Neutrino mass variables in three active and two sterile neutrino scenario

Neutrino mass variables in three active and two sterile neutrino scenario

The three-flavor framework of neutrino oscillations successfully explains most experimental results, but persistent anomalies at short- and long-baseline experiments hint at the existence of additional light sterile states. In particular, electron volt-scale sterile neutrinos are motivated by LSND and MiniBooNE results, while sub-electron volt sterile states with mass-squared differences at the ten to the negative two and ten to the negative five electron volt squared scales have been proposed to address the T2K-NOVA tension and the absence of the expected upturn in the solar neutrino energy spectrum, respectively. Such sterile states are singlets under the Standard Model gauge group and mix only through their admixture with active neutrinos. In this work, we investigate the phenomenology of the three plus two scenario, incorporating one electron volt-scale sterile neutrino together with a sub-electron volt state, and analyze their impact on absolute-mass related observables: the sum of neutrino masses E constrained by cosmology, the effective electron neutrino mass M E from beta decay, and the effective Majorana mass M E G probed in neutrinoless double beta decay. We demonstrate that the presence of two sterile states can significantly modify the allowed parameter space compared to the three-flavor and three plus one frameworks, with some mass-ordering schemes already disfavored by current cosmological and laboratory limits. Finally, we assess the implications of upcoming sensitivities from KATRIN, Project Eight, and LEGEND-One Thousand, highlighting the complementary role of sub-electron volt sterile neutrinos in probing physics beyond the minimal three-flavor paradigm.

One. INTRODUCTION

The Standard Model of particle physics, formulated in the mid-1970s, has provided an extraordinarily successful description of the fundamental particles and their interactions. It has been subjected to stringent experimental tests at facilities ranging from fixed-target experiments and electron-positron colliders to the high-energy frontier explored by the Large Hadron Collider. Over the past four decades, precision measurements of electroweak observables, quark and lepton scattering processes, and rare decays have confirmed Standard Model predictions with remarkable accuracy. Nevertheless, the Standard Model is known to be incomplete. It offers no viable dark matter candidate, does not explain the observed baryon asymmetry of the universe, and, crucially, assumes neutrinos to be massless.

Within the Standard Model, neutrinos were originally postulated as exactly massless particles, appearing in three copies (V E, V P, V T) corresponding to the charged leptons. Furthermore, lepton number was assumed to be conserved independently for each lepton family. This paradigm was revised by the discovery of neutrino oscillations, which established that neutrinos possess tiny but nonzero masses and that lepton flavor is not conserved. The first compelling evidence arose from atmospheric neutrino observations at Super-Kamiokande and solar neutrino measurements at S N O. Subsequently independent confirmation of oscillations governed by the atmospheric mass scale came from accelerator experiments (K Two K, MINOS, T Two K, NOVA) and solar mass scale by reactor experiments (KamLAND). Afterwards, the non-zero value of zero one three was measured by Double Chooz, RENO, DayaBay experiments. These observations firmly establish that the three active neutrinos mix via the Pontecorvo-Maki-Nakagawa-Sakata matrix, characterized by two independent mass-squared splittings (A M two one, four M three one), three mixing angles, and one CP-violating phase.

While the three-flavor oscillation framework successfully accounts for the majority of experimental data, several anomalies persist that cannot be accommodated within this paradigm. The LSND experiment reported an excess of De events in a Du beam. Subsequently, the MiniBooNE experiment observed similar excesses in both neutrino and antineutrino modes. Gallium source experiments, GALLEX, SAGE, and BEST have measured fewer V E events than expected. Collectively, these short-baseline anomalies can be resolved considering the presence of additional oscillation frequencies, requiring at least one extra neutrino state (of one eV) beyond the three known active flavors. Since precision measurements of the invisible width of the Z boson at LEP restrict the number of light active neutrinos to three, any additional light neutrino species must be sterile, i.e., singlets under the Standard Model gauge group.

From a theoretical standpoint, sterile neutrinos arise naturally in many well-motivated extensions of the Standard Model. In seesaw frameworks, additional gauge-singlet fermions are introduced to generate small active neutrino masses, and if some of these states lie at the eV scale, they manifest as light sterile neutrinos accessible to oscillation experiments. Sterile neutrinos at other mass scales are also theoretically appealing: keV-scale sterile neutrinos can constitute warm dark matter candidates, while heavier sterile states in the GeV-TeV range play an important role in low-scale seesaw realizations and in explaining the baryon asymmetry of the universe through leptogenesis. Sterile neutrinos therefore provide a unique link between neutrino oscillation phenomenology, cosmology, and the fundamental origin of neutrino mass. This has motivated extensive studies of three plus N scenarios, where N denotes the number of sterile neutrinos mixing with the three active flavors. The simplest realization is the three plus one model, in which a single sterile neutrino introduces an additional mass-squared splitting A M two one approximately of one eV squared, providing a minimal framework to investigate active sterile mixing effects.

Early global analyses of short-baseline oscillation data indicated that simple three plus one models can partially accommodate the LSND and MiniBooNE anomalies, but they suffer from significant tensions between appearance and disappearance datasets. This motivated the exploration of more elaborate frameworks, such as three plus two scenarios, extending the spectrum by two independent mass-squared differences, A M two one and A M three one, and additional CP-violating phases can improve the overall fit quality. The increased parameters can significantly improve the description of short-baseline data and offers new possibilities for reconciling experimental anomalies. Subsequent global fits incorporating updated MiniBooNE, MINOS, reactor, and Gallium results reinforced these tensions, underscoring the difficulty of reconciling all datasets within minimal sterile neutrino models. Precision electroweak measurements, notably the invisible Z decay width, further constrain active sterile mixing and provide complementary bounds beyond oscillation data.

Reanalyses incorporating updated experimental inputs from NEOS, DANSS, and IceCube indicate that allowed sterile parameter regions can shift or be excluded at high confidence and that pragmatic fits excluding contested anomalies, such as the low-energy MiniBooNE excess, may favor regions around Am twenty-one approximately one point three to one point seven electron volt squared. Extensions involving non-standard interactions or non-unitary mixing further broaden the sterile neutrino landscape beyond simple oscillation interpretations. Recent experimental efforts continue to impose stringent constraints on sterile neutrino scenarios. High-energy atmospheric neutrino data from ANTARES exclude regions of active-sterile parameter space previously compatible with reactor experiments. Direct kinematic searches, notably KATRIN, have begun probing sterile mixing through spectral distortions in tritium beta decay. Meanwhile, updated reactor and short-baseline analyses, including Neutrino-four, suggest possible high-Am two sterile solutions, though these remain in tension with other constraints. The most recent MicroBooNE results report no evidence for light sterile neutrino oscillations at their sensitivity, further challenging minimal three plus one interpretations.

Joint analyses of oscillation and cosmological data have revealed a persistent tension between sterile neutrino interpretations of laboratory anomalies and cosmological observations. In particular, eV-scale sterile neutrinos favored by short-baseline oscillation data are strongly constrained by precision measurements of the cosmic microwave background and large-scale structure. Detailed studies of sterile neutrino thermalization in the early Universe show that active sterile mixing parameters consistent with short-baseline anomalies typically lead to nearly complete thermalization of the sterile state, yielding an effective number of relativistic species Neff approximately four, which is strongly disfavored by data. Nevertheless, these cosmological constraints can be relaxed if sterile neutrinos are produced non-thermally or are only partially thermalized in the early Universe. Such scenarios may arise in the presence of new sterile-sector interactions, modified cosmological expansion histories, or low reheating temperatures, which suppress the production of sterile states and reduce their contribution to Neff and the cosmological neutrino mass density. In these frameworks, sterile neutrinos with incomplete thermalization can remain compatible with cosmological observations while still accommodating short-baseline anomalies.

Neutrinoless double beta decay has the potential to be a powerful probe of light sterile neutrino scenarios. This study presents updated analytical bounds in the Am twenty-one-sin squared two thousand fourteen plane using the latest KamLAND-Zen data, systematically exploring the dependence on CP phases and mass ordering. The results exclude substantial regions favored by BEST and Neutrino-four and place strong tension on parameter space suggested by LSND and MiniBooNE when combined with muu disappearance constraints. The study also demonstrates that future neutrinoless double beta decay searches can provide sensitivity competitive with, or superior to, traditional oscillation experiments. Earlier, bounds on the sin squared zero fourteen - m lightest plane from the GERDA and KamLAND-Zen data were obtained.

Extensions of the three-flavor framework to include very light sterile neutrinos have also been extensively investigated. The authors have examined sub-eV sterile states with Am twenty-one approximately zero point seven to two times ten to the negative five electron volt squared, showing that they can mildly suppress the low-energy upturn in the solar ve survival probability and contribute to Neff. Precision solar neutrino measurements from Borexino enable stringent tests of such scenarios. It was shown that the tension between T two K and NOVA data can be alleviated with the inclusion of a very light sterile neutrino.

Complementary analyses suggest that introducing a massless or very light sterile state can relax cosmological bounds on neutrino masses while remaining testable in experiments such as IceCube. The implications of Sub-eV sterile neutrinos for future detectors like Hyper-Kamiokande and ESSvSB are performed. Such a study in the context of the DUNE experiment using both beam and atmospheric neutrinos has been performed. The sensitivity of the Icecube upgrade for sub-eV sterile neutrinos was investigated.

The presence of sterile neutrinos can significantly modify the effective masses probed in beta-decay and neutrinoless double beta decay experiments compared to the standard three-flavor expectations. In particular, the implications of eV-scale sterile neutrinos for the three mass observables-the cosmological sum of neutrino masses, the kinematic electron neutrino mass measured in beta decay, and the effective Majorana mass probed in neutrinoless double beta decay were analyzed within both the three plus one and three plus two sterile neutrino frameworks. The impact of a light sterile neutrino on these mass observables has also been studied more recently.

In this work, we investigate a three plus two scenario containing one eV-scale sterile neutrino, motivated by short-baseline anomalies, and one sub-eV sterile state, motivated by long-baseline and solar neutrino tensions. We focus on the impact of these sterile states on absolute neutrino mass observables: the cosmological sum of neutrino masses, the effective electron neutrino mass measured in beta decay, and the effective Majorana mass probed by neutrinoless double beta decay. We classify the possible mass spectra into four distinct ordering schemes and derive explicit expressions for these observables. Using the latest global oscillation fits and benchmark sterile parameters, we delineate the viable parameter space and discuss the implications for forthcoming experiments such as KATRIN, Project eight, LEGEND-one thousand.

The paper is organized as follows. In Section two we present the neutrino mixing framework extended to the three plus two case. Section three classifies the possible mass orderings. In Section four we discuss constraints from cosmology, beta decay, and neutrinoless double beta decay. Numerical results and discussion are given in Section five, and Section six summarizes our conclusions.