The eV-Scale Sterile Neutrino and Neutrinoless Double Beta Decay

This paper investigates eV-scale sterile neutrino mixing schemes (3+1, 1+3, and 2+2) in light of short-baseline anomalies and global fit data, finding the 3+1 model most viable and constraining the sterile neutrino mass to approximately 4.7 eV for both normal and inverted hierarchies through neutrinoless double beta decay analysis.

The Gist

Imagine the universe is a grand orchestra, and for a long time, physicists believed there were only three types of instruments playing the music of matter: the electron, the muon, and the tau neutrinos. These are the "active" musicians; they interact with everything around them, like a violinist playing loudly in a concert hall.

But recently, some scientists noticed a strange glitch in the sheet music. In short experiments (like LSND and MiniBooNE), they saw more "electron" notes appearing out of nowhere than the three-instrument theory allowed. It was as if a fourth, invisible instrument had joined the band, playing a note that the active musicians couldn't hear, but the detectors could.

This paper by Priya, Simran, and B.C. Chauhan is like a detective story trying to solve the mystery of this "ghostly" fourth instrument, which they call a Sterile Neutrino.

The Mystery: The "Ghost" in the Machine

The authors are investigating a specific type of ghost: a Sterile Neutrino that is heavy enough to weigh about 1 electron-volt (eV). To put that in perspective, if an active neutrino is as light as a feather, this sterile one is like a heavy stone.

They are asking: If this heavy ghost exists, how does it change the music of the universe, and can we prove it's there?

The Three Suspects (Mixing Schemes)

To solve the mystery, the team looked at three different ways the four neutrinos (3 active + 1 sterile) could be arranged in the "band lineup." Think of these as different seating charts for the orchestra:

1. The 3+1 Scheme (The Winner): Three light active musicians sit together, and one heavy sterile musician sits in a separate, heavy section.
2. The 1+3 Scheme: One light musician sits alone, while three heavy ones (including the sterile one) sit together.
3. The 2+2 Scheme: Two light musicians and two heavy ones (one active, one sterile) sit in pairs.

The Verdict: After running the numbers, the authors found that the 3+1 Scheme is the only one that makes sense with the current data. The other two arrangements (1+3 and 2+2) are like trying to fit a square peg in a round hole; they clash with what we know about the universe's energy budget and the "cosmic background noise" (cosmological bounds).

The Big Test: The "Silent Decay"

How do we catch this ghost? The authors use a very rare event called Neutrinoless Double Beta Decay (0νββ).

Imagine two atoms in a room trying to get rid of extra weight. Usually, they throw out two electrons and two invisible neutrinos (like throwing trash out a window). But in this special "neutrinoless" version, the atoms throw out the electrons but keep the neutrinos inside.

This is only possible if the neutrino is its own antiparticle (a Majorana particle). If the sterile neutrino exists, it acts like a hidden bridge that helps this "silent decay" happen. The authors calculated how heavy this ghost must be for this bridge to work, given the limits set by current experiments like KamLAND-Zen (which is like a super-sensitive microphone listening for this silent decay).

The Findings: How Heavy is the Ghost?

The team did a massive amount of math, mixing in data from global experiments and future predictions. Here is what they found:

• The Weight Limit: If this sterile neutrino exists, it cannot be too heavy. The authors calculated that its mass must be less than about 4.75 eV (for the "Normal" arrangement of neutrinos) or 4.72 eV (for the "Inverted" arrangement).
• The Total Band Weight: If you add up the weight of all four neutrinos (the three active ones plus the ghost), the total cannot exceed roughly 4.8 eV.
• The "Goldilocks" Zone: Interestingly, the math suggests the sterile neutrino's mass is likely in a very narrow, specific range (around 1.0 to 1.5 eV) to fit all the clues perfectly.

The Plot Twist: The KATRIN Experiment

There is a catch. The authors also looked at the KATRIN experiment, which is currently trying to weigh the lightest neutrino directly.

• Current Status: The ghost neutrino fits with what KATRIN has seen so far.
• Future Trouble: However, KATRIN is getting better. The authors predict that once KATRIN reaches its full sensitivity (its "super-vision"), it will likely rule out this specific scenario. It's like finding a suspect who fits the description, but then the police get a better photo that proves the suspect couldn't have been at the scene.

The Conclusion

This paper is a roadmap for the future. It tells us:

1. The 3+1 arrangement is the most likely way a sterile neutrino could exist.
2. We have a very tight leash on how heavy this ghost can be (under ~4.8 eV total).
3. We are on the edge of a breakthrough. New experiments (like PROSPECT, NEOS, and future 0νββ detectors) are currently gathering data.

The Big Picture:
Think of the Standard Model of physics as a puzzle with three missing pieces. This paper suggests the fourth piece might be a heavy, invisible "sterile" piece. While the current puzzle looks like it fits, the picture might change as soon as the new, sharper lenses (future experiments) come online. If the sterile neutrino is real, it would rewrite the history of the universe, explaining why neutrinos have mass and perhaps even why the universe is made of matter instead of antimatter.

For now, the ghost is still hiding in the shadows, but the authors have drawn a very precise map of where to look next.

Technical Summary

Here is a detailed technical summary of the paper "The eV-Scale Sterile Neutrino and Neutrinoless Double Beta Decay" by Priya, Simran Arora, and B. C. Chauhan.

1. Problem Statement

The paper addresses the persistent anomalies observed in short-baseline neutrino experiments (such as LSND, MiniBooNE, Gallium, and NEUTRINO-4), which suggest the existence of a fourth, "sterile" neutrino with a mass in the eV scale. These anomalies cannot be explained by the standard three-neutrino ($3\nu$) mixing framework.

The core challenge is to determine if these anomalies are consistent with **neutrinoless double beta decay ($0\nu\beta\beta$)** constraints. The$0\nu\beta\beta$process is a critical probe for lepton number violation and the Majorana nature of neutrinos. Current experiments (e.g., KamLAND-Zen) have set stringent upper limits on the effective Majorana mass ($m_{\beta\beta}$). The authors investigate whether various active-sterile mixing schemes can simultaneously explain the short-baseline anomalies and remain consistent with$0\nu\beta\beta$ limits, cosmological bounds, and future experimental sensitivities (e.g., KATRIN).

2. Methodology

The authors employ a phenomenological analysis combining global fit data from neutrino oscillation experiments with constraints from $0\nu\beta\beta$ and cosmology.

• Mixing Schemes: The study evaluates three primary mixing configurations involving three active neutrinos and one sterile neutrino ($N_s$):

  • 3+1: Three light active states, one heavy sterile state.
  • 1+3: One light active state, three heavy states (including the sterile).
  • 2+2: Two light active states, two heavy states (one active, one sterile).
  • Note: The paper analyzes sub-schemes within these frameworks for both Normal Hierarchy (NH) and Inverted Hierarchy (IH).

• Theoretical Framework:

  • The effective Majorana mass for four neutrinos ($m_{\beta\beta}^{4\nu}$) is calculated using an extended PMNS matrix that includes mixing angles with the sterile neutrino ($\theta_{14}, \theta_{24}, \theta_{34}$) and new CP-violating phases.
  • The formula used is:
    $$m_{\beta\beta}^{4\nu} = \left| \sum_{j=1}^{4} U_{ej}^2 m_j \right|$$
  • The analysis incorporates the third mass-squared difference ($\Delta m^2_{41}$ or $\Delta m^2_{4s}$) required to explain the LSND/MiniBooNE anomalies, exploring the range $1.1 - 2.4 , \text{eV}^2$(with a best fit at$1.73 , \text{eV}^2$) and the NEUTRINO-4 best fit ($\sim 7.3 , \text{eV}^2$).

• Data Inputs:

  • Oscillation Parameters: Updated global fit values for $\Delta m^2_{solar}$, $\Delta m^2_{atm}$, and mixing angles ($\theta_{12}, \theta_{13}, \theta_{23}$) at $1\sigma$and$3\sigma$ confidence levels.
  • Mass Constraints: The lightest neutrino mass ($m_{lightest}$) is varied from $10^{-5}$to$1$ eV.
  • Experimental Limits: Constraints from KamLAND-Zen, GERDA, CUORE, LEGEND, and nEXO on $m_{\beta\beta}$; KATRIN limits on absolute neutrino mass; and cosmological bounds on the sum of neutrino masses ($\Sigma m_\nu$).

3. Key Contributions

• Viability Assessment of Schemes: The authors systematically rule out the 1+3 and 2+2 schemes. They demonstrate that these configurations are incompatible with cosmological bounds (sum of masses) or fail to reproduce the required mass-squared differences for the LSND anomaly without violating other experimental constraints.
• Validation of the 3+1 Scheme: The 3+1 scheme is identified as the only viable framework that can accommodate the short-baseline anomalies while remaining consistent with current $0\nu\beta\beta$ limits.
• Quantitative Constraints: The paper provides precise numerical constraints on the sterile neutrino mass ($m_4$) and the sum of four neutrino masses ($\Sigma_{4\nu}$) for both Normal and Inverted Hierarchies at $1\sigma$and$3\sigma$ confidence levels.
• Future Sensitivity Analysis: The study evaluates the impact of future KATRIN sensitivity (targeting $0.2$ eV) on these models, showing that current allowed regions may be ruled out by upcoming data.

4. Key Results

The analysis yields the following specific constraints for the 3+1 scheme:

• Sterile Neutrino Mass ($m_4$):

  • At the $3\sigma$ level, the mass of the sterile neutrino is restricted to:
    • Normal Hierarchy (NH): $m_4 \leq 4.75$ eV.
    • Inverted Hierarchy (IH): $m_4 \leq 4.72$ eV.
  • Numerically calculated ranges are tighter (approx. $1.04 - 1.55$eV at$3\sigma$), but the graphical upper limits allow up to ~4.7 eV.

• Sum of Neutrino Masses ($\Sigma_{4\nu}$):

  • NH: Limited to $1.11 - 4.81$eV ($3\sigma$).
  • IH: Limited to $1.14 - 4.78$eV ($3\sigma$).

• Hierarchy Discrimination:

  • The limits on the sum of four neutrino masses are nearly identical for both NH and IH. Consequently, the study concludes that four-neutrino studies cannot distinguish between the Normal and Inverted mass hierarchies based on current $0\nu\beta\beta$ and mass sum constraints alone.

• NEUTRINO-4 Scenario:

  • When using the NEUTRINO-4 best-fit parameters ($\Delta m^2_{14} \approx 7.3$ eV$^2$), the effective Majorana mass remains compatible with KamLAND-Zen limits. However, the required lightest neutrino mass ($m_{lightest}$) is compatible with current KATRIN limits but would be ruled out by the proposed future sensitivity of KATRIN.

5. Significance

• Theoretical Consistency: The paper provides a rigorous test of the 3+1 sterile neutrino hypothesis against the most stringent low-energy constraints ($0\nu\beta\beta$). It confirms that while the 3+1 model is the most promising candidate for explaining short-baseline anomalies, it is highly constrained by the non-observation of neutrinoless double beta decay.
• Experimental Guidance: The results highlight a potential tension between short-baseline anomalies and future absolute mass measurements. If KATRIN reaches its projected sensitivity and finds no neutrino mass in the predicted range, the 3+1 explanation for LSND/MiniBooNE anomalies would be severely challenged.
• Model Selection: By definitively ruling out 1+3 and 2+2 schemes, the work narrows the search space for Beyond Standard Model (BSM) physics, focusing future experimental efforts on the 3+1 parameter space.
• Majorana Nature: The study reinforces that if eV-scale sterile neutrinos exist and are Majorana particles, their contribution to $0\nu\beta\beta$ must be carefully balanced with mixing angles and phases to avoid exceeding current experimental half-life limits.

In conclusion, the paper establishes that the 3+1 scheme is the only viable active-sterile mixing model under current constraints, but it predicts a sterile neutrino mass and total mass sum that are on the verge of being tested (and potentially excluded) by the next generation of neutrino mass and oscillation experiments.