Flavor Tomography of Long-Lived Neutrino-Mass Mediators: Probing the Neutrino Mass Ordering at the HL-LHC

For decades, physicists have been trying to solve a puzzle hidden inside the most abundant massive particles in the universe: neutrinos. These ghostly particles zip through everything, rarely interacting with matter, yet they hold the key to understanding why the universe has mass. We know that neutrinos come in three different "flavors"—electron, muon, and tau—and that they can change from one type to another as they travel. This shapeshifting ability, known as oscillation, proves they have mass. However, a fundamental question remains unanswered: which of the three neutrino types is the heaviest, and which is the lightest? Scientists call this the "mass ordering." Current experiments trying to answer this by watching neutrinos travel long distances through the Earth are stuck in a loop. Their measurements are tangled with another unknown variable, a phase related to how matter and antimatter behave differently, making it impossible to tell the mass order apart with certainty.

Now, a new approach proposes to solve this mystery not by watching neutrinos travel, but by catching a rare, slow-moving particle that might be created in high-energy collisions at the Large Hadron Collider. This method relies on a specific type of theoretical model where the same force that gives neutrinos their mass also creates a heavy, long-lived particle. If such a particle exists and decays inside the detector, it would leave behind a trail of electrons and muons. The researcher found that the ratio of these electrons to muons acts like a fingerprint. It does not matter how heavy the new particle is or how strongly it interacts; the number of electrons compared to muons is fixed entirely by the known properties of neutrino mixing. This ratio changes dramatically depending on whether the universe follows a "normal" or "inverted" mass order, offering a clean, direct way to distinguish between the two possibilities without the confusion that plagues current experiments.

The core of this discovery lies in a concept called "flavor tomography," which essentially means taking a picture of the neutrino mass spectrum by counting the flavors of particles produced when a heavy mediator decays. In the models the author studied, the heavy particle that mediates the neutrino mass is the same one that decays into the electrons and muons we can detect. Because of a mathematical relationship known as the Casas–Ibarra parametrization, the messy details of the new physics cancel out when you look at the ratio of electrons to muons. What remains is a number determined solely by the known mixing angles of neutrinos. If the mass ordering is normal, the theory predicts that for every electron produced, there will be roughly seven muons, resulting in a ratio of about 0.14. If the ordering is inverted, the situation flips completely: there will be far more electrons than muons, with a ratio of about 2.11. This is a difference of more than a factor of fifteen, a separation so large that it is easy to distinguish between the two scenarios even with a relatively small number of observed events.

What makes this finding particularly powerful is its independence from the unknown variables that have stalled other experiments. The ratio of electrons to muons does not depend on the mysterious CP-violating phase that confuses long-baseline oscillation studies. It also does not depend on the specific mass of the new heavy particle or the strength of its interactions, provided the particle is long-lived enough to be detected by the new timing sensors being built for the High-Luminosity Large Hadron Collider. These sensors, capable of measuring time with a precision of thirty picoseconds, can identify particles that arrive slightly later than expected, filtering out the overwhelming background of ordinary collisions. The researcher calculated that if such a signal is found, counting just twenty-five of these delayed electron or muon events would be enough to determine the mass ordering with high statistical confidence.

The study rigorously tested this idea across four different theoretical frameworks, including the Scotogenic model, the Type-III seesaw, and inverse seesaw mechanisms. In every case, the prediction held true: the ratio of electrons to muons was fixed by the neutrino data alone. The author also checked how robust this result would be against uncertainties in the known neutrino parameters, the absolute mass scale of neutrinos, and the efficiency of the detectors. They found that even with the worst-case variations in these factors, the gap between the normal and inverted predictions remained wide enough to be decisive. The only requirement is that the heavy particle decays into a charged lepton and an invisible partner, and that the detector can accurately measure the time delay of the resulting track.

This approach offers a complementary path to the JUNO experiment, which aims to solve the mass ordering problem by observing neutrinos from nuclear reactors. While JUNO relies on the vacuum oscillations of antineutrinos, this collider method relies on the decay products of a heavy mediator. Both methods are independent of the confusing CP phase, but the collider approach has a unique advantage: it directly probes the mechanism that generates neutrino mass. If a signal is observed and the ratio matches the prediction, it would not only solve the mass ordering puzzle but also confirm that the heavy particle is indeed the mediator responsible for giving neutrinos their mass. The author emphasizes that this is a testable hypothesis for the upcoming run of the collider, where the necessary timing infrastructure is already under construction. If the universe contains these long-lived mediators, the answer to the mass ordering question could be found simply by counting the electrons and muons they leave behind.