Probing eV-scale sterile neutrinos with neutrinoless double-beta decay and beta decay

Neutrinos are the most abundant massive particles in the universe, yet they remain among the most elusive. They zip through the Earth and our bodies by the trillions every second, rarely interacting with anything. For decades, experiments have confirmed that these particles have mass and that they can change their identity, a phenomenon known as oscillation. However, a complete picture of the neutrino family remains incomplete. Standard models describe three types of active neutrinos, but several experimental anomalies have hinted at the existence of a fourth, "sterile" type. Unlike the active ones, a sterile neutrino would not interact via the weak nuclear force, making it invisible to most detectors. If such a particle exists with a mass around one electron-volt, it could fundamentally alter our understanding of particle physics and the evolution of the cosmos.

The search for this hidden particle relies on two distinct but complementary methods. One approach looks for a rare nuclear process called neutrinoless double-beta decay, where two neutrons in an atom transform into two protons and two electrons without emitting any neutrinos. This process would only occur if neutrinos are their own antiparticles, a property known as being Majorana particles. The rate of this decay depends on a specific combination of the masses of the neutrinos and their internal quantum phases. The second method involves direct measurements of beta decay, where scientists analyze the energy spectrum of electrons emitted by decaying atoms to determine the total mass of the neutrinos involved. While the first method is sensitive to the quantum phases and the nature of the particles, the second provides a direct, phase-independent measurement of the mass scale.

Researchers Ruisha Yang and Jiajun Liao from Sun Yat-Sen University have combined these two lines of inquiry to test the viability of the sterile neutrino hypothesis. They focused on a specific scenario where a fourth, sterile neutrino exists with a mass in the electron-volt range. Their work addresses a critical problem: in the standard three-neutrino model, the predicted rate of neutrinoless double-beta decay has a minimum value for certain mass arrangements. However, if a sterile neutrino exists, its contribution could interfere destructively with the contributions from the three known neutrinos. This interference could cancel out the signal, driving the predicted decay rate down to zero and effectively hiding the sterile neutrino from detection by this method alone. The authors investigated whether the independent constraints from beta-decay mass measurements could prevent this cancellation, thereby exposing the sterile neutrino.

Using the most recent and precise data from neutrino oscillation experiments, including the first results from the JUNO detector, the team mapped out the possible properties of this hypothetical sterile particle. They calculated the allowed regions for the sterile neutrino's mass and its mixing strength with the known neutrinos. Their analysis revealed that imposing an upper limit on the mass of the three light neutrinos, as determined by beta-decay experiments, significantly tightens the constraints on the sterile neutrino. By restricting the mass of the active neutrinos, the beta-decay limit reduces the amount of "cancellation" the sterile neutrino can achieve. In simpler terms, if the known neutrinos are too light to provide a large signal, the sterile neutrino cannot simply cancel it out to zero; it must have specific properties to fit within the remaining narrow window of possibilities.

The study found that the outcome depends heavily on the ordering of the neutrino masses. In the scenario where the masses increase in a specific sequence, a broad range of quantum phases for the sterile neutrino is allowed when the sterile mass is small. However, as the sterile mass increases, the allowed phases narrow, favoring values near a specific point that maximizes destructive interference. In the alternative mass ordering, the constraints are even stricter. The researchers discovered that for the inverted mass arrangement, the sterile neutrino must be large enough to cancel the residual signal from the active neutrinos, but not so large that it exceeds the limits set by beta-decay measurements. Under the specific conditions they tested, including a projected future sensitivity for beta-decay mass measurements, no valid solution exists for the inverted ordering if the beta-decay mass limit is pushed below a certain threshold.

A key insight from their work involves the quantum phase of the sterile neutrino, a property that determines how its contribution interferes with the others. The authors used a geometric approach to visualize this interaction, treating the contributions of the different neutrinos as vectors in a complex plane. They showed that for the sterile neutrino to cancel the signal from the active neutrinos, its phase must align in a very specific way relative to the others. As the sterile neutrino becomes heavier, the range of phases that allow for this cancellation shrinks. If the experimental limits on the decay rate become more stringent, the allowed range of phases becomes even narrower, eventually eliminating the possibility of cancellation altogether. This geometric relationship provides a clear physical explanation for why certain combinations of mass and phase are allowed while others are forbidden.

The researchers also examined how new data from the JUNO experiment, which has improved the precision of measurements for the known neutrinos, affects these results. They found that while the updated data slightly narrows the uncertainty in the allowed regions, particularly for the inverted mass ordering, the primary driver of the new constraints is the combination of the two different experimental methods. The synergy between the neutrinoless double-beta decay limits and the beta-decay mass bounds creates a much tighter net than either method could cast alone. The study concludes that future experiments capable of measuring the beta-decay mass with high precision, such as Project 8, will be crucial. If these experiments can confirm that the light neutrinos are lighter than a specific value, they will effectively rule out the possibility of a sterile neutrino hiding through destructive interference in the inverted mass ordering scenario, and severely restrict the parameter space for the normal ordering.

This work demonstrates that the quest to find the sterile neutrino is not just about looking for a signal, but also about understanding how different pieces of the puzzle fit together. By combining the phase-sensitive information from double-beta decay with the phase-independent mass limits from beta decay, physicists can test the consistency of the sterile neutrino hypothesis with unprecedented rigor. The findings suggest that if a sterile neutrino exists in the electron-volt range, it must possess very specific properties regarding its mass, mixing strength, and quantum phase. The study does not prove the existence of the particle, nor does it definitively rule it out, but it provides a clear roadmap for how future data will either confirm its presence or close the door on this particular version of the theory. The interplay between these two experimental frontiers offers a powerful tool for probing the fundamental nature of matter and the hidden sectors of the universe.