Neutrino decays as a natural explanation of the neutrino mass tension

This paper demonstrates that neutrino decays into massless BSM particles with lifetimes of 0.01–1 Gyr can reconcile the tension between cosmological upper bounds and oscillation lower limits on the total neutrino mass by relaxing the bound to 0.23 eV, whereas decays into lighter neutrinos fail to resolve this discrepancy.

The Gist

Imagine the universe as a giant, cosmic scale. For decades, scientists have been trying to weigh the three types of ghostly particles called neutrinos. These particles are so light and elusive that they barely interact with anything, yet they are everywhere.

Here is the problem: The scale is broken, or at least, it's giving two conflicting readings.

The Great Neutrino Tension

On one side of the scale, we have particle physicists. They have built massive underground detectors and watched neutrinos "oscillate" (change flavors) as they travel. These experiments tell us that neutrinos must have some weight. Based on how they change, the lightest they could possibly be is about 0.06 eV (a tiny, tiny amount of mass).

On the other side, we have cosmologists. They look at the entire history of the universe—the Cosmic Microwave Background (the afterglow of the Big Bang) and the distribution of galaxies. They use the universe itself as a giant lab to weigh these particles. Their latest, most precise measurements say: "Neutrinos must be even lighter than 0.06 eV." In fact, their data is so sensitive that it sometimes suggests the neutrinos might have negative mass, which is physically impossible.

This is a crisis. The universe seems to be saying neutrinos are lighter than the laws of physics (as we know them) allow them to be.

The Proposed Solution: The "Cosmic Escape Artist"

The authors of this paper suggest a clever workaround: What if neutrinos aren't staying put?

Imagine a room full of heavy balloons (the neutrinos). If the balloons stay there, they weigh down the floor (the universe's expansion and structure). But, what if some of these balloons have tiny holes and slowly leak air, turning into invisible gas that floats away unnoticed?

In this paper, the authors propose that neutrinos might be decaying (falling apart) into invisible particles that we can't see. They call these invisible particles "Dark Radiation."

They tested two specific scenarios:

Scenario A: The "Vanishing Act" (Decaying into Dark Radiation)

In this version, a heavy neutrino decays into a lighter, invisible particle and a massless ghost particle (called a Majoron).

• The Analogy: Imagine a heavy backpack (the neutrino) suddenly turning into a feather and a puff of smoke. The heavy weight is gone.
• The Result: Because the heavy neutrinos disappear and turn into light, invisible stuff, they stop weighing down the universe as much as they used to. This allows the cosmological "scale" to read a higher total mass (up to 0.23 eV) without breaking the laws of physics.
• The Outcome: This fixes the tension! The universe's weight limit is now high enough to match what the particle physicists see. The "leaky balloon" theory makes the two sides agree.

Scenario B: The "Passing the Buck" (Decaying into Lighter Neutrinos)

In this version, a heavy neutrino decays into a lighter neutrino (one of the other types) plus the invisible ghost particle.

• The Analogy: Imagine a heavy backpack being swapped for a slightly lighter backpack, plus a puff of smoke. The total weight in the room hasn't changed much; it's just shifted around.
• The Result: Because the mass is still there (just in a lighter form), the universe still feels the weight. In fact, the authors found that this scenario makes the tension worse or barely helps at all. It's like trying to fix a heavy floor by swapping a 50lb weight for a 40lb weight; the floor is still too heavy.
• The Outcome: This version doesn't solve the problem. Depending on the specific arrangement of the neutrinos, it might even make the cosmological limits stricter.

The Bottom Line

The paper concludes that if neutrinos are indeed "escaping" into invisible dark radiation (Scenario A), it solves the mystery of why the universe seems to think they are too light. It restores harmony between the particle experiments and the cosmic observations.

However, if they are just swapping places with lighter neutrinos (Scenario B), the problem remains. The authors also note that while this is a mathematically sound idea, it requires the neutrinos to decay at a very specific speed—fast enough to matter, but not so fast that we would have seen it in other experiments like supernova explosions.

In short: Neutrinos might be playing hide-and-seek with the universe, turning into invisible ghosts to hide their true weight. If they do, everything adds up. If they don't, we still have a mystery to solve.

Technical Summary

Technical Summary: Neutrino Decays as a Natural Explanation of the Neutrino Mass Tension

Problem Statement
A significant tension has emerged between cosmological upper bounds on the total neutrino mass ($\sum m_\nu$) and lower limits derived from neutrino oscillation experiments. Recent cosmological data, specifically the combination of DESI DR2 Baryon Acoustic Oscillation (BAO) measurements and Planck PR3 Cosmic Microwave Background (CMB) likelihoods, constrain $\sum m_\nu \lesssim 0.06$ eV (95% CL). This limit is in conflict with the minimum mass required by oscillation data, which implies $\sum m_\nu > 0.059$ eV for Normal Ordering (NO) and $\sum m_\nu > 0.098$ eV for Inverted Ordering (IO). In some analyses, the cosmological posterior even peaks in the unphysical negative mass region, creating a tension of up to $3\sigma$. While various cosmological solutions (e.g., dynamical dark energy, modified recombination) have been proposed, this paper investigates whether new physics within the neutrino sector—specifically invisible neutrino decays—can resolve this discrepancy.

Methodology
The authors perform a cosmological analysis of late-time invisible neutrino decays using the latest DESI DR2 and Planck PR3 datasets. The study utilizes a modified version of the Einstein-Boltzmann solver CLASS, extended to model warm species decaying into Dark Radiation (DR) or lighter neutrinos. To overcome the computational prohibitive nature of solving the full phase-space evolution for decaying neutrinos in Markov Chain Monte Carlo (MCMC) analyses, the authors employ neural network emulators built with CONNECT to approximate the solver's output.

The analysis considers two distinct decay scenarios based on the nature of the decay products:

1. Scenario A (Decays into DR): Heavy active neutrinos ($\nu_H$) decay into a massless sterile neutrino ($\nu_4$) and a massless scalar ($\phi$). The products behave as a Dark Radiation fluid. The authors assume three degenerate neutrino masses ($\sum m_\nu = 3m_{\nu_H}$) and a common decay rate.
2. Scenario B (Decays into Lighter SM Neutrinos): Heavy neutrinos decay into lighter active neutrinos ($\nu_L$) and a massless scalar ($\phi$). This scenario respects the measured mass splittings ($\Delta m^2_{31}$ and $\Delta m^2_{21}$). The system is approximated as a two-state system due to the hierarchy of decay rates, distinguishing between Normal Ordering (B1: $\nu_3 \to \nu_{1,2} + \phi$) and Inverted Ordering (B2: $\nu_{1,2} \to \nu_3 + \phi$).

The analysis assumes neutrinos decay after becoming non-relativistic ($\tau_\nu > H^{-1}(z_{nr})$) and that the Dark Radiation population is produced solely via these decays. The baseline dataset includes Planck TT, EE, TE power spectra, CMB lensing, and DESI DR2 BAO, excluding supernovae data and newer Planck PR4/ACT DR6 likelihoods to avoid complications with non-linear corrections.

Key Contributions and Results

• Decays into Dark Radiation (Scenario A):
  The authors find that invisible decays into DR significantly relax the cosmological bound on the total neutrino mass. For neutrino lifetimes $\tau_\nu \sim 0.01 - 1$ Gyr, the 95% CL upper bound on $\sum m_\nu$ is relaxed from $0.062$ eV (stable case) to $0.23$ eV. This relaxation is driven primarily by the increased constraining power of DESI DR2 data and the use of a prior $\sum m_\nu > 0$ rather than the oscillation-motivated lower bound.

  • Tension Resolution: This updated bound restores full agreement with oscillation data. The tension with NO is reduced from $\sim 2.1\sigma$ to $\sim 1.3\sigma$, and with IO from $\sim 3.0\sigma$ to $\sim 1.5\sigma$.
  • Model Compatibility: The required neutrino-Majoron couplings ($g \sim 10^{-14}$) and masses are consistent with minimal neutrino mass models based on a spontaneously broken $U(1)_{\mu-\tau}$ symmetry and GUT-scale seesaw mechanisms, evading current constraints from SN1987A, Big Bang Nucleosynthesis, and CMB free-streaming.

• Decays into Lighter Neutrinos (Scenario B):
  In contrast to Scenario A, decays into lighter active neutrinos provide no significant relaxation of the mass bounds and, in some cases, tighten them.

  • Normal Ordering (B1): The bound remains nearly unchanged ($\sum m_\nu < 0.102$ eV vs. $0.1$ eV stable).
  • Inverted Ordering (B2): The bound actually tightens ($\sum m_\nu < 0.132$ eV vs. $0.139$ eV stable).
  • Mechanism: This result arises from a competition between two effects: the reduction of the Hubble rate boost and matter power spectrum suppression (which weakens the mass imprint) versus a reduction in the free-streaming cutoff wavenumber ($k_{nr}$). In Scenario B, the decay produces a high-energy tail in the phase-space of the lighter neutrino, delaying its transition to the non-relativistic regime and lowering $k_{nr}$. This enhances the sensitivity of CMB lensing to neutrino masses, particularly in the IO case, leading to tighter constraints.

Significance and Claims
The paper claims that invisible neutrino decays into Dark Radiation offer a theoretically well-motivated mechanism to reconcile the cosmological mass tension with oscillation data without invoking exotic cosmological parameters. The authors emphasize that this framework possesses a concrete Lagrangian formulation connected to neutrino mass generation mechanisms (Majoron models).

Crucially, the paper highlights a new cosmological signature: a reduction in the free-streaming cutoff scale ($k_{nr}$) for decays into lighter neutrinos ($\nu_i \to \nu_j + \phi$), a feature previously unpointed out in the literature. The authors assert that a full Boltzmann treatment is essential for analyzing these decays, as simplified estimates fail to capture the interplay of competing effects that can lead to tightened bounds.

The study concludes that while decays into DR effectively resolve the tension, decays into lighter SM neutrinos do not. The authors suggest that upcoming tomographic weak-lensing surveys (e.g., Euclid, LSST) could independently determine neutrino mass and lifetime by detecting these characteristic imprints on the matter power spectrum, and that future direct detection of the Cosmic Neutrino Background (C$\nu$B) could further constrain or rule out these decay scenarios.