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Neutrino mass variables in 3 active and 2 sterile neutrino scenario

Srubabati Goswami, Hemanth M., Debashis Pachhar, N Rajeev

Abstract

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, eV-scale sterile neutrinos are motivated by LSND and MiniBooNE results, while sub-eV sterile states with mass-squared differences at the $10^{-2}$ and $10^{-5}$~eV$^2$ scales have been proposed to address the T2K--NO$ν$A 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 $3+2$ scenario, incorporating one eV-scale sterile neutrino together with a sub-eV state, and analyze their impact on absolute-mass related observables: the sum of neutrino masses $Σ$ constrained by cosmology, the effective electron neutrino mass $m_β$ from beta decay, and the effective Majorana mass $m_{ββ}$ 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 $3+1$ 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~8, and LEGEND-1000, highlighting the complementary role of sub-eV sterile neutrinos in probing physics beyond the minimal three-flavor paradigm.

Neutrino mass variables in 3 active and 2 sterile neutrino scenario

Abstract

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, eV-scale sterile neutrinos are motivated by LSND and MiniBooNE results, while sub-eV sterile states with mass-squared differences at the and ~eV scales have been proposed to address the T2K--NOA 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 scenario, incorporating one eV-scale sterile neutrino together with a sub-eV state, and analyze their impact on absolute-mass related observables: the sum of neutrino masses constrained by cosmology, the effective electron neutrino mass from beta decay, and the effective Majorana mass 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 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~8, and LEGEND-1000, highlighting the complementary role of sub-eV sterile neutrinos in probing physics beyond the minimal three-flavor paradigm.
Paper Structure (18 sections, 23 equations, 5 figures, 8 tables)

This paper contains 18 sections, 23 equations, 5 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Neutrino Mixing Framework
  3. The Standard Three-Neutrino Paradigm
  4. The $3+2$ Sterile Neutrino Framework
  5. Classification of mass orderings in $3+2$ sterile neutrino framework
  6. Bounds on $3+2$ sterile neutrino scenario
  7. Sum of Neutrino Masses and Cosmological Constraints
  8. Effective Electron Neutrino Mass in Beta Decay
  9. Effective Majorana Mass in Neutrinoless Double Beta Decay
  10. Results and Discussion
  11. Cosmological Constraints on the $3+2$ Scenario
  12. Implications for Beta Decay in the $3+2$ Scenario
  13. Implications for Neutrinoless Double Beta Decay in the $3+2$ Scenario
  14. SSN
  15. SSI
  16. ...and 3 more sections

Figures (5)

  • Figure 1: Four mass spectra with three active and two sterile neutrinos. In the two cases above the lightest mass state is an active neutrino state and in the below the lightest state is a sterile state.
  • Figure 2: Total effective mass $\Sigma$ vs the lightest neutrino mass $m_{\rm lightest}$ in different scenarios: SSN (top-left), SSI (top-right), SNS (bottom-left), and SIS (bottom-right). The red and blue colors correspond to $\Delta m_{s_2}^2 = 10^{-2}\, \&\, 10^{-4}$$\rm eV^2$, respectively. The horizontal black dashed line corresponds to the bound from the 10 parameter cosmological (10-PCM) model.
  • Figure 3: The figure shows the variation of $m_{\beta}$ as a function of the lightest neutrino mass for the $3+2$ spectrum. The red and blue bands correspond to $\Delta m_{s_2}^2 = 10^{-2} \text{ and } 10^{-4}~\text{eV} ^2$ mass square differences. The magenta (black) dashed line shows the projected sensitivity of KATRIN (Project 8) experiment.
  • Figure 4: Variation of $m_{\beta\beta}$ as function of the light neutrino mass is shown for SSN (left panel) and SSI (right panel) scenario. The hatch-filled regions denotes variation for the standard NO and IO case. The green band represents the current KamLAND-Zen exclusion region whereas the black dashed line shows the future LEGEND-1000 sensitivity.
  • Figure 5: Variation of $m_{\beta\beta}$ as function of the light neutrino mass is shown for SNS (left panel) and SIS (right panel) scenario. The hatch-filled regions denotes variation for the standard NO and IO case. The green band represents the current KamLAND-Zen exclusion region whereas the black dashed line shows the future LEGEND-1000 sensitivity.