Probing a heavy neutral lepton in a radiative neutrino model at a muon collider

The universe is filled with particles that we can see and touch, like the electrons that power our lights and the protons that form the core of every atom. Yet, there are also ghostly particles that barely interact with anything at all. Among these are neutrinos, tiny, nearly massless particles that stream through the Earth by the trillions every second without leaving a trace. For decades, scientists believed these particles were weightless, but experiments have since proven they carry a tiny amount of mass. This discovery is a problem for the standard rules of physics, which cannot easily explain why these particles are so light while everything else is so heavy. To solve this mystery, theorists have proposed that there might be heavier, hidden cousins to these neutrinos, waiting to be discovered. If these heavy particles exist, they could be the key to understanding why the universe has mass at all, and they might reveal new forces that govern the cosmos.

A team of researchers has now taken a close look at how we might find one of these hidden particles using a future machine called a muon collider. This proposed facility would smash beams of muons—particles similar to electrons but much heavier—together at incredibly high energies. The scientists focused on a specific type of heavy particle that is predicted by a theory where neutrino mass is generated through complex, looping interactions rather than appearing directly. They wanted to see if this machine could spot a heavy neutral lepton, a particle that is electrically neutral and interacts only through the weak force, a fundamental interaction that is much weaker than the force holding atoms together. The researchers simulated what would happen if such a particle existed with a mass between that of the Z boson and the Higgs boson, two known particles that act as benchmarks for energy scales in physics.

The team ran detailed computer simulations to predict how these heavy particles would behave if they were created in the collisions. They looked for two ways these particles could be made. The first is a direct creation, where the colliding muons produce the heavy particle alongside a standard neutrino. The second is a more indirect path, where the collision first creates a Higgs boson, which then decays into the heavy particle and a neutrino. Once created, the heavy particle would not last long. It would quickly break apart into a charged particle, like an electron or a muon, and a W boson, which itself would decay into a spray of smaller particles called jets. The final scene in the detector would be a single charged particle, a pair of jets, and a significant amount of missing energy, which represents the invisible neutrinos escaping the scene.

To find this faint signal hidden among millions of ordinary collisions, the researchers trained a sophisticated computer program to act as a filter. They fed the program data from millions of simulated background events—ordinary collisions that mimic the signal but do not contain the heavy particle—and compared them to the rare events where the heavy particle was present. The program learned to spot subtle differences in the angles and energies of the particles, distinguishing the true signal from the noise. After running this analysis on a simulated dataset equivalent to one year of running at the collider, the team calculated how sensitive the machine would be. They found that the collider could set strict limits on how often these heavy particles might be produced, effectively narrowing the search for their existence.

The results showed that while the collider would be capable of probing the existence of these heavy particles within the mass range the team studied, none of the specific scenarios they tested would be ruled out by the median expected results. This means that if these heavy particles exist within the parameters they examined, they would not be detected or excluded at the expected sensitivity. The study established that the machine could probe mixing strengths as low as a few parts in a million, meaning it could detect even very weak connections between the heavy particle and the known neutrinos. Interestingly, the researchers found that while the indirect path through the Higgs boson contributed a significant portion of the potential signal—sometimes up to three-quarters of the total events—it did not dramatically improve the overall ability to set limits. This is because the events created through the Higgs boson looked very similar to the background noise in the specific ways the computer program was trained to look.

Ultimately, the study concluded that none of the specific scenarios they tested would be ruled out by the median expected results, meaning the heavy particles could still exist within the parameters they examined. However, the work provides a clear roadmap for what to look for. It demonstrates that a muon collider would be a powerful tool for hunting these elusive particles, capable of peering into a mass range that is difficult to explore with other machines. The research highlights that while the Higgs boson offers a new way to create these particles, the most effective strategy for discovery relies on a combined approach that considers all possible production methods. By mapping out exactly what the data would look like, the team has prepared the ground for future experiments that could finally reveal the hidden mass of the neutrino and the new physics that lies beyond our current understanding.