Joint probes of dark matter annihilation from neutrino detectors and CMB targets

This paper proposes that combining neutrino detector observations with measurements of the effective number of neutrino species and cosmic microwave background spectral distortions can uniquely identify and constrain dark matter annihilation into neutrinos with MeV-GeV masses, addressing the ambiguity of current neutrino excess signals.

The Gist

Imagine the universe as a giant, expanding balloon. Inside this balloon, there is a mysterious, invisible substance called Dark Matter. For decades, scientists have been trying to figure out what this stuff is. One popular idea is that Dark Matter particles occasionally bump into each other and vanish, turning into a burst of neutrinos—tiny, ghostly particles that zip through everything without leaving a trace.

This paper proposes a clever new way to catch these ghosts, not just by looking for them in one place, but by checking two different "receipts" left behind by the universe itself.

The Mystery: A Ghostly Excess

Recently, a giant underwater telescope in Japan called Super-Kamiokande (think of it as a giant, deep-sea camera) noticed something strange. It saw a few more "ghost" particles (electron antineutrinos) than it should have. It's like hearing a faint, extra tap on a window in a quiet house.

Scientists are excited but cautious. Is this just a glitch? Is it a known cosmic event? Or is it a sign of Dark Matter? The problem is, looking at the neutrinos alone isn't enough to solve the mystery. It's like finding a footprint in the sand; you know something walked there, but you don't know who or how they got there.

The Problem: The "Missing Inventory"

Here is the tricky part. If Dark Matter is annihilating (disappearing) into neutrinos at the rate needed to create that extra "tap" Super-Kamiokande heard, there's a math problem.

Imagine you have a bank account. If you withdraw money every day at a very high rate, your account should be empty by now. But if you look at your bank statement, you still have a full balance. That's the Density-Deficit Problem.

• The Reality: If Dark Matter is disappearing that fast to make neutrinos, it should have run out long ago.
• The Fix: To explain why we still have Dark Matter today, there must have been a "refill" event in the past. Something must have produced extra Dark Matter in the middle of the universe's history to top up the account after the withdrawals started.

The Solution: Checking Two Receipts

The authors of this paper say: "Let's not just look at the neutrinos. Let's look at the receipts the universe kept when that 'refill' happened."

They propose checking two specific cosmic receipts:

1. The "Neutrino Count" Receipt ($N_{eff}$):
   When Dark Matter was being "refilled," it dumped extra energy into the universe. This energy acts like extra radiation. Scientists can measure the "effective number of neutrino species" ($N_{eff}$) in the Cosmic Microwave Background (CMB)—the afterglow of the Big Bang. If Dark Matter was refilled, this number should be slightly higher than expected. It's like checking the water level in a pool; if someone dumped a bucket of water in, the level rises.

2. The "Heat Distortion" Receipt ($\mu$-distortion):
   When the extra Dark Matter annihilated into neutrinos, those neutrinos sometimes crashed into other particles, creating pairs of electrons and positrons. These particles heated up the universe's background light (photons). This heating left a specific "smudge" or distortion in the spectrum of the CMB light, called a $\mu$-distortion.

   • Analogy: Imagine the CMB is a perfectly smooth sheet of ice. If you throw hot rocks (energy from Dark Matter) onto it, the ice melts and refreezes in a slightly warped shape. That warp is the $\mu$-distortion.

The Big Discovery: The Sweet Spot

The authors ran the numbers to see if these two receipts would match what the neutrino detectors (like Super-Kamiokande, JUNO, and others) are looking for.

They found a perfect overlap for Dark Matter that is relatively light (between the mass of a few millionths of a proton and a few billionths of a proton).

• The Sweet Spot: If Dark Matter is in this specific weight range and is annihilating fast enough to explain the neutrino "taps," it must have caused a "refill" event.
• The Result: That "refill" event would have left a clear mark on the CMB (a higher neutrino count and a heat distortion).

Why This Matters

This paper suggests a powerful strategy: Don't just look for the ghost; look for the footprints it left on the floor.

If we see the extra neutrinos in the detectors and we see the corresponding "smudge" and "extra count" in the Cosmic Microwave Background, we can be almost certain that:

1. Dark Matter is indeed annihilating into neutrinos.
2. There was a specific event in the early universe that replenished the Dark Matter supply.

Currently, the "smudge" ($\mu$-distortion) is too faint for our current telescopes to see clearly, but future missions (like PIXIE or Voyage 2050) are being designed specifically to find it. The paper shows that if these future telescopes come online, they could team up with neutrino detectors to finally solve the mystery of the "missing inventory" and confirm the existence of this specific type of Dark Matter.

In short: The paper argues that to solve the puzzle of the extra neutrinos, we need to look at the universe's "thermal history" (the CMB) as well as the neutrinos themselves. If the two stories match, we win.

Technical Summary

Technical Summary: Joint Probes of Dark Matter Annihilation from Neutrino Detectors and CMB Targets

Problem Statement
Dark matter (DM) annihilation into Standard Model (SM) neutrinos represents a poorly constrained channel in indirect detection, offering a potential explanation for recent hints of an electron antineutrino excess observed by Super-Kamiokande (SK). However, a significant theoretical challenge arises: to produce observable neutrino fluxes in current and future terrestrial detectors (such as JUNO, Hyper-Kamiokande, and DUNE) for DM masses in the MeV–GeV range, the annihilation cross-section $\langle \sigma v \rangle$ must often exceed the standard thermal freeze-out value ($\sim 2.2 \times 10^{-26} \text{ cm}^3/\text{s}$).

If DM annihilates at such a high rate, the relic abundance resulting from standard thermal freeze-out would be insufficient to account for the observed DM density today, creating a "density-deficit problem." Resolving this deficit requires an intermediate stage of DM production (or depletion followed by production) occurring after thermal freeze-out but before matter-radiation equality. The paper posits that while terrestrial neutrino detectors can observe the resulting flux, they cannot uniquely determine the cosmological origin or the specific production history required to solve the density deficit.

Methodology
The authors employ a model-independent analysis to investigate the cosmological signatures of large DM annihilation rates into neutrinos, specifically focusing on the MeV to 10 GeV mass range. The methodology involves:

1. Parameterization of Intermediate Production: Instead of constructing specific particle physics models (e.g., neutrinophilic DM), the authors adopt a benchmark parameterization for the DM yield $Y_\chi \equiv n_\chi/s$. They assume an intermediate stage where the DM abundance is enhanced by a factor $f_\chi$ over a temperature interval $[T_{end}, T_{pro}]$, as illustrated in their Figure 1. This approach isolates the effects purely from DM annihilation to neutrinos.
2. Neutrino Injection and $N_{eff}$: They solve the Boltzmann equation for the distribution of neutrinos injected by DM annihilation after neutrino decoupling ($T \lesssim 10$ keV). They calculate the resulting energy density contribution to the radiation sector, quantified as a shift in the effective number of neutrino species, $N_{eff}^{inj}$.
3. CMB Spectral Distortions: The authors analyze the conversion of injected neutrino energy into electromagnetic energy via electron-positron pair production. They consider two channels:
   • Pair Annihilation: $\nu_{inj} + \bar{\nu}_{inj} \to e^+ + e^-$.
   • Co-annihilation: $\nu_{inj} + \bar{\nu}_{bg} \to e^+ + e^-$.
     They calculate the heating rate of the photon bath and the resulting primordial $\mu$-distortion in the Cosmic Microwave Background (CMB) spectrum, which forms during the epoch $12 \text{ eV} \lesssim T \lesssim 0.47 \text{ keV}$.
4. Comparative Analysis: The study maps the detection windows of these cosmic observables ($N_{eff}^{inj}$ and CMB $\mu$-distortion) against the projected sensitivities of neutrino detectors (SK, JUNO, HK, DUNE) in the $(m_\chi, \langle \sigma v \rangle)$ parameter space.

Key Contributions and Results

• Resolution of the Density-Deficit via Cosmic Probes: The paper demonstrates that the intermediate DM production required to resolve the density-deficit problem naturally generates observable shifts in $N_{eff}$ and CMB spectral distortions. These signals serve as complementary probes to terrestrial neutrino flux measurements.
• MeV-Scale Overlap (Low Mass): For DM masses in the range $m_\chi \in [10, 100]$ MeV, the authors find a significant overlap between the parameter space accessible to JUNO and Hyper-Kamiokande and the sensitivity of future CMB experiments (e.g., Simons Observatory) to $N_{eff}^{inj}$. In this regime, the CMB $\mu$-distortion is generally too small to be detected given current $N_{eff}$ constraints.
• GeV-Scale Overlap (High Mass): For $m_\chi \gtrsim 500$ MeV, the co-annihilation channel becomes dominant. The authors show that the CMB $\mu$-distortion becomes a sensitive probe, potentially reaching the forecasted sensitivity of future missions like (Super-)PIXIE and Voyage 2050. In this high-mass regime, the $\mu$-distortion and $N_{eff}^{inj}$ can jointly probe the same parameter space accessible to HK and DUNE.
• Kinematic Thresholds: The study identifies a kinematic threshold of $m_\chi \gtrsim 500$ MeV for efficient co-annihilation to produce CMB distortions, dependent on the production temperature $T_{pro}$. Below this mass, pair annihilation dominates but yields a $\mu$-distortion that remains below future detection limits if $N_{eff}$ constraints are satisfied.
• Interpretation of SK Excess: The analysis suggests that if the SK antineutrino excess is confirmed and corresponds to a cross-section requiring intermediate production (i.e., $\langle \sigma v \rangle$ significantly above the thermal freeze-out value), it would imply a measurable shift in $N_{eff}$ and potentially a CMB $\mu$-distortion, linking the terrestrial anomaly to early Universe cosmology.

Significance and Claims
The paper claims that joint probes using neutrino detectors and CMB experiments offer a natural and necessary strategy to test the hypothesis of large DM annihilation rates into neutrinos. The authors emphasize that their results are conservative, representing "irreducible contributions" from the annihilation process itself, independent of specific model-dependent extra contributions.

The significance lies in the ability to:

1. Break Degeneracies: Distinguish between astrophysical backgrounds and new physics origins for neutrino excesses by cross-referencing with cosmological constraints.
2. Constrain Production Histories: Use the correlation between neutrino fluxes and cosmic observables ($N_{eff}$, $\mu$) to probe the underlying mechanism of intermediate DM production (parameterized by $f_\chi$).
3. Validate the Density-Deficit Solution: Demonstrate that resolving the density-deficit problem for MeV-GeV DM via intermediate production is not just a theoretical necessity for high cross-sections but is accompanied by distinct, testable cosmological signatures.

The authors conclude that while specific particle physics models may introduce additional effects, the strategy of combining terrestrial neutrino data with CMB spectral distortion and $N_{eff}$ measurements provides a robust, model-independent framework for investigating DM annihilation into neutrinos.