We show that when the neutrino minimal standard model ($νMSM$) with a light sterile neutrino has a long range interaction between the neutrino vacuum charge density and a dark U(1) gauge potential, late time acceleration is dynamically realized. Moreover, the relation between the scale of dark energy, the weak and Planck masses derived by Arkani-Hamed et. al \cite{ArkaniHamed:2000tc} that addresses the coincidence problem arises naturally in this model. Assuming that the cosmological constant is zero by some as yet known mechanism, the only fine tuning in our model is the mass of the sterile neutrino. We show that perturbations of the vector fields are oscillatory and hence, there are no instabilities.
A convincing explanation for the observed pulsar large peculiar velocities is still missing. We argue that any viable particle physics solution would most likely involve the resonant production of a non-interacting neutrino $ν_s$ of mass $m_{ν_s}\sim 20$--50 keV. We propose a model where anisotropic magnetic field configurations strongly bias the resonant spin flavour precession of tau antineutrinos into $ν_s$. For internal magnetic fields $B_{int} \gsim 10^{15}$ G a $\barν_τ$-$ν_s$ transition magnetic moment of the order of $10^{-12}$ Bohr magnetons is required. The asymmetric emission of $ν_…
Light sterile neutrinos represent a well-motivated extension of the 3-neutrino paradigm. However, the impressive agreement between standard cosmology and data casts doubts on their existence. Here we present a class of scenarios that robustly avoids this tension. In these models the sterile neutrinos are light, chiral states of a new sector interacting with the Standard Model via the right-handed neutrino portal and, crucially, active-sterile neutrino oscillations require a phase transition in the hidden sector. We explore the hidden-couplings/critical-temperature plane and identify regions wh…
A relic lepton asymmetry orders of magnitude bigger than the baryon one may hide in the relic neutrino background. No direct theoretical or experimental limitations on its magnitude and sign are known. Indirect cosmological constraints exist ranging from $|L|<0.01$ to $L<10$. We discuss a BBN model with late electron-sterile neutrino oscillations which is a fine leptometer - it is capable of feeling extremely small relic lepton asymmetry - $|L|>10^{-8}$. This sensitivity is achieved through the influence of such small $L$ on the neutrino oscillations, suppressing or enhancing them, and thus ch…
We develop a thorough description of neutrino oscillations in a magnetized protoneutron star, based on a resonance layer for neutrinos with different momentum directions. We apply our approach to the calculation of the asymmetry in the neutrino emission during the birth of a neutron star and the pulsar acceleration in the case of an active-sterile neutrino resonant conversion. The observed velocities can be obtained with the magnetic fields expected in the interior of a protoneutron star, for sterile neutrino masses of the order of KeV and small mixing angles.
We report the result of a search for sterile neutrinos with the latest cosmological observations. Both cases of massless and massive sterile neutrinos are considered in the $Λ$CDM cosmology. The cosmological observations used in this work include the Planck 2015 temperature and polarization data, the baryon acoustic oscillation data, the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck lensing data, and the cosmic shear data. We find that the current observational data give a hint of the existence of massless sterile neutrino (as dark radiat…
We propose the minimal supersymmetric sterile neutrino model (MSSNM) where the sterile neutrino masses are about 1 eV, while the active neutrino masses and the mixings among the active and sterile neutrinos are generated during late time phase transition. All the current experimental neutrino data include the LSND can be explained simultaneously, and the constraints on the sterile neutrinos from the big bang nucleosynthesis and large scale structure can be evaded. To realize the MSSNM naturally, we consider the supersymmetric intermediate-scale U(1)' model, the low energy U(1)' model with a se…
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…
Recent IceCube search results for sterile neutrino increased tension between the combined appearance and disappearance experiments. On the other hand, MiniBooNE latest data confirms at $4.9σ$ CL the short-baseline oscillation anomaly. We analyze published IceCube data based on two different active-sterile mixing schemes using one additional sterile neutrino flavor. We present exclusion regions in the parameter ranges $0.01 \le \sin^2 θ_{24} \le 0.1$ and $0.1~{\rm eV}^2 \le Δm^2_{42} \le 10~{\rm eV}^2$ for the mass-mixing and flavor-mixing schemes. Under the more conservative mass-mixing scheme…
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.
An experimentally verifiable Higgs-triplet model of neutrino masses from large extra dimensions was recently proposed. We extend it to accomodate a light sterile neutrino which also mixes with the three active neutrinos. A previously proposed phenomenological model of four neutrinos (\underline {the only viable such model now left}, in view of the latest atmospheric and solar neutrino-oscillation data) is specifically realized.
We search for sterile neutrinos in the holographic dark energy cosmology by using the latest observational data. To perform the analysis, we employ the current cosmological observations, including the cosmic microwave background temperature power spectrum data from the Planck mission, the baryon acoustic oscillation measurements, the type Ia supernova data, the redshift space distortion measurements, the shear data of weak lensing observation, the Planck lensing measurement, and the latest direct measurement of $H_0$ as well. We show that, compared to the $Λ$CDM cosmology, the holographic dark…
We point out that in models that explain the LSND result for neutrino oscillation using the mirror neutrinos, the big bang nucleosynthesis constraint can be avoided by using the late time phase transition that only helps to mix the active and the sterile neutrinos. We discuss the astrophysical as well as cosmological implications of this proposal.
A generalized phenomenological (3 + 2 + 1)-model with three active and three sterile neutrinos is considered for the calculation of the neutrino oscillation characteristics at normal mass hierarchy of active neutrinos and significant splitting between the mass of one sterile neutrino and the masses of other two sterile neutrinos. A new parametrization and a certain form of the general neutrino mixing matrix for active and sterile neutrinos are suggested taking into account the possible violation of CP invariance in the lepton sector. The test values of the neutrino masses and the mixing parame…
The observed velocities of pulsars suggest the possibility that sterile neutrinos with mass of several keV are emitted from a cooling neutron star. The same sterile neutrinos could constitute all or part of cosmological dark matter. The neutrino-driven kicks can exhibit delays depending on the mass and the mixing angle, which can be compared with the pulsar data. We discuss the allowed ranges of sterile neutrino parameters, consistent with the latest cosmological and X-ray bounds, which can explain the pulsar kicks for different delay times.
We investigate the implications of a sterile neutrino on the physics potential of the proposed experiment DUNE and future runs of NO$ν$A using latest NO$ν$A results. Using combined analysis of the disappearance and appearance data, NO$ν$A reported preferred solutions at normal hierarchy (NH) with two degenerate best-fit points one in the lower octant (LO) and $δ_{13}$ = 1.48$π$ and other in higher octant (HO) and $δ_{13}$ = 0.74$π$. Another solution of inverted hierarchy (IH) which is 0.46$σ$ away from best fit was also reported. We discuss chances of resolving these degeneracies in the presen…
The extension of the minimal standard model by three right-handed sterile neutrinos with masses smaller than the electroweak scale (nuMSM) is discussed in a Q_6 flavor symmetry framework. The lightness of the keV sterile neutrino and the near mass degeneracy of two heavier sterile neutrinos are naturally explained by exploiting group properties of Q_6. A normal hierarchical mass spectrum and an approximately mu-tau symmetric mass matrix are predicted for three active neutrinos. Nonzero theta_{13} can be obtained together with a deviation of theta_{23} from the maximality, where both mixing ang…
Motivated by recent hints for sterile neutrinos from the reactor anomaly, we study active-sterile conversions in a three-flavor scenario (2 active + 1 sterile families) for three different representative times during the neutrino-cooling evolution of the proto-neutron star born in an electron-capture supernova. In our "early model" (0.5 s post bounce), the nu_e-nu_s MSW effect driven by Delta m^2=2.35 eV^2 is dominated by ordinary matter and leads to a complete nu_e-nu_s swap with little or no trace of collective flavor oscillations. In our "intermediate" (2.9 s p.b.) and "late models" (6.5 s …
We study the phenomenology of a light (GeV scale) sterile neutrino sector and the pseudo-Goldstone boson (not the majoron) associated with a global symmetry in this sector that is broken at a high scale. Such scenarios can be motivated from considerations of singlet fermions from a hidden sector coupling to active neutrinos via heavy right-handed seesaw neutrinos, effectively giving rise to a secondary, low-energy seesaw framework. Such scenarios allow for rich phenomenology with observable implications for cosmology, dark matter, and direct searches, involving novel sterile neutrino dark matt…
We study the production of sterile neutrinos in the early universe from $π\rightarrow l ν_s$ shortly after the QCD phase transition in the absence of a lepton asymmetry while including finite temperature corrections to the $π$ mass and decay constant $f_π$. Sterile neutrinos with masses $\lesssim 1 MeV$ produced via this mechanism freeze-out at $T_f \simeq 10 MeV$ with a distribution function that is highly non-thermal and features a sharp enhancement at low momentum thereby making this species \emph{cold} even for very light masses. Dark matter abundance constraints from the CMB and phase spa…
Short baseline neutrino oscillation experiments have shown hints of the existence of additional sterile neutrinos in the eV mass range. Such sterile neutrinos are incompatible with cosmology because they suppress structure formation unless they can be prevented from thermalising in the early Universe or removed by subsequent decay or annihilation. Here we present a novel scenario in which both sterile neutrinos and dark matter are coupled to a new, light pseudoscalar. This can prevent thermalisation of sterile neutrinos and make dark matter sufficiently self-interacting to have an impact on ga…
We examine active-sterile neutrino conversion in the late time post-core-bounce supernova environment. By including the effect of feedback on the Mikheyev-Smirnov-Wolfenstein (MSW) conversion potential, we obtain a large range of neutrino mixing parameters which produce a favorable environment for the r-process. We look at the signature of this effect in the current generation of neutrino detectors now coming on line. We also investigate the impact of the neutrino-neutrino forward scattering-induced potential on the MSW conversion.
We propose an abelian extension of the Standard Model which can explain the origin of eV scale masses and mixing for active and sterile neutrinos and at the same time providing a natural cold dark matter candidate. One of the three active neutrinos acquires mass at tree level through seesaw mechanism whereas the other two active neutrinos and one sterile neutrino acquire eV scale masses at one-loop level. The model also allows non-trivial mixing between active and sterile neutrinos at one-loop level which could have interesting signatures at neutrino experiments. After the abelian gauge symmet…
A number of short baseline neutrino oscillation experiments have observed an anomalous excess of neutrinos in the low energy range. This may hint towards the existence of additional neutrino mass splittings. If true, additional sterile (non-interacting) neutrino states above the current 3 neutrino model would be required. On the other hand, many parameters of the allowed space are limited by experiments that have seen no anomaly. We will introduce models which accommodate these additional neutrinos, and then discuss our work towards fitting these models to the available global high $Δm^{2}$ os…
We explore the thermal light sterile neutrino situation from cosmological perspective in the $Λ\textrm{CDM} + r_{0.05} + N_{\textrm{eff}} + m^{\textrm{eff}}_{\textrm{s}}$ model using combinations of latest data sets available. Here, $r_{0.05}$ is the tensor-to-scalar ratio at the pivot scale of $k_*=0.05h$ Mpc$^{-1}$, $N_{\textrm{eff}}$ is the effective number of relativistic species during recombination, and $m^{\textrm{eff}}_{\textrm{s}}$ is the effective mass of the sterile neutrino. Among Cosmic Microwave Background (CMB) datasets, we use Planck 2015 temperature and low-$l$ ($l <$ 30) pola…
We study the possibility of simultaneously addressing neutrino phenomenology and the dark matter in the framework of inverse seesaw. The model is the extension of the standard model by the addition of two right handed neutrinos and three sterile fermions which leads to a light sterile state with the mass in the keV range along with three light active neutrino states. The lightest sterile neutrino can account for a feasible dark matter(DM) candidate. We present a $S_{4}$ flavor symmetric model which is further augmented by $Z_{4}\times Z_{3}$ symmetry to constrain the Yukawa Lagrangian. The str…
We show that mass varying neutrinos (MaVaNs) can behave as a negative pressure fluid which could be the origin of the cosmic acceleration. We derive a model independent relation between the neutrino mass and the equation of state parameter of the neutrino dark energy, which is applicable for general theories of mass varying particles. The neutrino mass depends on the local neutrino density and the observed neutrino mass can exceed the cosmological bound on a constant neutrino mass. We discuss microscopic realizations of the MaVaN acceleration scenario, which involve a sterile neutrino. We cons…
Sterile neutrinos can be generated in the early universe through oscillations with active neutrinos and represent a popular and well-studied candidate for our universe's dark matter. Stringent constraints from X-ray and gamma-ray line searches, however, have excluded the simplest of such models. In this letter, we propose a novel alternative to the standard scenario in which the mixing angle between the sterile and active neutrinos is a dynamical quantity, induced through interactions with a light axion-like field. As the energy density of the axion-like particles is diluted by Hubble expansio…
It has been proposed that in a part of the parameter space of the Standard Model completed by three generations of keV...GeV right-handed neutrinos, neutrino masses, dark matter, and baryon asymmetry can be accounted for simultaneously. Here we numerically solve the evolution equations describing the cosmology of this scenario in a 1+2 flavour situation at temperatures $T \le 5$ GeV, taking as initial conditions maximal lepton asymmetries produced dynamically at higher temperatures, and accounting for late entropy and lepton asymmetry production as the heavy flavours fall out of equilibrium an…
Models with low-scale breaking of global symmetries in the neutrino sector provide an alternative to the seesaw mechanism for understanding why neutrinos are light. Such models can easily incorporate light sterile neutrinos required by the LSND experiment. Furthermore, the constraints on the sterile neutrino properties from nucleosynthesis and large scale structure can be removed due to the non-conventional cosmological evolution of neutrino masses and densities. We present explicit, fully realistic supersymmetric models, and discuss the characteristic signatures predicted in the angular distr…
We present a framework to combine data from the latest neutrinoless double-beta decay experiments for multiple isotopes and derive a limit on the effective neutrino mass using the experimental energy distributions. The combined limits on the effective mass range between 130-310 meV, where the spread is due to different model calculations of nuclear matrix elements (NMEs). The statistical consistency (p values) between this result and the signal observation claimed by the Heidelberg-Moscow experiment is derived. The limits on the effective mass are also evaluated in a (3+1) sterile neutrino mod…
We employ state-of-the art cosmological observables including supernova surveys and BAO information to provide constraints on the mass and mixing angle of a non-resonantly produced sterile neutrino species, showing that cosmology can effectively rule out sterile neutrinos which decay between BBN and the present day. The decoupling of an additional heavy neutrino species can modify the time dependence of the Universe's expansion between BBN and recombination and, in extreme cases, lead to an additional matter-dominated period; while this could naively lead to a younger Universe with a larger Hu…
We show that the effective decay asymmetry for resonant Leptogenesis in the strong washout regime with two sterile neutrinos and a single active flavour can in wide regions of parameter space be approximated by its late-time limit $\varepsilon=X\sin(2φ)/(X^2+\sin^2φ)$, where $X=8πΔ/(|Y_1|^2+|Y_2|^2)$, $Δ=4(M_1-M_2)/(M_1+M_2)$, $φ=\arg(Y_2/Y_1)$, and $M_{1,2}$, $Y_{1,2}$ are the masses and Yukawa couplings of the sterile neutrinos. This approximation in particular extends to parametric regions where $|Y_{1,2}|^2\gg Δ$, {\it i.e.} where the width dominates the mass splitting. We generalise the f…
To quantitatively assess the impact of an eV-mass sterile neutrino on the neutrinoless double-beta ($0νββ$) decays, we calculate the posterior probability distribution of the relevant effective neutrino mass $|m^\prime_{ee}|$ in the (3+1)$ν$ mixing scenario, following the Bayesian statistical approach. The latest global-fit analysis of neutrino oscillation data, the cosmological bound on the sum of three active neutrino masses from {\it Planck}, and the constraints from current $0νββ$ decay experiments are taken into account in our calculations. Based on the resultant posterior distributions, …
We revisit the possibility of generating non-zero reactor mixing angle in a scenario where there is a sterile neutrino at the eV scale apart from the usual three sub-eV scale active neutrinos. We show that the $3\times3$ active neutrino mass matrix can possess a $μ-τ$ symmetry and can still be consistent with non-zero value of the reactor mixing angle $θ_{13}$, if this $μ-τ$ symmetry is broken in the sterile neutrino sector. We first propose a simple model based on the discrete flavour symmetry $A_4 \times Z_3 \times Z^{\prime}_3$ to realise such a scenario and then numerically evaluate the co…
We provide a microphysical model that connects neutrino oscillations to dark energy, which has predictions of Lorentz and CPT violating neutrino oscillations. We argue that the DE is a BCS condensate of flavored neutrinos. As neutrinos propigate in their own condensate they naturally have oscillations proportional to the DE energy density. All that is assumed in this model is a covariant coupling of neutrinos to gravity and a finite number density of neutrinos in the cosmic rest frame; this situation yields an attractive channel for the formation of a spin zero neutrino condensate leading to l…
We analyze the energy and zenith angle distributions of the latest 2-year IceCube dataset of upward going atmospheric neutrinos to constrain sterile neutrinos at the eV scale in the 3+1 scenario. We find that the parameters favored by a combination of LSND and MiniBooNE data are excluded at more than the 99% C.L. We explore the impact of nonstandard matter interactions on this exclusion, and find that the exclusion holds for nonstandard interactions (NSI) that are within the stringent model-dependent bounds set by collider and neutrino scattering experiments. However, for large NSI parameters …
We study in detail the impact of a light sterile neutrino in the interpretation of the latest data of the long baseline experiments NO$ν$A and T2K, assessing the robustness/fragility of the estimates of the standard 3-flavor parameters with respect to the perturbations induced in the 3+1 scheme. We find that all the basic features of the 3-flavor analysis, including the weak indication ($\sim$1.4$σ$) in favor of the inverted neutrino mass ordering, the preference for values of the CP-phase $δ_{13} \sim 1.2π$, and the substantial degeneracy of the two octants of $θ_{23}$, all remain basically u…
The muon-to-electron conversion in nuclei like aluminum, titanium and gold is studied in the context of a class of mirror fermion model with non-sterile right-handed neutrinos having mass at the electroweak scale. At the limit of zero momentum transfer and large mirror lepton masses, we derive a simple formula to relate the conversion rate with the on-shell radiative decay rate of muon into electron. Current experimental limits (SINDRUM II) and projected sensitivities (Mu2e, COMET and PRISM) for the muon-to-electron conversion rates in various nuclei and latest limit from MEG for the radiative…
Sterile neutrinos can affect the evolution of the universe, and thus using the cosmological observations can search for sterile neutrinos. In this work, we use the cosmic microwave background (CMB) anisotropy data from the Planck 2018 release, combined with the latest baryon acoustic oscillation (BAO), type Ia supernova (SN), and Hubble constant ($H_0$) data, to constrain the cosmological models with considering sterile neutrinos. In order to test the influences of the properties of dark energy on the {results} of searching for sterile neutrinos, in addition to the $Λ$ cold dark matter ($Λ$CDM…
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…
In the scenario with four generation quarks and leptons and using a 3 + 1 neutrino model having one sterile and the three standard active neutrinos with a $4 \times 4$ unitary transformation matrix, $U_{PMNS_{4}}$, we perform a model-based analysis using the latest global data and determine bounds on the sterile neutrino parameters i.e. the neutrino mixing angles. Motivated by our previous results, where, in a quark-lepton complementarity (QLC) model we predicted the values of $θ_{13}^{PMNS}=(9_{-2}^{+1})^{\circ}$ and $θ_{23}^{PMNS}=(40.60_{-0.3}^{+0.1})^{\circ}$. In the QLC model the non-triv…
The possible existence of an eV-mass sterile neutrino, slightly mixing with ordinary active neutrinos, is not yet excluded by neutrino oscillation experiments. Assuming neutrinos to be Majorana particles, we explore the impact of such a sterile neutrino on the effective neutrino mass of neutrinoless double-beta decays $\langle m \rangle^\prime_{ee} \equiv m^{}_1 |V^{}_{e1}|^2 e^{{\rm i}ρ} + m^{}_2 |V^{}_{e2}|^2 + m^{}_3 |V^{}_{e3}|^2 e^{{\rm i}σ} + m^{}_4 |V^{}_{e4}|^2 e^{{\rm i}ω}$, where $m^{}_i$ and $V^{}_{ei}$ (for $i = 1, 2, 3, 4$) denote respectively the absolute masses and the first-row…
Of late, a number of instances of neutrino flux anomalies observed at short-baselines have given traction to the hypothesis of adding new neutrino flavours to our Standard Model set, albeit ones not associated with a partnered lepton. Anomalies observed at LSND, MiniBooNE and at short distances from nuclear reactors have suggested the existence of sterile mass states with masses on the scale of $\sim1\text{eV}$, prompting further investigations. Subsequently, Fermilab is set to host a Short-Baseline Neutrino (SBN) oscillation program which will cross-check each of these anomalies by deploying …
The presence of a super-light sterile neutrino can lead to a dip in the survival probability of solar neutrinos, and explain the suppression of the upturn in the low energy solar neutrino data. In this work, we systematically study the survival probabilities in the 3+1 framework by taking into account of the non-adiabatic transitions and the coherence effect. We obtain an analytic equation that can predict the position of the dip. We also place constraints on the parameter space of sterile neutrinos by using the latest Borexino and KamLAND data. We find that the low and high energy neutrino da…
Contact interactions between sterile neutrinos and dark matter particles in a hidden sector have been suggested as a good solution to simultaneously resolve the dark matter problem and anomalies in neutrino experiments. In this non-standard particle physics model, sterile and active neutrinos change their through vacuum oscillations and matter (or Mikheyev--Smirnov--Wolfenstein) oscillations, in which the latter mechanism of flavor oscillation depends strongly on the concentration of dark matter in the Sun's core. We found that a large concentration of dark matter in the Sun's interior changes…
We perform a study of the flavour evolution in the early universe of a multi-flavour active-sterile neutrino system with parameters inspired by the short-baseline neutrino anomalies. In a neutrino-symmetric bath a "thermal" population of the sterile state would quickly grow, but in the presence of primordial neutrino asymmetries a self-suppression as well as a resonant sterile neutrino production can take place, depending on temperature and chosen parameters. In order to characterize these effects, we go beyond the usual average momentum and single mixing approximations and consider a multi-mo…
The electric dipole moment of the electron is studied in detail in an extended mirror fermion model with the following unique features of (a) right-handed neutrinos are non-sterile and have masses at the electroweak scale, and (b) a horizontal symmetry of the tetrahedral group is used in the lepton and scalar sectors. We study the constraint on the parameter space of the model imposed by the latest ACME experimental limit on electron electric dipole moment. Other low energy experimental observables such as the anomalous magnetic dipole moment of the muon, charged lepton flavor violating proces…
Cosmology and short baseline neutrino oscillation data both hint at the existence of light sterile neutrinos with masses in the 1 eV range. Here we perform a detailed analysis of the sterile neutrino scenario using both cosmological and SBL data. We have additionally considered the possibility that the extra neutrino degrees of freedom are not fully thermalised in the early universe. Even when analyzing only cosmological data we find a preference for the existence of massive sterile neutrinos in both (3+1) and (3+2) scenarios, and with the inclusion of SBL data the evidence is formally at the …
We provide a consistent framework to set limits on properties of light sterile neutrinos coupled to all three active neutrinos using a combination of the latest cosmological data and terrestrial measurements from oscillations, $β$-decay and neutrinoless double-$β$ decay ($0νββ$) experiments. We directly constrain the full $3+1$ active-sterile mixing matrix elements $|U_{\alpha4}|^2$, with $α\in ( e,μ,τ)$, and the mass-squared splitting $Δm^2_{41} \equiv m_4^2-m_1^2$. We find that results for a $3+1$ case differ from previously studied $1+1$ scenarios where the sterile is only coupled to one of…
