Inclusive weak decays of the $J/\psi$: single-charm decay and weak annihilation

The subatomic world is populated by particles that are far too small to see, yet they follow strict rules of interaction that govern how matter is built and how it changes. Among these particles are quarks, the fundamental building blocks that stick together to form larger particles like protons and neutrons. Sometimes, quarks of different types pair up to create short-lived, heavy particles called quarkonia. One of the most famous of these is the J/psi, a particle made of a charm quark and its antimatter twin, the anticharm quark. For decades, physicists have known that the J/psi is a restless particle that usually decays by shedding its energy through strong or electromagnetic forces, processes that happen almost instantly. However, there is a much rarer possibility: the weak force, which is responsible for radioactive decay, can also cause the J/psi to fall apart. Because this weak decay is so incredibly rare compared to the other ways the particle disappears, it has been difficult to predict exactly how often it happens or to catch it in the act. Understanding this process is important because it tests our fundamental theories about how quarks behave when they are bound together, offering a glimpse into the subtle interplay between the forces that hold matter together and the forces that break it apart.

For a long time, the standard way to estimate how often the J/psi decays via the weak force was to treat its two internal quarks as if they were independent passengers in a car, each waiting to get out on their own. In this old view, the charm quark would decay on its own, and the anticharm would do the same, with the total rate simply being the sum of these two separate events. This approach suggested that the J/psi would decay weakly about once in every one hundred million attempts. However, this simple picture ignores the fact that the two quarks are tightly bound and can interact directly with each other. A new study by researchers at the Hangzhou Institute for Advanced Study challenges this old estimate by looking at the J/psi not as two separate parts, but as a single, unified system where the quarks can annihilate each other. By using a sophisticated mathematical tool known as the optical theorem, which allows physicists to calculate the total rate of all possible decay outcomes at once, the team has constructed a much more complete picture of what happens inside the particle.

The researchers found that the old method of adding up independent decays misses the most significant part of the story. In reality, the charm and anticharm quarks can meet and destroy each other, a process called pair annihilation, which opens up a vast number of new ways for the particle to disappear. This annihilation is not a single event but a complex interaction involving different types of force carriers. The study reveals that the dominant way the J/psi decays weakly is actually through this annihilation, specifically through a mechanism involving the neutral current, where the quarks exchange a Z boson, a heavy particle that carries the weak force but does not change the electric charge of the particles involved. This neutral-current contribution is so large that it dwarfs the simple decay of the individual quarks. Furthermore, the researchers calculated how the different ways the quarks interact interfere with one another, finding that the interplay between the charged and neutral forces creates a delicate balance that is highly sensitive to the energy scale at which the calculation is performed.

When the team combined all these effects—the independent decays, the annihilation, and the interference between them—they arrived at a new prediction for how often the J/psi should decay weakly. Their calculation suggests that the branching fraction, which is the probability of this specific decay happening compared to all other ways the particle can decay, is approximately 7.96 times ten to the power of negative eight. This number is slightly higher than the old estimate of one times ten to the power of negative eight, but more importantly, it shows that the annihilation process accounts for about 77 percent of the total weak decay rate. This means that the old method, which only looked at the quarks decaying separately, was missing the vast majority of the action. The study also broke down the results by the types of particles produced, showing that the most common outcome involves the creation of particles without any charm quarks, a direct result of the annihilation process.

The researchers were careful to quantify how sure they are about these numbers. They identified two main sources of uncertainty. The first comes from the mathematical approximations used in the calculation, which they estimated by varying the energy scale of their model. This variation produced a range where the true value likely sits, with the upper limit being significantly higher than the central value due to the sensitive nature of the interference between forces. The second source of uncertainty comes from the complex internal structure of the J/psi itself, which is difficult to calculate precisely. By varying the inputs related to the particle's internal motion and binding energy, they found a second margin of error. Even with these uncertainties, the conclusion remains robust: the weak decay of the J/psi is dominated by the annihilation of its quark pair, not by the independent decay of its parts.

This work provides a crucial theoretical target for experimentalists who are searching for these rare decays. Experiments at facilities like the BESIII detector have already collected billions of J/psi particles, looking for signs of these weak decays, but have so far only been able to set upper limits on how often they occur. The new prediction suggests that these rare events are happening at a rate that is within reach of current and future experiments. If the experimentalists can observe the decay at the rate predicted by this new calculation, it will confirm that our understanding of how heavy quarks interact and annihilate is correct. If they find a different rate, it could signal that there are new, unknown forces or particles at play. For now, the study stands as a detailed map of a hidden corner of the subatomic world, showing that even in a particle as well-studied as the J/psi, there are still profound interactions waiting to be fully understood. The researchers emphasize that while their calculation is a major step forward, it is not the final word; future work will need to include more precise corrections and a deeper look at the internal structure of the particle to refine these numbers further.