Probing scalar-neutrino and scalar-dark-matter interactions with PandaX-4T

Using $^{136}$Xe double $\beta$-decay data from the PandaX-4T experiment, this study performs the first direct spectral search to establish the most stringent limits to date on scalar-mediated neutrino self-interactions for mediator masses below 2 MeV$/c^2$, thereby constraining models aimed at resolving the Hubble Tension and providing new bounds on scalar-mediated dark matter interactions.

The Gist

Imagine the universe is a giant, bustling party. For a long time, physicists have had a very good "guest list" and a set of rules (called the Standard Model and ΛCDM) that explain how the guests interact. But recently, they've noticed two major problems with the party:

1. The Hubble Tension: If you measure how fast the party is expanding by looking at the decorations from the very beginning of the night, you get a different speed than if you measure it by watching the guests dance right now. The numbers don't match.
2. The Small-Scale Problem: When you look closely at the smaller groups of guests (like dwarf galaxies), they seem to be moving differently than the rules predict. They are too "clumpy" or too "smooth" depending on how you look.

To fix these glitches, some scientists have proposed a new idea: maybe there's a secret invisible messenger (a particle called a scalar) that neutrinos (tiny, ghostly particles) and Dark Matter (the invisible stuff holding galaxies together) use to talk to each other.

The Experiment: PandaX-4T as a "Super-Sensitive Microphone"

The PandaX-4T experiment is like a massive, ultra-sensitive microphone buried deep underground in a mine in China. Its main job is usually to listen for Dark Matter. It is filled with liquid Xenon (a heavy gas turned liquid).

The scientists in this paper decided to use this microphone to listen for a very specific sound: Double Beta Decay.

• The Normal Sound: Usually, a Xenon atom decays by spitting out two electrons and two neutrinos. It's a predictable, rhythmic beat.
• The Secret Sound: If that secret "scalar messenger" exists, the Xenon atom might spit out the two electrons and the scalar messenger instead of the usual neutrinos.

The "Missing Energy" Mystery

Here is the clever part. The scalar messenger is invisible. It slips out of the atom and vanishes, taking some energy with it.

Think of it like this: Imagine you are at a magic show. The magician (the atom) pulls two rabbits (electrons) out of a hat. You know exactly how much energy the rabbits should have based on the size of the hat.

• Scenario A (Normal): The rabbits come out with the full expected energy.
• Scenario B (The New Physics): The rabbits come out, but they are slightly tired and have less energy than expected. Why? Because a third, invisible creature (the scalar) stole some of the energy and ran away.

The PandaX-4T team looked at thousands of these "rabbit pulls" (decay events) and measured the energy of the electrons very precisely. They were looking for that specific "tired rabbit" signature—a shift in the energy pattern that would prove the invisible messenger exists.

The Results: Silence in the Room

After listening carefully to the data from 2020 to 2022, the scientists found nothing.

• The energy of the electrons matched the "normal" prediction perfectly.
• There was no sign of the "missing energy" that would indicate the scalar messenger was stealing energy.

What does this mean?
It means that if this secret messenger exists, it must be very weak or very heavy in a way that PandaX-4T can't see yet. The team set the strictest limits to date on how strong this interaction can be for particles with a mass below 2 million electron-volts (a very light weight in particle physics terms).

The Ripple Effect: Why This Matters for the Universe

The paper connects this silence to the two big problems mentioned earlier:

1. The Hubble Tension: Some theories tried to fix the "expansion speed mismatch" by saying neutrinos were chatting with each other via this scalar messenger. But since PandaX-4T didn't find evidence of this chat, those specific theories are now in trouble. The "fix" might not work.
2. Dark Matter: If this same scalar messenger also helps Dark Matter particles talk to each other (which would fix the "small-scale galaxy" problems), then the lack of a signal for neutrinos puts a heavy constraint on Dark Matter too. It's like saying, "If the messenger isn't talking to the neutrinos, it probably isn't talking to the Dark Matter either, at least not strongly enough to solve our galaxy problems."

The Bottom Line

The PandaX-4T experiment acted like a high-tech detective, checking the energy receipts of atomic decay. They found no evidence of a "stolen energy" thief (the scalar particle).

This doesn't mean the universe is boring; it just means that the specific "secret handshake" between neutrinos and Dark Matter that some scientists hoped would fix our cosmic math problems doesn't happen in the way they thought, at least not at the energy levels PandaX-4T can detect. The search for the solution to the universe's mysteries continues, but this particular path has hit a dead end.

Technical Summary

Technical Summary: Probing Scalar-Neutrino and Scalar-Dark-Matter Interactions with PandaX-4T

Problem Statement
The standard cosmological model ($\Lambda$CDM) faces significant observational tensions, most notably the "Hubble tension" (discrepancies in Hubble constant measurements from early vs. late universe data) and "small-scale problems" (discrepancies in dwarf galaxy and cluster modeling). Proposed solutions often involve new physics, such as neutrino self-interactions (νSI) mediated by a light boson to resolve the Hubble tension, and self-interacting dark matter (SIDM) mediated by a light boson to resolve small-scale structure issues. If a single light scalar mediator ($\phi$) couples to both neutrinos and dark matter, it creates a unified framework linking these sectors. However, such models require specific coupling strengths and mediator masses that must be constrained experimentally. While double $\beta$-decay experiments are sensitive to such exotic interactions, a direct spectral search for massive scalar emission in the relevant energy range had not been performed with high sensitivity.

Methodology
This study utilizes data from the PandaX-4T experiment, located at the China Jinping Underground Laboratory (CJPL-II). The analysis focuses on the double $\beta$-decay of $^{136}$Xe using a combined dataset from the commissioning run (Run 0) and the first scientific run (Run 1), corresponding to an exposure of 37.8 kg·yr of $^{136}$Xe.

1. Theoretical Framework: The authors adopt a minimal scenario involving a real scalar field $\phi$ with mass $m_\phi$ mediating interactions between Majorana neutrinos and Dirac fermion dark matter ($\chi$). The relevant Lagrangian includes Yukawa couplings $g_{\nu\phi}$ and $g_{\chi\phi}$. The process of interest is the double $\beta$-decay accompanied by the emission of a real scalar $\phi$, which subsequently decays into undetectable particles (neutrinos or dark matter), resulting in a characteristic missing energy signature.
2. Nuclear Physics Calculations: The decay rate is calculated using a nuclear matrix element (NME) generalized for massive scalar emission. The authors approximate the NME for massive scalar emission ($|M_{\nu\phi}|$) to be equivalent to the standard neutrinoless double $\beta$-decay NME ($|M_{0\nu}| \approx 3.11$), acknowledging a $\sim$20% uncertainty from different nuclear calculation methods. The phase space factor ($G_{0\nu,\phi}$) is derived analytically, accounting for the mediator mass.
3. Experimental Analysis:
   • Event Selection: Single-site (SS) events were selected within an energy region of interest (ROI) of 20–2800 keV.
   • Background Modeling: A binned-likelihood spectral fit was performed. Background components included contributions from detector materials, solar neutrinos, liquid xenon isotopes (e.g., $^{85}$Kr, $^{214}$Pb, $^{212}$Pb), and the standard two-neutrino double $\beta$-decay of $^{136}$Xe.
   • Signal Search: The analysis scanned mediator masses ($m_\phi$) from 10 keV to 2390 keV. The signal amplitude was allowed to float in the fit, with Gaussian penalty terms applied to nuisance parameters (efficiency, background modeling).
   • Combined Constraints: For the dark matter sector, the study combines the experimental limits on $g_{\nu\phi}$ with cosmological constraints on neutrino-dark matter scattering derived from Cosmic Microwave Background (CMB) observations. These are compared against the parameter space required for SIDM to explain dwarf galaxy observations (cross-section per unit mass $\sigma_T/m_\chi \sim 0.1-10$ cm$^2$/g).

Key Results

• Spectral Search: No significant excess of events above the expected background was observed in the 20–2800 keV range.
• Coupling Limits: The study sets the most stringent laboratory limits to date on the neutrino-scalar coupling constant ($g_{\nu\phi}$) for mediator masses between 0.8 MeV and 2 MeV. For masses below 1.3 MeV, these results provide complementary constraints to those derived from Big Bang Nucleosynthesis (BBN).
• Hubble Tension Implications: The derived limits challenge neutrino self-interaction models proposed to alleviate the Hubble tension. Specifically, models requiring "moderately interacting" ($g_{\nu\phi} \sim 10^{-2}$) or "strongly interacting" ($g_{\nu\phi} \sim 10^{-1}$) neutrinos for a mediator mass of $\sim$1 MeV are excluded by the PandaX-4T data.
• Dark Matter Constraints: By assuming the same scalar mediates SIDM, the authors derive upper bounds on the dark matter-scalar coupling ($g_{\chi\phi}$) by combining the PandaX-4T limit on $g_{\nu\phi}$ with CMB constraints on $\nu$-$\chi$ scattering. The analysis indicates that if $g_{\nu\phi}$ saturates the current experimental upper limit, the resulting allowed region for $g_{\chi\phi}$ becomes largely incompatible with the SIDM parameter space inferred from small-scale structure observations. To maintain consistency, $g_{\nu\phi}$ would need to be at least three orders of magnitude lower than the current upper limit.

Significance and Claims
The paper claims to present the first direct spectral search for neutrino-scalar interactions in the 20–2800 keV energy range using $^{136}$Xe double $\beta$-decay data. The primary significance lies in:

1. Exclusion of Hubble Tension Models: The results place significant constraints on scalar-mediated neutrino self-interaction models intended to resolve the Hubble tension, effectively ruling out the parameter space where such interactions are strong enough to impact cosmological evolution at the relevant scales.
2. Unified Constraints: The work demonstrates how combining laboratory double $\beta$-decay data with cosmological observations can rigorously test unified models of neutrino and dark matter interactions mediated by a light scalar.
3. Future Prospects: The study highlights the potential of double $\beta$-decay data to probe fundamental properties of neutrinos and dark matter, suggesting that ultra-sensitive observatories like PandaX can continue to push boundaries in physics beyond the Standard Model.

The authors note that while their results conflict with specific models addressing the Hubble tension, alternative explanations (e.g., early dark energy, modified recombination) remain viable. The paper concludes that the tension between small-scale structure observations, the Hubble constant, and the PandaX constraints persists, potentially pointing to additional new physics beyond the simple scalar mediator scenario.