Measurement of the p$-\Sigma^+$ correlation function in pp collisions at $\sqrt{\textit{s}}=13$ TeV

Deep inside the heart of matter, where protons and neutrons bind together to form the nuclei of atoms, there exists a hidden layer of complexity involving particles known as hyperons. These are cousins to the familiar protons and neutrons, but they carry a property called "strangeness," which makes them heavier and unstable. Understanding how hyperons interact with ordinary protons is not just a matter of curiosity about the subatomic world; it is essential for solving a cosmic mystery. In the dense, crushing cores of neutron stars, where matter is packed so tightly that a single teaspoon would weigh billions of tons, physicists believe hyperons must appear. However, if they interact too strongly in certain ways, they would cause these stars to collapse under their own gravity, preventing them from reaching the massive sizes astronomers actually observe. To resolve this conflict, scientists need precise measurements of how hyperons and protons push or pull on each other, a task that has remained difficult because hyperons decay almost instantly and are hard to catch in the act of interacting.

A researcher using the ALICE detector at the Large Hadron Collider in Geneva has finally taken a major step forward by measuring this interaction for the first time. They focused on a specific pair: a proton and a positively charged hyperon called the $\Sigma^+$. To study them, they collided protons together at an energy of 13 trillion electronvolts, creating a shower of new particles. Among the billions of collisions, they looked for high-multiplicity events, where the debris was so crowded that the chances of finding a proton and a $\Sigma^+$ hyperon born close together were significantly higher. The challenge was that the $\Sigma^+$ decays immediately into a proton and a neutral pion, which then vanishes into two photons. Because the $\Sigma^+$ lives for such a fleeting moment, they could not track it directly. Instead, they used a clever reconstruction method, tracking the visible proton and one of the photons while mathematically deducing the path and momentum of the missing second photon to pinpoint exactly where the $\Sigma^+$ had been.

Once they had identified millions of these pairs, they analyzed how often they appeared close together compared to how often they would appear if they were just random neighbors. If the particles did not interact, their proximity would be purely a matter of chance. However, the data revealed a clear pattern: the protons and $\Sigma^+$ hyperons were avoiding each other in a specific way that indicated a repulsive force. By comparing their measurements against a wide range of theoretical models, they were able to rule out several long-standing predictions. Specifically, they found that the interaction is not strongly repulsive, as some older theories suggested, nor is it attractive, as other models proposed. Instead, the data points to a very weak repulsion. This subtle push is strong enough to distinguish between competing theories, effectively narrowing the field of possibilities for how matter behaves at these extreme densities.

The significance of this finding lies in its ability to constrain the equation of state for dense matter, which describes how pressure changes as density increases. The results suggest that the repulsive force between protons and $\Sigma^+$ hyperons is just right to prevent the collapse of neutron stars while still allowing them to exist at the massive scales observed in the universe. They calculated the scattering parameters, which are essentially the numbers that define the strength and range of this interaction, with a high degree of confidence. Their analysis shows that the interaction is consistent with a specific class of models based on meson exchange, while excluding others that predict either too much attraction or too much repulsion. This measurement provides a rare, direct glimpse into the forces that govern the most extreme environments in the cosmos, turning a theoretical puzzle into a measured reality.