesaw entails large mass hierarchies among the singlet neutrinos. We show that such hierarchies can be naturally explained by moderate fluctuations of the five-dimensional fermion …
We address the impact of sterile fermions on charged lepton electric dipole moments. We show that in order to have a non-vanishing contribution to electric dipole moments, the minimal extension necessitates the addition of at least two sterile fermion states. Sterile neutrinos can give significant contributions to the charged lepton electric dipole moments if the masses of the non-degenerate sterile states are both above the electroweak scale. In addition, the Majorana nature of neutrinos is also important. Furthermore, we apply the computations of the electric dipole moments for the most mini…
We explore the possibility of light and superlight sterile neutrinos in the recently proposed Minimal Radiative Inverse Seesaw extension of the Standard Model for neutrino masses, in which all existing neutrino data can be explained. In particular, we discuss two benchmark scenarios with one of the three sterile neutrino states in the keV-range, having very small mixing with the active neutrinos to account for the Dark Matter in the Universe, while (i) the other two light sterile neutrino states could be in the eV-range, possessing a nonzero mixing with the active states as required to explain…
We consider the so-called "eV seesaw" scenario, with right-handed Majorana mass $M_R$ at eV order, extended to four lepton generations. The fourth generation gives a heavy pseudo-Dirac neutral lepton, which largely decouples from other generations and is relatively stable. The framework naturally gives 3 active and 3 sterile neutrinos. We update a previous numerical analysis of a 3+3 study of the LSND anomaly, taking into account the more recent results from the MiniBooNE experiment. In particular, we study the implications for the third mixing angle $\mathrm{sin}^2θ_{13}$, as well as CP viola…
We consider an inverse seesaw mechanism of neutrino mass generation in which the Standard Model is extended by $3+3$ (heavy) sterile states, and endowed with a flavour symmetry $G_f$, $G_f=Δ(3 \, n^2)$ or $G_f=Δ(6 \, n^2)$, and a CP symmetry. These symmetries are broken in a peculiar way, so that in the charged lepton sector a residual symmetry $G_\ell$ is preserved, while the neutral fermion sector remains invariant under the residual symmetry $G_ν=Z_2 \times CP$. We study the concrete setup, where the Majorana mass term for three of the sterile states conserves $G_ν$, while the remaining mas…
We propose the inverse seesaw mechanism as a way to understand small Majorana masses for neutrinos in warped extra dimension models with seesaw scale in the TeV range. The ultra-small lepton number violation needed in implementing inverse seesaw mechanism in 4D models is explained in this model as a consequence of lepton number breaking occurring on the Planck brane. We construct realistic models based on this idea that fit observed neutrino oscillation data for both normal and inverted mass patterns. We compute the corrections to light neutrino masses from the Kaluza-Klein modes and show that…
Knowledge of the mechanism of neutrino mass generation would help understand a lot more about Lepton Number Violation (LNV), the cosmological evolution of the Universe, or the evolu tion of astronomical objects. Here we propose a verifiable and viable extension of the Standard model for neutrino mass generation, with a low-scale seesaw mechanism via LNV condensation in the sector of sterile neutrinos. To prove the concept, we analyze a simplified model of just one single family of elementary particles and check it against a set of phenomenological constraints coming from electroweak symmetry b…
Some of basic problems in neutrino physics such as new energy scales, the enormous gap between neutrino masses and the lightest charged fermion mass, possible existance of sterile neutrinos in eV mass range are studied in the local gauge group $SU_{L}(4)\times U(1)$ for electroweak unification, which does not contain fermions with exotic electric charges. It is shown that neutrino mass spectrum can be decoupled from that of the other fermions. Further normal seesaw mechanism for neutrinos, with right handed neutrino Majorana masses to be of order $M\gg M_{\text{weak}}$ as well a new eV-scale c…
We have explored an extended seesaw model accommodating a keV sterile neutrino adopting $U(1)_{B-L}$ symmetry. This model provides a natural platform for achieving resonant leptogenesis to account for the observed baryon asymmetry of the Universe. The required lepton asymmetry is sourced by the CP violating decay of the lightest heavy right handed neutrino to Standard Model leptons and Higgs. The presence of the light sterile neutrino in the model brings out an enhancement in the final lepton asymmetry through an additional self-energy contribution. Adopting a proper treatment for all the wash…
We studied models of leptogenesis where three right-handed Majorana neutrinos are involved and the minimal-extended seesaw mechanism including an additional singlet field produces four light neutrinos. This study shows that the type of mass ordering and heavy Majorana scales can be determined by inputting the simplest orthogonal matrix into the Casas-Ibarra(CI) representation of seesaw. The CP asymmetry produced from the decays of heavy neutrinos and the dilution mass are predicted in terms of the mass and mixing elements of the fourth neutrino. Upon the choice of CI matrix, the existence of a…
If the Standard Model particle content is extended by gauge singlet fermions (right-handed neutrinos), active neutrinos generically acquire (Majorana) masses, in agreement with our current understanding of the lepton sector. If the right-handed neutrino masses are of the same order as the electroweak symmetry breaking scale, it is usually expected that these will not mediate any experimentally observable effects. Here, I explore the fact that this is not necessarily the case. If neutrino masses are "accidentally small", active-sterile mixing angles can, according to current experimental bounds…
We propose a new production mechanism for keV sterile neutrino dark matter which relies neither on the oscillations between sterile and active neutrinos nor on the decay of additional heavier particles. The dark matter neutrinos are instead produced by thermal freeze-out, much like a typical WIMP. The challenge consists in balancing a large Yukawa coupling so that the sterile neutrinos thermalize in the early universe on the one hand, and a small enough Yukawa coupling such that they are stable on cosmological scales on the other. We solve this problem by implementing varying Yukawa couplings.…
Seesaw mechanism constrains from below mixing between active and sterile neutrinos for fixed sterile neutrino masses. Signal events associated with sterile neutrino decays inside a detector at fixed target experiment are suppressed by the mixing angle to the power of four. Therefore sensitivity of experiments such as SHiP and DUNE should take into account minimal possible values of the mixing angles. We extend the previous study of this subject arXiv:1312.2887 to a more general case of non-zero CP-violating phases in the neutrino sector. Namely, we provide numerical estimate of minimal value o…
We explore the possibility of having a successful leptogenesis through oscillations between new sterile fermion states added to the Standard Model field content in a well motivated framework, naturally giving rise to the required mass splitting between the sterile states through a small total lepton number violation. We propose a framework with only two sterile states forming a pseudo-Dirac state, in which their mass difference as well as the smallness of the neutrino masses are due to two sources of lepton number violation with $ΔL=2$, corresponding to an Inverse Seesaw framework extended by …
For Leptogenesis based on the type-I seesaw mechanism, we present a systematic calculation of lepton-number violating and purely flavoured asymmetries within nonequilibrium Quantum Field Theory. We show that sterile neutrinos with non-degenerate masses in the GeV range can explain the baryon asymmetry of the Universe via flavoured Leptogenesis. This is possible due to the interplay of thermal and flavour effects. Our approach clarifies the relation between Leptogenesis from the oscillations of sterile neutrinos and the more commonly studied scenarios from decays and inverse decays. We explain …
We consider a variant of seesaw mechanism by introducing extra singlet neutrinos, with which we show how the low scale leptogenesis is realized without imposing the tiny mass splitting between two heavy Majorana neutrinos required in the resonant leptogenesis. Thus, we can avoid the so-called gravitino problem when our scenario is supersymmetrized. We show that an introduction of the new singlet fermion leads to a new contribution which can enhance the lepton asymmetry for certain range of parameter space. We also examine how both the light neutrino mass spectrum and relatively light sterile n…
This brief report is an extension of a prediction of neutrino oscillation with a sterile neutrino using parameters of the sterile neutrino mass and mixing angle recently extracted from experiment.
We consider the contribution of the extra sterile states in generic low-scale seesaw models to extra radiation, parametrized by $N_{\rm eff}$. We find that the value of $N_{\rm eff}$ is roughly independent of the seesaw scale within a wide range. We explore the full parameter space in the case of two extra sterile states and find that these models are strongly constrained by cosmological data for any value of the seesaw scale below ${\mathcal O}(100$MeV).
We construct a neutrino mass model based on the flavour symmetry group $A_4\times C_4 \times C_6 \times C_2$ which accommodates a light sterile neutrino in the minimal extended seesaw (MES) scheme. Besides the flavour symmetry, we introduce a $U(1)$ gauge symmetry in the sterile sector and also impose CP symmetry. The vacuum alignments of the scalar fields in the model spontaneously break these symmetries and lead to the construction of the fermion mass matrices. With the help of the MES formulas, we extract the light neutrino masses and the mixing observables. In the active neutrino sector, w…
