Flavorful Lepton-Number-Violating SMEFT: Loop Mixing, $0\nu\beta\beta$ and Rare Meson Decays

The universe is built on a set of invisible rules that govern how particles interact, decay, and transform. For decades, physicists have relied on a standard model to describe these rules, a framework that has successfully predicted almost every particle interaction observed in laboratories. However, this model has a glaring gap: it cannot explain why the universe is made of matter rather than antimatter, nor can it fully account for the mysterious, tiny masses of neutrinos. One of the most promising ways to bridge this gap is to look for a specific violation of a fundamental conservation law called lepton number. In the standard model, the total number of leptons—particles like electrons and neutrinos—remains constant in any reaction. If scientists could find a process where this number changes by two units, it would be a smoking gun for new physics, potentially revealing that neutrinos are their own antiparticles and offering clues to the origin of mass.

Two distinct types of experiments have emerged as the primary hunters for this elusive signal. The first involves watching for a rare nuclear event called neutrinoless double beta decay, where an atomic nucleus transforms into a different element by emitting two electrons but no neutrinos. This process is sensitive to the behavior of the lightest particles and the first generation of matter. The second approach involves watching heavy particles, like kaons and B-mesons, as they decay into pions or other particles while emitting invisible energy carried away by neutrinos. Traditionally, physicists viewed these two experimental avenues as probing completely separate corners of the particle world. The nuclear decay was thought to be a window into the first generation of matter, while the rare meson decays were seen as probes for the heavier second and third generations. It was assumed that if new physics existed in the heavy sector, it would remain hidden from the nuclear experiments, and vice versa.

A new study challenges this separation, revealing that the two worlds are far more connected than previously thought. Researchers from institutions in the Czech Republic, Spain, and the United States have performed a detailed analysis showing that quantum effects at the loop level—subtle interactions that occur when particles briefly fluctuate into virtual states—act as a bridge between these seemingly isolated sectors. They found that the flavor structure of new physics, which determines how it interacts with different generations of particles, does not stay fixed as it evolves from high energies down to the scales we can measure. Instead, the interactions of heavy quarks can radiatively feed into the interactions of light quarks, and vice versa. This means that an experiment designed to look for heavy-particle physics can, through these quantum loops, become sensitive to the same new physics that drives neutrinoless double beta decay.

The team investigated a specific set of theoretical interactions known as dimension-7 operators, which represent the first layer of new physics beyond the standard model that can generate lepton-number violation. They approached the problem from two directions. First, they used a "bottom-up" method, assuming that a single type of new interaction exists and calculating how it would manifest across different experiments. They considered two scenarios: one where the new physics treats all lepton flavors equally, and another where every possible combination of quark and lepton flavors is independent. In the scenario where flavors are treated equally, they discovered that neutrinoless double beta decay is actually a much more powerful probe than previously believed. It can constrain new physics involving heavy second- and third-generation quarks, even though those heavy quarks do not appear directly in the nuclear decay. This happens because the heavy quarks mix with lighter ones through quantum loops, effectively bringing their influence into the nuclear experiment.

In the more complex scenario where every flavor combination is independent, the picture becomes even richer. Here, the rare decays of kaons and B-mesons remain the most sensitive tools for certain specific flavor combinations, particularly those involving the transition of a strange quark to a down quark or a bottom quark to a strange quark. However, for many other combinations, the nuclear decay experiment still provides the strongest limits. The study demonstrates that the relative importance of these experiments is not fixed; it depends entirely on the specific flavor structure of the new physics. If the new interactions are lepton-flavor universal, the nuclear decay dominates. If they are highly specific to certain flavors, the meson decays take the lead. This interplay means that to fully understand the nature of new physics, scientists cannot rely on a single experiment; they must combine data from nuclear decays and rare meson decays to map out the full flavor landscape.

To confirm these findings, the researchers also constructed a "top-down" example using a specific theoretical model involving scalar leptoquarks, which are hypothetical particles that carry both quark and lepton properties. They tested six different ways these particles could couple to the known matter in the universe. In some of these configurations, the new physics would produce a signal in meson decays at the tree level, which is the most direct and strongest interaction. In others, the signal would only appear through the loop mixing effects they had identified. The results showed a dramatic shift in sensitivity: in cases where the direct signal was absent, the loop-induced signal in neutrinoless double beta decay became the leading constraint, pushing the possible mass scale of the new particles from the range of a few tera-electronvolts up to hundreds of tera-electronvolts. This suggests that even if a new particle is too heavy to be produced directly in current colliders, its indirect influence could be detected through these subtle quantum connections.

The implications of this work are profound for the future of particle physics. It suggests that the search for lepton-number violation is not a series of disconnected experiments but a unified effort where the results of one experiment inform the interpretation of another. The study rules out the idea that these observables probe independent sectors of new physics; instead, they are deeply intertwined through the machinery of quantum mechanics. By accounting for these loop effects, physicists can now interpret experimental limits more accurately, avoiding false conclusions about where new physics might hide. The research highlights that the sensitivity of neutrinoless double beta decay extends far beyond the first generation of matter, reaching deep into the heavy quark sector, while rare meson decays provide the necessary complementary view to pin down the specific flavor patterns of any potential discovery.

Ultimately, this paper provides a roadmap for how to interpret the next generation of experimental data. As experiments like NA62, KOTO, Belle II, and various neutrinoless double beta decay searches improve their sensitivity, the ability to distinguish between different flavor structures will become critical. The study shows that a positive signal in one of these experiments would not just point to the existence of new physics, but would immediately constrain the properties of that physics in the other sectors. The synergy between nuclear and flavor physics is no longer just a theoretical possibility but a necessary tool for discovery. By treating the flavor and scale evolution of these interactions simultaneously, scientists can turn what appeared to be unrelated measurements into a powerful, complementary set of probes capable of identifying the scale and structure of the next layer of reality.