Measurement of $e^{+} e^{-}\to p\bar{p}$ around $\psi(2S)$ with scan method

Inside the heart of matter, where protons and neutrons are built from even smaller particles called quarks, there is a set of rules governing how these tiny pieces stick together and fly apart. These rules are described by a theory called Quantum Chromodynamics, which acts as the instruction manual for the strong force, the most powerful glue in the universe. While this theory works perfectly for some situations, it becomes incredibly difficult to solve when particles move slowly or interact in complex ways. Physicists have long been fascinated by a specific family of particles called charmonium, which are made of a heavy charm quark and its antimatter twin. These particles are heavy enough to be studied with high precision, yet light enough that the messy, complex rules of the strong force still dominate their behavior. By watching how these particles are created and how they decay into other particles, scientists hope to uncover the hidden mechanics of the strong force and see how it competes with the electromagnetic force, the same force that makes magnets stick and lightning strike.

A recent study by the BESIII Collaboration has taken a fresh look at one of these charmonium particles, known as the psi-2S. This particle is a slightly heavier version of the famous J/psi particle, and it is unstable, meaning it quickly breaks apart into other particles. The researchers were particularly interested in what happens when the psi-2S decays into a proton and an antiproton. In the world of particle physics, this decay can happen in two different ways at the same time: either through the strong force, which involves the exchange of gluons, or through the electromagnetic force, which involves a virtual photon. Because both processes can occur simultaneously, they interfere with each other, much like two ripples in a pond meeting to create a new pattern. The key to understanding this interaction lies in measuring the relative timing, or phase, between these two forces. If the timing is off, the forces might cancel each other out; if they are aligned, they might boost the result. Determining this timing is crucial because it helps physicists understand whether the strong and electromagnetic forces behave in a predictable, universal way or if there are surprises hidden in the details.

To solve this puzzle, the team did not rely on a single snapshot of data. Instead, they performed a careful scan, collecting data at nine slightly different energy levels around the mass of the psi-2S particle. This method allowed them to map out the exact shape of the resonance, which is the peak in the data that marks the presence of the particle. By analyzing how the number of proton-antiproton pairs changed as they moved through these energy levels, the researchers could separate the contributions of the strong force, the electromagnetic force, and a background process that happens even without the resonance. They used the BESIII detector, a massive instrument located at the Beijing Electron Positron Collider, to record the collisions. The detector acts like a giant, high-speed camera that tracks the paths of charged particles and measures their energy, allowing the team to identify the specific events where a proton and an antiproton were created.

After gathering a total of 495 inverse picobarns of data, the team applied strict criteria to ensure they were looking at the right events. They filtered out cosmic rays and other background noise, focusing only on pairs of particles that matched the expected behavior of a proton and an antiproton. The analysis revealed a clear signal, with the number of detected events rising and falling in a pattern that matched the theoretical predictions for the psi-2S resonance. The researchers then used a sophisticated mathematical model to fit the shape of this data, extracting the values of the underlying physical parameters. They found that the relative phase between the strong and electromagnetic amplitudes is not zero or one hundred and eighty degrees, as some simple theories might suggest, but rather sits at a value of approximately one hundred and six degrees or negative one hundred and five degrees. These two solutions represent two different ways the math can work, but both point to the same physical reality: the two forces are nearly perpendicular to each other in their timing.

With this phase measurement in hand, the team calculated the probability, or branching fraction, of the psi-2S decaying into a proton and an antiproton. They found this probability to be roughly three point two one times ten to the negative fourth, or three point four seven times ten to the negative fourth, depending on which of the two mathematical solutions is chosen. These results are slightly higher than previous measurements but remain consistent within the margin of error. The study also provided a new, precise measurement of the effective form factor, a quantity that describes the internal structure of the proton as seen by the colliding particles. The results showed a smooth curve that aligns well with earlier findings from other experiments, filling in a gap in the data around the psi-2S energy region.

The significance of these findings lies in their ability to test the limits of our current understanding. The fact that the phase is not zero suggests that the simple idea of the strong and electromagnetic forces being perfectly in sync or perfectly out of sync is incorrect. Instead, the data supports a more complex picture where these forces interact in a way that is universal across different types of particle decays. While the exact reason for this specific angle remains a mystery for theoretical physicists to explain, the experimental measurement provides a solid anchor for future theories. By confirming that the interference between these forces follows a predictable pattern, the study helps refine the models that describe how matter is built from the ground up. The work stands as a testament to the power of precision measurement, showing how carefully scanning the energy landscape can reveal the subtle, hidden rhythms of the subatomic world.