Search for the lepton-flavor-violating decay at Belle II
Using a dataset corresponding to 428 fb of integrated luminosity, the Belle II collaboration searched for the lepton-flavor-violating decay , found no significant excess over the expected background, and set an upper limit on the branching fraction of at the 90% confidence level.
Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
In the universe of subatomic particles, there is a set of rules known as the Standard Model that describes how matter behaves. One of these rules is that a heavy particle called a tau, which is a type of lepton, should never spontaneously turn into a lighter particle called a muon while emitting a flash of light. According to our current understanding, this specific transformation is so incredibly rare that it is effectively impossible to ever see it happen. However, many physicists believe that the Standard Model is incomplete and that there are hidden forces or new particles waiting to be discovered. If a tau particle were ever observed turning into a muon and a photon, it would be a clear sign that these new laws of physics exist, opening a window into a deeper reality than we currently know.
A team of researchers using the Belle II detector at the SuperKEKB collider in Japan has conducted a massive search for this forbidden event. They analyzed a vast amount of data collected over several years, representing billions of particle collisions. To find the needle in the haystack, the team built a sophisticated computer system trained to recognize the unique signature of a tau decaying into a muon and a photon, while ignoring the millions of other collisions that look similar but are just ordinary background noise. After sifting through the data with extreme care, they found no evidence that this forbidden decay ever occurred. Instead, they calculated the strictest limit yet on how often it could possibly happen, confirming that if it does occur, it is even rarer than previously thought.
The experiment took place at a facility where beams of electrons and positrons smash into each other at nearly the speed of light. When these particles collide, they can briefly create pairs of tau particles, which are heavy cousins of the electron. These tau particles live for only a tiny fraction of a second before they decay into other, lighter particles. The researchers were looking for a very specific outcome: one tau particle turning into a muon and a single photon of light, while its partner tau particle decayed in a different, known way. The challenge is that this specific event is expected to happen so rarely that it is easily drowned out by other processes that produce similar-looking particles. For instance, a tau particle might decay into a muon and a neutrino, and a stray photon from the collision environment could accidentally be recorded, mimicking the signal the scientists were hunting for.
To separate the real signal from the noise, the team used a powerful machine-learning tool called a gradient-boosted decision tree. This tool acts like a highly experienced filter, trained on millions of simulated collisions to learn the subtle differences between the background noise and the rare event they wanted to find. It looked at many features of each collision, such as the direction the particles flew, their energy, and how they were arranged in space. By applying this filter, the team was able to reject more than 99 percent of the background events while retaining nearly 6 percent of the potential signal events. This level of precision allowed them to look at a smaller, cleaner sample of data where a signal would be much easier to spot if it existed.
The researchers examined a data sample corresponding to 428 units of collision intensity, a volume of data that allowed them to observe 393 million tau particle pairs. They focused their search on a specific region of energy and momentum where the signal would appear if it were real. After unblinding the data, meaning they finally looked at the results they had been protecting from bias, they found eight events in the target area. However, when they compared this number to what they expected from the background noise alone, the result was consistent with random chance. The background processes, which are well-understood but messy, were expected to produce about six events in that same spot, and the eight they saw fit comfortably within the range of normal statistical fluctuation.
Because no clear signal emerged, the team could not claim to have discovered the decay. Instead, they used their data to set a new upper limit on how frequently this event could possibly occur. They calculated that the probability of a tau particle turning into a muon and a photon is less than 9.5 in 100 million attempts, with a 90 percent confidence level. This means that if the decay happens at all, it is even more elusive than the previous best limit set by the earlier Belle experiment. The new limit is a significant improvement because the team achieved a much higher efficiency in spotting the signal and a much better ability to reject the background, thanks to their advanced selection methods.
This result reinforces the current Standard Model, which predicts that this decay should not happen at a detectable rate. While the search did not find the new physics some theorists had hoped for, it provides a crucial benchmark for the future. By pushing the limits of how rare this event can be, the researchers have narrowed the search space for any new theories that might explain the universe's deeper secrets. The work also demonstrates the power of the Belle II detector and its ability to handle complex data with high precision, laying the groundwork for even more sensitive searches as the experiment collects more data in the years to come. The absence of a discovery is, in itself, a powerful piece of information, telling us that the rules of the subatomic world remain stubbornly consistent with our current understanding, at least for this particular transformation.
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