Of every 10 billion kaons that decay, roughly one does so in a particular way: it becomes a pion and a pair of neutrinos, which fly off undetected. Physicists have spent 10 years trying to count exactly how often, and on Tuesday the team at CERN responsible for the hunt announced the answer to a precision no one had reached before. The answer was, to within the error bars, what the Standard Model of particle physics predicts.

The experiment recorded 51 of the decays, after sifting through roughly 500 trillion kaons produced by a beam from the laboratory’s Super Proton Synchrotron and subtracting a background of about 14 events that merely looked right. The result, a branching ratio of 1.1 in 10 billion with an uncertainty of about 25 percent, is consistent with the theoretical prediction of 0.84 in 10 billion.

“It is the most boring possible result, and it is enormously important,” said Chiara Lombardi, the experiment’s spokeswoman, at a seminar here. “Every theory of new particles that people have written down in the past 20 years makes a prediction for this number. Most of them are now in trouble.”

The decay is prized because the Standard Model’s prediction for it is unusually clean, with theoretical uncertainty below 10 percent, while most proposed extensions to the model, including many that would explain dark matter or the imbalance of matter and antimatter in the universe, would nudge the rate up or down by a factor of two or more. A measurement that agrees with the model rules out large swaths of those possibilities, or forces them into corners where their effects are small.

Detecting the decay is notoriously difficult because the neutrinos cannot be seen; the experiment must identify a kaon going in, a single pion coming out, and nothing else, while rejecting far more common decays that mimic the signature. Piotr Zieliński, who led the analysis, said the team had spent most of the decade not on finding the signal but on proving it had not fooled itself. “For every event we kept, we threw away 10 billion,” he said. “You have to be very sure about the 10 billion.”

Markus Reinholt, a theorist at Heidelberg University who was not involved in the experiment, said the result closed one of the last wide windows for new physics at the energy scales current accelerators can reach. “We have been told for 15 years that the new particles are just around the corner. This corner, at least, is now empty,” he said. “That is not a failure. That is what a map looks like when you have explored a region.”

The team plans a successor experiment that would collect 10 times as many events by 2032, reducing the uncertainty to the level of the theory. Dr. Lombardi said she expected the model to hold there, too. “But I have been wrong before,” she said, “and I would be delighted to be wrong again.”