⚛️ phenomenology

Dark matter motivated sterile neutrino contribution to neutrinoless double beta decay

This paper investigates the impact of keV-scale sterile neutrinos, motivated by dark matter and constrained by the exact seesaw relation in a type-I framework, on neutrinoless double beta decay, revealing that their presence significantly modifies the effective mass by eliminating cancellation regions in the normal hierarchy and distorting the parameter space in the inverted hierarchy.

Original authors: Debashree Priyadarsini Das, Sasmita Mishra

Published 2026-01-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Debashree Priyadarsini Das, Sasmita Mishra

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A Cosmic Mystery and a Tiny Particle

Imagine the universe is a giant puzzle. We know most of the pieces (stars, planets, you, me), but there is a huge, invisible part of the puzzle called Dark Matter that we can't see, only feel through its gravity. Scientists have a strong hunch that a specific type of ghostly particle, called a sterile neutrino, might be the missing piece that makes up this Dark Matter.

This paper asks a very specific question: If these ghostly sterile neutrinos exist and are heavy enough to be Dark Matter (but light enough to be measured in a lab), how would they change the behavior of a rare atomic event called "neutrinoless double beta decay"?

The Cast of Characters

To understand the paper, let's meet the players:

The Active Neutrinos (The "Socialites"): These are the standard neutrinos we know. They interact with other particles, like socialites at a party. They are very light and come in three flavors.
The Sterile Neutrinos (The "Hermit"): These are the new, hypothetical particles. They are "sterile" because they don't interact with anything except gravity (and maybe a tiny bit of mixing with the socialites). They are the "hermits" of the particle world.
The Seesaw Mechanism (The "Balance Scale"): This is the mathematical rule the authors use. Imagine a playground seesaw. If one side (the active neutrinos) is very light, the other side (the sterile neutrinos) must be heavy to balance it. The paper uses a very precise version of this rule to calculate exactly how heavy the sterile neutrinos must be based on the known properties of the active ones.

The Experiment: The Atomic "Double-Check"

The paper focuses on Neutrinoless Double Beta Decay ( $0\nu\beta\beta$ ).

The Analogy: Imagine a nuclear atom as a house with two very shy guests (neutrons). Usually, when they leave, they take a "ticket" (an electron) and a "receipt" (an antineutrino) with them.
The Twist: In this rare decay, the two guests leave, take two tickets, but no receipts are left behind. This is impossible in standard physics unless the "receipt" (the neutrino) is its own twin (a Majorana particle).
The Goal: Scientists are building giant detectors (like KamLAND-Zen) to catch this event. If they see it, it proves neutrinos are their own twins and helps us weigh them.

What the Authors Did

The authors built a mathematical model with six neutrinos total: the three known "socialites" and three new "hermits."

Setting the Rules: They used the "Exact Seesaw" rule to force a relationship between the known neutrinos and the new ones. This meant they couldn't just pick random weights for the new particles; their masses were locked in by the math.
The Dark Matter Target: They specifically looked for a scenario where one of these new "hermit" neutrinos weighs about 7,000 times the mass of an electron (the keV scale). This is the "Goldilocks" zone for Dark Matter candidates.
The Calculation: They used a sophisticated tool called Chiral Effective Field Theory ( $\chi$ EFT).
- The Analogy: Think of the atomic nucleus as a crowded dance floor. To predict how the dance (decay) happens, you need to know if the dancers are moving slowly (long-distance) or bumping into each other quickly (short-distance). $\chi$ EFT is the rulebook that tells you how to calculate the dance steps for particles of different speeds and weights.

The Key Findings

The authors ran simulations to see how the presence of these keV-scale "hermits" would change the results of the experiment.

1. The "Cancellation" Vanishes
In standard physics (without the heavy hermits), there is a specific scenario where the contributions of the three known neutrinos cancel each other out perfectly, making the decay rate drop to almost zero.

The Paper's Claim: When they added a keV-scale sterile neutrino, this "perfect cancellation" disappeared. The decay rate didn't drop to zero; it stayed at a measurable level.
Why it matters: This means future experiments won't just see "nothing" in this scenario; they will see a signal they can actually measure.

2. The "Scattered" Pattern
When the sterile neutrinos are very heavy (like in the TeV range), the results look like a neat, organized line.

The Paper's Claim: When they introduced the lighter, keV-scale sterile neutrinos, the neat line got messy. The data points became "distorted" and "scattered" around the main trend.
Why it matters: This scattering is a unique fingerprint. If future experiments see this messy pattern instead of a clean line, it could be evidence that these specific Dark Matter particles exist.

3. The "Sweet Spot" for Detection
The authors tested three different sets of mixing angles (how much the hermits mix with the socialites).

Set 3 (The Winner): This set allowed for the keV-scale masses. They found specific combinations of angles and phases where the predicted decay rate fits within the current limits of the KamLAND-Zen experiment but is high enough to be caught by next-generation experiments like LEGEND or nEXO.

The Conclusion

The paper concludes that if Dark Matter is made of these specific keV-scale sterile neutrinos, they would leave a distinct "fingerprint" in the data of neutrinoless double beta decay.

They would break the silence of the "cancellation" zone, making the decay visible.
They would scramble the pattern of the data, making it look different from standard predictions.

Essentially, the authors are saying: "If you look closely at the next generation of these experiments, and you see this specific kind of 'messy' signal rather than a clean line or total silence, you might have just found the Dark Matter particle hiding in the neutrino sector."

Technical Summary: Dark Matter Motivated Sterile Neutrino Contribution to Neutrinoless Double Beta Decay

Problem Statement
The paper investigates the phenomenological impact of sterile neutrinos, specifically those in the keV mass range motivated by dark matter (DM) constituents, on the neutrinoless double beta ( $0\nu\beta\beta$ ) decay process. While the Standard Model (SM) extension via the type-I seesaw mechanism naturally generates active neutrino masses, the inclusion of sterile neutrinos introduces a complex parameter space involving active-sterile mixing angles and CP-violating phases. Previous studies have noted that sterile neutrinos can significantly alter $0\nu\beta\beta$ decay rates, potentially canceling SM contributions or enhancing them depending on their mass scale. However, a systematic analysis within a model-independent framework that connects the exact seesaw relation to the specific keV-scale DM motivation, while utilizing a rigorous Chiral Effective Field Theory ( $\chi$ EFT) approach for nuclear matrix elements, is required to determine the observable signatures in current and future experiments.

Methodology
The authors employ a $3+3$ model within a type-I seesaw framework, extending the SM by adding three right-handed (sterile) neutrinos corresponding one-to-one with the three active neutrinos.

Theoretical Framework: The neutrino sector is described by a $6 \times 6$ unitary mixing matrix $U$ , parametrized by 15 mixing angles and 15 phases. The analysis relies on the "exact seesaw relation," which imposes strict constraints on the sterile neutrino masses ( $M_i$ ) based on active neutrino masses ( $m_i$ ), mixing angles, and CP-violating phases. Analytical expressions for $M_i$ are derived from the condition $\sum m_i U_{ei}^2 = 0$ .
Parameter Space: The study scans a parameter space defined by three active-active mixing angles (fixed to experimental values), nine active-sterile mixing angles (varied in three distinct sets to explore different mass regimes), and five dominant CP-violating phases.
Calculation of Observables: The inverse half-life ( $t_{1/2}^{0\nu\beta\beta}$ ) and the effective neutrino mass ( $m_{ee}$ ) are calculated for the $^{136}\text{Xe}$ isotope.
$\chi$ EFT Approach: To handle the nuclear physics uncertainties and the varying mass scales of the sterile neutrinos, the authors utilize the Chiral Effective Field Theory ( $\chi$ $χ$ EFT). This approach categorizes contributions based on momentum regions:
- Hard neutrinos: Short-distance interactions for masses $> 2$ GeV.
- Soft neutrinos: Long-distance interactions involving nucleons and pions for masses between 100 MeV and 2 GeV.
- Potential/Ultrasoft neutrinos: Long-distance interactions for masses $< 100$ MeV.
  The decay amplitude is constructed as a coherent sum of contributions from active and sterile neutrinos across these momentum regions, incorporating Nuclear Matrix Elements (NMEs) calculated via the nuclear shell model.

Key Contributions and Results

Mass Range Determination: By varying the active-sterile mixing angles (Set 1: $10^{-5}-10^{-3}$ , Set 2: $10^{-4}-10^{-2}$ , Set 3: $10^{-3}-10^{-1}$ ), the authors determine the resulting sterile neutrino mass ranges. Set 3 is identified as the most relevant for the dark matter motivation, yielding sterile neutrino masses in the range of $10^{-4}$ to $10^4$ MeV (spanning the keV scale).
Modification of Effective Mass ( $m_{ee}$ ):
- Normal Hierarchy (NH): For TeV-scale sterile neutrinos (Set 1), the analysis reproduces the standard cancellation region associated with the normal hierarchy. However, the introduction of keV-scale sterile neutrinos (Set 3) eliminates this cancellation region, resulting in a finite, non-vanishing effective mass that is accessible to future experiments.
- Inverted Hierarchy (IH): The inclusion of keV-scale sterile neutrinos distorts the standard band of predictions, causing the parameter space to scatter around the main trend rather than forming a coherent band.
Half-Life Predictions: The calculated half-lives for $^{136}\text{Xe}$ $^{136} Xe$ vary significantly based on the sterile neutrino mass and mixing parameters.
- For Set 1 (heavy sterile neutrinos), the results closely resemble the SM three-neutrino contribution.
- For Sets 2 and 3 (lighter sterile neutrinos), the cancellation effects are reduced. Specifically, Set 3 shows the least cancellation, indicating an enhanced contribution to $m_{ee}$ .
Experimental Constraints: The study compares results against current bounds from KamLAND-Zen ( $t_{1/2} > 2.3 \times 10^{26}$ $t_{1/2} > 2.3 \times 1 0^{26}$ yr) and projected sensitivities of next-generation experiments (LEGEND, nEXO, CUPID).
- In the Normal Hierarchy, the parameter space largely approaches the sensitivity of future experiments.
- In the Inverted Hierarchy, while Set 1 and Set 2 results comply with current KamLAND-Zen bounds, Set 3 results (involving keV scales) show regions that are currently allowed but may be disfavored by future sensitivities, particularly in the quasi-degenerate region.

Significance and Claims
The paper claims that the exact seesaw relation, when combined with a $\chi$ EFT treatment, provides a constrained yet predictive framework for studying sterile neutrinos. The primary significance lies in demonstrating that the introduction of keV-scale sterile neutrinos—motivated by dark matter—fundamentally alters the $0\nu\beta\beta$ phenomenology compared to high-scale seesaw scenarios. Specifically, the authors assert that:

The "cancellation region" typical of the normal hierarchy in standard scenarios disappears when keV-scale sterile neutrinos are present, leading to a finite effective mass.
The inverted hierarchy scenario becomes "distorted" with scattered data points, offering a distinct signature.
The low-scale variant of the type-I seesaw (masses from $10^{-4}$ MeV to $10^8$ MeV) offers a promising, experimentally testable platform that links neutrino physics, cosmology (via DM), and collider phenomenology.
The study does not propose new experimental setups but rather interprets existing and future $0\nu\beta\beta$ search capabilities within the context of a specific, constrained theoretical model.