Probing Dark Sector Particles Coupling to Neutrinos with Double Beta Decay

This paper investigates the sensitivity of current and future neutrinoless double beta decay experiments to massive Majoron-like scalar particles coupled to neutrinos and dark sector fermions by analyzing characteristic distortions in the electron energy spectrum, ultimately projecting the ability to probe scalar-neutrino couplings as small as $|a_\nu| \approx 2\times 10^{-6}$ for sub-MeV particles.

The Gist

The Big Picture: Listening for a Whisper in a Storm

Imagine the universe is a giant, noisy room. Inside this room, atoms are constantly undergoing a very rare event called Double Beta Decay. Think of this like a specific type of atom (a heavy isotope) trying to get lighter. To do this, it usually spits out two electrons and two invisible "ghosts" called neutrinos. This is the standard, boring version of the event (called 2νββ).

Scientists have built massive, ultra-sensitive detectors to listen to this event. Their main goal is to find a "ghostly" version where no neutrinos are emitted at all (called 0νββ), which would prove neutrinos are their own antiparticles.

However, while they are listening for that specific ghost, they have collected a huge amount of data on the standard version (the one with neutrinos). This paper asks: What if, hidden inside that standard data, there are signs of something even stranger?

The New Characters: The Scalar and the Dark Fermion

The authors propose a new story involving two invisible characters from the "Dark Sector" (a part of physics we haven't seen yet):

1. The Scalar (S): Think of this as a heavy, invisible messenger particle. It's like a delivery drone that flies between particles.
2. The Dark Fermion (χ): Think of this as a mysterious, invisible passenger. It could be a candidate for Dark Matter, the stuff that holds galaxies together but we can't see.

In this new story, when an atom decays, it doesn't just spit out electrons and neutrinos. Instead, it might create this Scalar messenger (S).

• Scenario A: The messenger flies away and disappears (decays) into two neutrinos.
• Scenario B: The messenger flies away and drops off two invisible Dark Fermions (χ) instead.

The Detective Work: Finding the Distortion

How do we know if this is happening? We look at the energy spectrum.

Imagine you are listening to a choir singing a song. You know exactly how loud the song should be at every note (this is the standard decay).

• The Standard Song: The energy of the electrons comes out in a smooth, predictable curve.
• The New Story: If the atom creates that heavy Scalar messenger, it has to spend some energy to make it. This changes the song. The electrons might be slightly quieter, or the song might have a weird "kink" or a bump in the melody where the energy drops off.

The paper calculates exactly what these "kinks" and "bumps" look like for different masses of the Scalar and the Dark Fermion.

• If the Scalar is light: It's like a light drone; the song changes a little bit, but the melody is still mostly the same.
• If the Scalar is heavy: It's like a heavy anchor; the song changes drastically, creating a sharp cut-off or a new shape entirely.

The Investigation: Current and Future Experiments

The authors looked at data from current experiments (like KamLAND-Zen, NEMO-3, and GERDA) and planned future ones (like LEGEND-1000, CUPID, and nEXO).

They asked: If these invisible particles exist, could our current detectors see them?

The Findings:

1. Current Limits: Existing experiments are already good enough to rule out some versions of this theory. They have already checked the "song" and said, "We don't see the distortion you predicted for these specific heavy particles."
2. Future Potential: The future experiments are like upgrading from a basic microphone to a super-sensitive studio recording booth. The paper predicts these new machines will be able to detect these invisible particles even if they are heavier than the energy usually available in the decay (a concept called "off-shell production").
3. The Reach: They found that future experiments could detect the coupling (the strength of the connection) between these particles and neutrinos down to a level of about 2 × 10⁻⁶. This is incredibly small, but the new detectors are sensitive enough to hear it.

The "No-Go" Zones: Rules from the Universe

Before declaring victory, the authors checked the "rules of the universe" to see if their proposed particles are even allowed to exist. They looked at three big sources of evidence:

1. The Big Bang (Cosmology): If these particles existed in the early universe, they would have changed how the universe expanded and cooled. The paper shows that for certain masses, the universe would look different than it does today, so those specific masses are ruled out.
2. Supernovas: When stars explode, they release a flood of neutrinos. If our invisible messenger existed, it would steal energy from the explosion, making the star cool down too fast. The data from the famous Supernova 1987A puts strict limits on how strong the messenger can be.
3. Particle Collisions (Kaon Decays): In particle accelerators, rare decays of particles called Kaons happen. If our messenger existed, it would show up there too. The lack of such signals in Kaon data sets another limit.

The Conclusion

The paper concludes that Double Beta Decay experiments are a powerful, unique tool for hunting these dark sector particles.

• They act as a "microscope" for the dark sector, capable of seeing particles that are too heavy to be made in the decay itself but can still leave a fingerprint on the energy of the electrons.
• While other methods (like looking at the Big Bang or Supernovas) rule out some possibilities, Double Beta Decay experiments can probe a specific "sweet spot" of masses and interaction strengths that other methods miss.
• Essentially, by carefully listening to the "song" of decaying atoms, we might finally hear the whisper of Dark Matter or new physics that has been hiding in plain sight.

Technical Summary

Technical Summary: Probing Dark Sector Particles Coupling to Neutrinos with Double Beta Decay

Problem Statement
While the primary objective of current double beta decay ($\beta\beta$) experiments is the search for neutrinoless double beta decay ($0\nu\beta\beta$) to probe the Majorana nature of neutrinos, these experiments have accumulated substantial high-statistics data on the standard two-neutrino double beta ($2\nu\beta\beta$) decay. This paper investigates the potential of utilizing this existing and future $2\nu\beta\beta$ spectral data to search for physics beyond the Standard Model (BSM). Specifically, the authors explore scenarios involving a light scalar particle $S$ (a Majoron-like particle) that couples to active neutrinos and potentially to a dark sector fermion $\chi$. The presence of such particles can induce distortions in the emitted electron energy spectrum, either through the on-shell production of $S$ (if $m_S < Q$) or off-shell production (if $m_S > Q$), offering a probe for light dark sector particles that complements cosmological and astrophysical constraints.

Methodology
The authors construct simplified ultraviolet-complete models to describe the interactions between the scalar mediator $S$, active neutrinos, and exotic fermions $\chi$. Three distinct models are proposed:

1. Model I: Features Dirac neutrinos mixing with a sterile Dirac fermion $\chi$, allowing for $\nu-\chi$ mixing.
2. Model I': Imposes a discrete $Z_2$ symmetry to stabilize $\chi$, making it a viable dark matter candidate. In this model, $\chi$ does not mix with active neutrinos, and $S$ couples to both sectors independently.
3. Model II: Involves a scenario with both Dirac and Majorana exotic fermions to illustrate broader interaction possibilities.

The study calculates the differential decay rates for several processes:

• Standard Model $2\nu\beta\beta$ decay.
• Scalar emission ($0\nu\beta\beta S$) where $S$ is a real final-state particle.
• $2\nu S\beta\beta$ decay where $S$ decays into active neutrinos (interfering with the SM process).
• $2\chi S\beta\beta$ decay where $S$ decays into exotic fermions $\chi$.

The calculations utilize the closure approximation and standard nuclear matrix elements (NMEs) ($M^{0\nu}$ and $M^{2\nu}$) consistent with $0\nu\beta\beta$ literature. The authors derive analytical expressions for the phase space factors, accounting for the finite decay width of the scalar $S$ and the masses of the final-state fermions.

To assess experimental sensitivity, the authors employ a frequentist statistical approach using a $\chi^2$ analysis. They incorporate:

• Experimental parameters: Exposure, energy resolution, and systematic uncertainties for current experiments (GERDA II, NEMO-3, KamLAND-Zen) and future projects (LEGEND-1000, CUPID, nEXO).
• Theoretical uncertainties: Variations in NMEs ($M^{0\nu}$ and $M^{2\nu}$) treated as Gaussian nuisance parameters, including potential correlations between them.
• Constraints: The derived sensitivities are compared against a comprehensive set of cosmological (CMB, BBN, thermal relic density, collisional damping), astrophysical (supernova cooling), and laboratory (kaon decays) bounds.

Key Contributions and Results

1. Spectral Signatures: The paper demonstrates that the production of a scalar $S$ coupled to neutrinos and dark fermions leads to characteristic distortions in the $2\nu\beta\beta$ electron spectrum.

   • On-shell production ($m_S < Q$): Results in a spectrum similar to standard Majoron emission but shifted to lower energies due to the scalar mass.
   • Off-shell production ($m_S > Q$): Even when the scalar is too heavy to be produced on-shell, it can mediate the decay via a virtual state, leading to spectral modifications at higher electron energies ($T > Q - m_S$).
   • Dark Fermion Mass Effects: If the dark fermion $\chi$ has a non-zero mass, the spectrum exhibits a "kink" at the kinematic threshold, though this feature becomes harder to distinguish from the SM background as $m_\chi$ increases.

2. Sensitivity Projections:

   • For scalar emission ($0\nu\beta\beta S$) and scenarios where $S$ decays to neutrinos, current experiments can probe couplings $|a_\nu| \sim 10^{-2}$ to $10^{-1}$ for scalar masses up to the isotope $Q$-value.
   • Future experiments (LEGEND-1000, nEXO, CUPID) are projected to reach sensitivities of $|a_\nu| \approx 2 \times 10^{-6}$ for sub-MeV scalar particles.
   • Crucially, the analysis shows that double beta decay experiments remain sensitive to off-shell production of scalars with masses exceeding the $Q$-value of the isotopes, a regime where traditional on-shell searches lose sensitivity.

3. Comparison with Other Bounds:

   • The authors map the double beta decay sensitivities against cosmological and laboratory constraints.
   • While BBN, supernova luminosity, and rare kaon decays impose stringent limits on couplings for light scalars ($m_S \lesssim 0.6$ MeV), double beta decay experiments provide the most stringent laboratory bounds for scalar masses $m_S \gtrsim 0.6$ MeV.
   • The paper highlights that double beta decay can probe parameter spaces relevant for dark matter candidates (specifically in Model I' where $\chi$ is stable) that are complementary to direct detection and cosmological observations.

Significance and Claims
The paper claims that double beta decay experiments serve as a powerful, independent laboratory probe for light exotic physics, specifically light scalars coupled to neutrinos and dark sector fermions. The authors emphasize that:

• The high-statistics $2\nu\beta\beta$ data currently available and expected from future ton-scale experiments can be repurposed to search for BSM spectral distortions.
• These experiments can probe scalar-neutrino couplings down to $|a_\nu| \approx 2 \times 10^{-6}$, extending the reach to scalar masses significantly above the $Q$-value of the decaying isotopes via off-shell production.
• The results provide a unique window into the dark sector, offering constraints on light dark matter candidates and their interactions with neutrinos that are competitive with, and in some mass ranges superior to, cosmological bounds.

The authors modestly note that their statistical approach provides an estimate of sensitivity rather than an exact reproduction of experimental limits, and they acknowledge that the interpretation of results depends on the theoretical uncertainties of nuclear matrix elements. They also note that an independent analysis by the PandaX collaboration on a similar topic was finalized concurrently with their work.