The self-interacting neutrino hypothesis is well motivated for addressing the tension between the origin of sterile neutrino dark matter and indirect detection constraints. It can also result in a number of testable signals from the laboratories to the cosmos. We explore a model of neutrino self-interaction mediated by a Majoron-like scalar with sub-MeV mass, and show that explaining the relic density of sterile neutrino dark matter implies a lower bound on the amount of extra radiation in early universe, in particular $ΔN_{\rm eff}>0.12$ at the CMB epoch. This lower bound will be further strengthened with an improved $X$-ray search at the Athena observatory. Such an intimate relationship will be unambiguously tested by the upcoming CMB-S4 project.
It is generally expected that adding light sterile species would increase the effective number of neutrinos, $N_{eff}$. In this paper we discuss a scenario that $N_{eff}$ can actually decrease due to the neutrino oscillation effect if sterile neutrinos have self-interactions. We specifically focus on the eV mass range, as suggested by the neutrino anomalies. With large self-interactions, sterile neutrinos are not fully thermalized in the early Universe because of the suppressed effective mixing angle or matter effect. As the Universe cools down, flavor equilibrium between active and sterile sp…
Neutrino-neutrino interactions, as mediated by standard model Z exchange, can drastically enhance the Dodelson-Widrow mechanism for the production of sterile neutrinos in the region of temperature $5-15$MeV. For a sterile mass in the KeV region with the usual type of active-sterile neutrino coupling, the production can be copious enough to provide ample dark matter, even when the active-sterile coupling is small enough to avoid the bounds set by laboratory results.
If sterile neutrinos have a neutral coupling to standard model fermions, matter effect resonant transitions to sterile neutrinos and excess neutral-current events could manifest at long baseline experiments. Assuming a single sterile neutrino with a neutral coupling to fermionic matter, we re-examine bounds on sterile neutrino production at long baselines from the MINOS result $P_{ν_μ \rightarrow ν_s} < 0.22$ (90% CL). We demonstrate that sterile neutrinos with a neutral vector coupling to fermionic matter could evade the MINOS limit, allowing a higher fraction of active to sterile neutrino co…
The XENON1T collaboration recently reported the excess of events from recoil electrons, possibly giving an insight into new area beyond the Standard Model (SM) of particle physics. We try to explain this excess by considering effective interactions between the sterile neutrinos and the SM particles. In this paper, we present an effective model based on one-particle-irreducible interaction vertices at low energies that are induced from the SM gauge symmetric four-fermion operators at high energies. The effective interaction strength is constrained by the SM precision measurements, astrophysical…
We perform a comparative analysis of constraints on sterile neutrinos from the Planck experiment and from current and future neutrino oscillation experiments (MINOS, IceCube, SBN). For the first time, we express the Planck constraints on $N_{\rm eff}$ and $m_{\rm eff}^{\rm sterile}$ from the Cosmic Microwave Background in the parameter space used by oscillation experiments using both mass-squared differences and mixing angles. In a model with a single sterile neutrino species and using standard assumptions, we find that the Planck data and the oscillation experiments measuring muon-neutrino di…
We study the effects of kination and scalar-tensor pre-Big Bang Nucleosynthesis cosmologies on the non-resonant production of sterile neutrinos. We show that if the peak of the production rate of sterile neutrinos occurs during the non-standard cosmological phase, the relic number density of sterile neutrinos could be reduced with respect to the number expected in the standard cosmology. Consequently, current bounds on active-sterile neutrino mixing derived from the relic energy density of sterile neutrinos could be greatly relaxed. In particular, we show that the sterile neutrinos which could…
Large numbers of $τ$ leptons are produced at Belle II. These could potentially decay into sterile neutrinos that, for the mass range under consideration, are typically long-lived, leading to displaced-vertex signatures. Here, we study a displaced-vertex search sterile-neutrino-extended Standard Model Effective Field Theory. The production and decay of the sterile neutrinos can be realized via either the standard active-sterile neutrino mixing or higher-dimensional operators in the effective Lagrangian. We perform Monte-Carlo simulations to estimate the Belle II sensitivities to such interactio…
Charged-Current Quasi-Elastic (CCQE) neutrino scattering is the signal channel for sterile neutrino oscillation experiments. Recent cross-section measurements have made it clear that the current understanding of this channel in the few-GeV region is incomplete, and several sophisticated theoretical models have been proposed to tackle this issue, although it is not clear which model best describes the global dataset. In this paper we argue that the current uncertainty surrounding CCQE cross-sections is a serious problem for experiments seeking to produce sterile neutrino limits. We perform a st…
We investigate how hypothetical particles - sterile neutrinos - can be produced in the interior of exploding supernovae via the resonant conversion of $\barν_μ$ and $\bar ν_τ$. The novelty of our treatment lies in the proper account of the resulting lepton number diffusion. We compute the yield of sterile neutrinos and find that even after taking into account back reaction, sterile neutrinos can carry out a sizeable fraction of the total energy of the explosion comparable to that of active neutrinos. The production is, however, exponentially sensitive to the temperature in the inner supernovae…
We analytically calculate the neutrino conversion probability $P_{μe}$ in the presence of sterile neutrinos, with exact dependence on $Δm^2_{41}$ and with matter effects explicitly included. Using perturbative expansion in small parameters, the terms involving the small mixing angles $θ_{24}$ and $θ_{34}$ can be separated out, with $θ_{34}$ dependence only arising due to matter effects. We express $P_{μe}$ in terms of the quantities of the form $\sin(x)/x$, which helps in elucidating its dependence on matter effects and a wide range of $Δm^2_{41}$ values. Our analytic expressions allow us to p…
We analyze the most recent cosmological data, including Planck, taking into account the possible existence of a sterile neutrino with a mass at the eV scale indicated by short-baseline neutrino oscillations data in the 3+1 framework. We show that the contribution of local measurements of the Hubble constant induces an increase of the value of the effective number of relativistic degrees of freedom above the Standard Model value, giving an indication in favor of the existence of sterile neutrinos and their contribution to dark radiation. Furthermore, the measurements of the local galaxy cluster…
We describe two new generation mechanisms for Dark Matter composed of sterile neutrinos with ${\cal O}(1)$ keV mass. The model contains a light scalar field which coherently oscillates in the early Universe and modulates the Majorana mass of the sterile neutrino. In a region of model parameter space, the oscillations between active and sterile neutrinos are resonantly enhanced. This mechanism allows us to produce sterile neutrino DM with small mixing angle with active neutrinos, thus evading the X-ray constraints. At the same time the spectrum of produced DM is much cooler, than in the case of…
Recent neutrino oscillation results have evoked renewed interest in sterile neutrino oscillation models. This paper reviews the data from MiniBooNE and short-baseline reactor antineutrino experiments within the context of sterile neutrinos. The results are incorporated into combined fits to test the viability of sterile neutrino oscillation models, which are later expanded to address matter effects. Finally, future experiments that can resolve the questions that have been raised are discussed.
We summarize the impact of sterile neutrino dark matter on core-collapse supernova explosions. We explore various oscillations between electron neutrinos or mixed $μ-τ$ neutrinos and right-handed sterile neutrinos that may occur within a core-collapse supernova. In particular, we consider sterile neutrino masses and mixing angles that are consistent with sterile neutrino dark matter candidates as indicated by recent X-ray flux measurements. We find that the interpretation of the observed 3.5 keV X-ray excess as due to a decaying 7 keV sterile neutrino that comprises 100\% of the dark matter wo…
We briefly discuss the main effects of the presence of a Light Sterile Neutrino (LS$ν$) in Cosmology and how its properties can be constrained by Cosmic Microwave Background (CMB) and other cosmological measurements.
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…
After a brief review of the results of solar, atmospheric and long-baseline neutrino oscillation experiments which led to the current three-neutrino mixing paradigm, we discuss indications of neutrino oscillation experiments in favor of short-baseline oscillations which require the existence of one or more sterile neutrinos. We show that the simplest possibility of existence of one sterile neutrino is not enough to fit all data of short-baseline neutrino oscillation experiments because of two tensions: a tension between neutrino and antineutrino data and a tension between appearance and disapp…
Sterile neutrinos with keV-scale masses are popular candidates for warm dark matter. In the most straightforward case they are produced via oscillations with active neutrinos. We introduce effective self-interactions of active neutrinos and investigate the effect on the parameter space of sterile neutrino mass and mixing. Our focus is on mixing with electron neutrinos, which is subject to constraints from several upcoming or running experiments like TRISTAN, ECHo, BeEST and HUNTER. Depending on the size of the self-interaction, the parameter space moves closer to, or further away from, the one…
We investigate the sensitivity of tritium $β$-decay experiments for keV-scale sterile neutrinos. Relic sterile neutrinos in the keV mass range can contribute both to the cold and warm dark matter content of the universe. This work shows that a large-scale tritium beta-decay experiment, similar to the KATRIN experiment that is under construction, can reach a statistical sensitivity of the active-sterile neutrino mixing of $\sin^2θ\sim 10^{-8}$. The effect of uncertainties in the known theoretical corrections to the tritium $β$-decay spectrum were investigated, and found not to affect the sensit…
We investigate how the dark energy properties change the cosmological limits on sterile neutrino parameters by using recent cosmological observations. We consider the simplest dynamical dark energy models, the $w$CDM model and the holographic dark energy (HDE) model, to make an analysis. The cosmological observations used in this work include the Planck 2015 CMB temperature and polarization data, the baryon acoustic oscillation data, the type Ia supernova data, the Hubble constant direct measurement data, and the Planck CMB lensing data. We find that, $m_{ν,{\rm{sterile}}}^{\rm{eff}}<0.2675$ e…
In sterile neutrino (3+1) parameterisation, we observe that sterile phases ($δ_{14},δ_{24}$) are always together in oscillation probability, even when the MSW effect is considered. We see that the difference between the sterile phases has a more dominating effect over event rates compared to small variations due to changes in individual values. In this work, we show the value of sterile phase difference ($δ_{14}-δ_{24}$) that least affects the parameter degeneracy resolution of $δ_{13},θ_{23}$ at long-baseline experiments.
We consider the possibility that there exist sterile neutrinos which are closely degenerate in mass with the active neutrinos and mixed with them. We investigate the effects of this kind of active-sterile neutrino mixing on the composition of supernova neutrino flux at the Earth. If an adiabatic MSW-transition between active and sterile neutrinos takes place, it could dramatically diminish the electron neutrino flux.
Sterile neutrinos can be produced in the early universe via interactions with their active counterparts. For small active-sterile mixing angles, thermal equilibrium with the standard model plasma is not reached and sterile neutrinos are only produced via flavor oscillations. We study in detail this regime, taking into account matter potentials and decoherence effects caused by elastic scatterings with the plasma. We find that resonant oscillations occurring at temperatures $T\lesssim 10\,\mathrm{GeV}$ lead to a significant enhancement of the sterile neutrino production rate. Taking this into a…
Secret interactions among sterile neutrinos have been recently proposed as an escape-route to reconcile eV sterile neutrino hints from short-baseline anomalies with cosmological observations. In particular models with coupling g_X \gtrsim 10^{-2} and gauge boson mediators $X$ with $M_X \lesssim 10$ MeV lead to large matter potential suppressing the sterile neutrino production before the neutrino decoupling. With this choice of parameter ranges, big bang nucleosynthesis is left unchanged and gives no bound on the model. However, we show that at lower temperatures when active-sterile oscillation…
Sterile neutrino dark matter, a popular alternative to the WIMP paradigm, has generally been studied in non-supersymmetric setups. If the underlying theory is supersymmetric, we find that several interesting and novel dark matter features can arise. In particular, in scenarios of freeze-in production of sterile neutrino dark matter, its superpartner, the sterile sneutrino, can play a crucial role in early Universe cosmology as the dominant source of cold, warm, or hot dark matter, or of a subdominant relativistic population of sterile neutrinos that can contribute to the effective number of re…
We study a large extra dimension model with active and sterile Dirac neutrinos. The sterile neutrino masses stem from compactification of an extra dimension with radius $R$ and are chosen to have masses around eV or keV, in order to explain short-baseline anomalies or act as warm dark matter candidates. We study the effect of the sterile neutrino Kaluza-Klein tower in short-baseline oscillation experiments and in the beta spectrum as measurable by KATRIN-like experiments.
Motivated by recent hints in particle physics and cosmology, we study the realization of eV-scale sterile neutrinos within both the seesaw mechanism and flavor symmetry theories. We show that light sterile neutrinos can rather easily be accommodated in the popular A_4 flavor symmetry models. The exact tri-bimaximal mixing pattern is perturbed due to active-sterile mixing, which we discuss in detail for one example. In addition, we find an interesting extension of the type I seesaw, which can provide a natural origin for eV-scale sterile neutrinos as well as visible admixtures between sterile a…
The theory and phenomenology of light sterile neutrinos at the eV mass scale is reviewed. The reactor, Gallium and LSND anomalies are briefly described and interpreted as indications of the existence of short-baseline oscillations which require the existence of light sterile neutrinos. The global fits of short-baseline oscillation data in 3+1 and 3+2 schemes are discussed, together with the implications for beta-decay and neutrinoless double-beta decay. The cosmological effects of light sterile neutrinos are briefly reviewed and the implications of existing cosmological data are discussed. The…
We calculate the effect of sterile neutrinos and nonstandard neutrino interactions on the flux of active neutrinos from the Earth's crust and mantle taking matter effect into account in both cases. For simple Earth model and using previous emission flux estimates at the source, we find that for reasonable choice of parameters for both the sterile neutrino and nonstandard interaction, the effect on the neutrino flux is a few percent or less.
We consider the cosmological effects of sterile neutrinos with the masses of $150- 450$ MeV. The decay of sterile neutrinos changes the thermal history of the Universe and affects the energy density of radiation at the recombination and the big bang nucleosynthesis (BBN) results. We derive severe constraints on the parameters of sterile neutrinos from the primordial abundances of helium-4 and deuterium. We also find that in a particular model the constraints can be considerably relaxed by assuming a large lepton asymmetry in the active neutrinos. In this case, the consistent parameters result …
We explore the energy and entropy transport as well as the lepton number variation induced from the mixing between electron and sterile neutrinos with keV mass in the supernova core. We develop a radial- and time-dependent treatment of the sterile-electron neutrino mixing, by including ordinary matter effects, reconversions between sterile and electron antineutrinos, as well as the collisional production of sterile particles for the first time. The dynamical feedback due to the production of sterile particles on the composition and thermodynamic properties of the core only leads to major impli…
We briefly review recent work exploring the effect of light sterile neutrino states on the neutrino magnetic moment as explored by the reactor and solar neutrino experiments.
In this work we analyze the effects of quantum decoherence upon the precession of the neutrino polarization vector in a supernovae-like environment. In order to perform the study we have determined the time-dependence of the polarization vector by solving the equation of motion for different neutrino-mixing schemes. The results of the calculations show that the onset of decoherence depends strongly on the parameters of the adopted mixing scheme. As examples we have considered : a) the mixing between active neutrinos and b) the mixing between active end sterile neutrinos.
Day-night asymmetries in active-sterile solar neutrino oscillations are discussed in the general $3+N_{s}$ mixing framework with three active and N_s sterile neutrinos. Analytical expressions of the probability of neutrino flavor transitions in the Earth in the perturbative approximation and in the slab approximation are presented and the effects of active-sterile mixing and of the CP-violating phases are discussed. The accuracy of the analytical approximations and the properties of the day-night asymmetries are illustrated numerically in the 3+1 neutrino mixing framework.
Tantalizing cosmological and terrestrial evidence suggests the number of light neutrinos may be greater than 3, motivating a careful re-examination of cosmological bounds on extra light species. Big Bang Nucleosynthesis constrains the number of relativistic neutrino species present during nucleosynthesis, $N_{eff}^{BBN}$, while measurements of the CMB angular power spectrum constrain the effective energy density in relativistic neutrinos at the time of matter-radiation equality, $N_{eff}^{CMB}$. There are a number of scenarios where new sterile neutrino species may have different contributions…
A number of anomalous results in short-baseline oscillation may hint at the existence of one or more light sterile neutrino states in the eV mass range and have triggered a wave of new experimental efforts to search for a definite signature of oscillations between active and sterile neutrino states. The present paper aims to provide a comprehensive review on the status of light sterile neutrino searches in mid-2019: we discuss not only the basic experimental approaches and sensitivities of reactor, source, atmospheric, and accelerator neutrino oscillation experiments but also the complementary…
The MiniBooNE NCEL and CCQE cross-section measurements (neutrino running) are used to set limits in the $Δm^{2}-\sin^{2}\vartheta_{μs}$ plane for a 3+1 sterile neutrino model with a mass splitting $0.1 \leq Δm^{2} \leq 10.0$ eV$^{2}$. GENIE is used, with a relativistic Fermi gas model, to relate $E_ν$ and the reconstructed quantities measured. The issue of uncertainty in the underlying cross-section model and its effect on the sterile neutrino limits is explored, and robust sterile neutrino limits are produced by fitting the sterile parameters and the axial-mass cross-section parameter simulta…
Light sterile neutrinos can be excited by oscillations with active neutrinos in the early universe. Their properties can be constrained by their contribution as extra-radiation, parameterized in terms of the effective number of neutrino species N_ eff, and to the universe energy density today Ω_νh^2. Both these parameters have been measured to quite a good precision by the Planck satellite experiment. We use this result to update the bounds on the parameter space of (3+1) sterile neutrino scenarios, with an active-sterile neutrino mass squared splitting in the range (10^{-5} - 10^2 ) eV^2. We …
Interest in light dark matter candidates has recently increased in the literature; some of these works consider the role of additional neutrinos, either active or sterile. Furthermore, extragalactic neutrinos have been detected with energies higher than have ever been reported before. This opens a new window of opportunities to the study of neutrino properties that were unreachable up to now. We investigate how an interaction potential between neutrinos and dark matter might induce a resonant enhancement in the oscillation probability, an effect that may be tested with future neutrino data.
It has been recently suggested \cite{Bezrukov:2017ike,Bezrukov:2018wvd} that a cosmic scalar field can completely change the keV-scale sterile neutrino production in the early Universe. Its effect may, for various parameter choices, either suppress sterile neutrino production and make moderate active-sterile mixing cosmologically acceptable, or increase the production and generate considerable dark matter component out of sterile neutrino with otherwise negligible mixing with SM. In this paper we provide analytic estimates complementing and providing details of the numerical calculations perfo…
Assuming that there is a sterile neutrino, we ask what then is the ability of long-baseline experiments to i) establish that neutrino oscillation violates CP, ii) determine the three-neutrino mass ordering, and iii) determine which CP-violating phase or phases are the cause of any CP violation that may be observed. We find that the ability to establish CP violation and to determine the mass ordering could be very substantial. However, the effects of the sterile neutrino could be quite large, and it might prove very difficult to determine which phase is responsible for an observed CP violation.…
We address the phenomenology of light sterile neutrinos, with emphasis on short-baseline neutrino oscillations. After a review of the observed short-baseline neutrino oscillation anomalies, we discuss the global fit of the data and the current appearance-disappearance tension. We also review briefly the effects of light sterile neutrinos in $β$ decay, neutrinoless double-$β$ decay and cosmology. Finally, we discuss the future perspective in the search for the effects of eV-scale sterile neutrinos.
We obtain non-linear kinetic equations for sterile neutrino occupancies and lepton minus baryon numbers by matching real time correlation functions of thermal fluctuations computed in an effective description to those computed in thermal quantum field theory. After expanding in the sterile-neutrino Yukawa couplings, the coefficients in the equations are written as real time correlation functions of Standard Model operators. Our kinetic equations are valid for an arbitrary number of sterile neutrinos of any mass spectrum. They can be used to describe, e.g., low-scale leptogenesis via neutrino o…
Since only recently, cosmological observations are sensitive to hot dark matter (HDM) admixtures with sub-eV mass, $m_\text{hdm}^\text{eff}$ < eV, that are not fully-thermalised, $N_\text{eff}$ < 1. We argue that their almost automatic interpretation as a sterile neutrino species is neither from theoretical nor practical parsimony principles preferred over HDM formed by decay products (daughters) of an out-of-equilibrium particle decay. While daughters mimic sterile neutrinos in $N_\text{eff}$ and $m_\text{hdm}^\text{eff}$, there are opportunities to assess this possibility in likelihood analy…
In this work we revisit the question of whether Cosmology can be made compatible with scenarios with light sterile neutrinos, as invoked to explain the SBL anomalies, in the presence of self-interaction among sterile neutrinos mediated by massive gauge bosons. We examine this proposal by deriving the cosmological predictions of the model in a wide range of the model parameters including the effective interaction strength $G_X$, sterile neutrino mass $m_{\rm st}$ and active-sterile mixings. With those we perform a statistical analysis of the cosmological data from BBN, CMB, and BAO data to infe…
The mixing of active neutrinos with their sterile counterparts with keV mass is known to have a potentially major impact on the energy loss from the supernova core. By relying on a set of three static hydrodynamical backgrounds mimicking the early accretion phase and the Kelvin-Helmoltz cooling phase of a supernova, we develop the first self-consistent, radial- and time-dependent treatment of sterile and tau neutrinos mixing in the dense stellar core. We follow the flavor evolution by including ordinary matter effects, collisional production of sterile neutrinos, as well as reconversions of st…
The renormalization-group equation (RGE) approach to neutrino matter effects is further developed in this work. We derive a complete set of differential equations for effective mixing elements, masses and Jarlskog-like invariants in presence of a light sterile neutrino. The evolutions of mixing elements as well as Jarlskog-like invariants are obtained by numerically solving these differential equations. We calculate terrestrial matter effects in long-baseline (LBL) experiments, taking NOvA, T2K and DUNE as examples. In both three-flavor and four-flavor frameworks, electron-neutrino survival pr…
Since most of the neutrino parameters are well-measured, we illustrate precisely the prediction of the Standard Model, minimally extended to allow massive neutrinos, for the electron neutrino magnetic moment. We elaborate on the effects of light sterile neutrinos on the effective electron neutrino magnetic moment measured at the reactors. We explicitly show that the kinematical effects of the neutrino masses are negligible even for light sterile neutrinos.
The transition magnetic moment of a sterile-to-active neutrino conversion gives rise to not only radiative decay of a sterile neutrino, but also its non-standard interaction (NSI) with matter. For sterile neutrinos of keV-mass as dark matter candidates, their decay signals are actively searched for in cosmic X-ray spectra. In this work, we consider the NSI that leads to atomic ionization, which can be detected by direct dark matter experiments. It is found that this inelastic scattering process for a nonrelativistic sterile neutrino has a pronounced enhancement in the differential cross sectio…
Recent neutrino experiment results show a preference for the normal neutrino mass ordering. The global efforts to search for neutrinoless double beta decays undergo a broad gap with the approach to the prediction in the three-neutrino framework based on the normal ordering. This research is intended to show that it is possible to find a neutrinoless double beta decay signal even with normal ordered neutrino masses. We propose the existence of a light sterile neutrino as a solution to the higher effective mass of the electron neutrino expected by the current experiments. A few short-baseline os…
We obtain the complete and independent bases of effective operators at mass dimension 5, 6, 7, 8, 9 in both standard model effective field theory with light sterile right-handed neutrinos ($ν$SMEFT) and low energy effective field theory with light sterile neutrinos ($ν$LEFT). These theories provide systematical parametrizations on all possible Lorentz-invariant physical effects involving in the Majorana/Dirac neutrinos, with/without the lepton number violations. In the $ν$SMEFT, we find that there are 2 (18), 29 (1614), 80 (4206), 323 (20400), 1358 (243944) independent operators with sterile n…
The existence of light sterile neutrinos is a long standing question for particle physics. Several experimental ``anomalies'' could be explained by introducing ~eV mass scaled light sterile neutrinos. Many experiments are actively hunting for such light sterile neutrinos through neutrino oscillation. For long baseline experiments, matter effect needs to be treated carefully for precise neutrino oscillation probability calculation. However, it is usually time-consuming or analytical complexity. In this manuscript we adopt the Jacobi-like method to diagonalize the Hermitian Hamiltonian matrix an…
We study the Peccei-Quinn (PQ) symmetry of the sterile right-handed neutrino sector and the gauge symmetries of the Standard Model. Due to four-fermion interactions, spontaneous breaking of these symmetries at the electroweak scale generates top-quark Dirac mass and sterile-neutrino Majorana mass. The top quark channel yields massive Higgs, $W^\pm$ and $Z^0$ bosons. The sterile neutrino channel yields the heaviest sterile neutrino Majorana mass, sterile Nambu-Goldstone axion (or majoron) and massive scalar $χ$boson. Four-fermion operators effectively induce their tiny couplings to SM particles…
