ALP Distributions from Hadron Structure

High-energy particle colliders are often imagined as giant smashing machines, where beams of protons crash together to break matter apart and reveal the fundamental building blocks of the universe. But there is another way to look at these collisions. When a proton travels at nearly the speed of light, it is not just a solid lump of matter; it is surrounded by a cloud of invisible fields and fleeting particles that it radiates as it moves. These radiated particles can act like their own beams, colliding with particles from the other side of the accelerator without the main protons ever touching. This concept allows physicists to treat a hadron collider as a factory for creating new, rare particles, such as axion-like particles. These hypothetical particles are cousins to the famous axion, a particle proposed to solve deep mysteries in physics, but unlike the axion, they can have a wide range of masses and interact with other matter in different ways. Understanding how these particles are produced is crucial for designing experiments that might finally detect them.

A recent study by Shuai Zhao at Tianjin University investigates exactly how the internal structure of a proton shapes the production of these axion-like particles. For a long time, physicists often treated protons as simple, point-like dots when calculating how many of these new particles they might produce. This simplification assumes the proton has no size or internal parts, much like treating a planet as a single point when calculating its gravity from far away. However, a proton is actually a complex object made of quarks and gluons, and it has a specific shape and size that changes how it interacts. The researcher set out to see what happens when you stop treating the proton as a simple dot and start accounting for its true, messy structure. The findings reveal that this internal structure dramatically changes the predictions, suppressing the number of particles produced by a massive factor and showing that the way these particles are created depends heavily on the specific types of heavy quarks inside the proton.

The study focuses on two main ways these particles can be created. The first is the "elastic" process, where the proton stays intact after radiating the particle, merely recoiling like a ball that has been hit. The second is the "resolved" process, where the radiation comes from the individual quarks inside the proton, effectively breaking the proton apart or probing its deep interior. The paper demonstrates that if you treat the proton as a simple point, your calculations suggest the number of particles produced grows endlessly as the energy of the collision increases. But when you use the real, measured shape of the proton, this growth stops. The internal structure acts as a natural brake. The research shows that the proton's shape causes the production rate to level off, or saturate, at a specific point. This means the old, simple calculations vastly overestimate how many particles should be created.

To prove this, the author compared the simple point-like model against two more realistic models based on actual physics. One model uses a concept called the pion pole, which relies on the known properties of pions, a type of particle closely related to the proton's structure. The other uses data from lattice quantum chromodynamics, a powerful computer simulation method that calculates the behavior of quarks and gluons from first principles. Both of these realistic models show that the number of particles produced is roughly one thousand times smaller than the simple point-like model predicts. This is a huge difference, equivalent to the difference between a loud shout and a whisper. The study confirms that the proton's internal structure is not a minor detail; it is the dominant factor that determines how many of these particles are created in an elastic collision.

The research also uncovers a surprising sensitivity to the specific types of heavy quarks inside the proton. Even if two different theories predict the exact same behavior for the proton at low energies, they can predict wildly different results for the high-energy, resolved process. The author constructed two different sets of rules for how the proton's heavy quarks interact. Both sets matched the known low-energy behavior perfectly, yet when applied to the high-energy collisions, they produced results that differed by a factor of ten thousand. One set predicted a very small amount of particle production, while the other predicted a massive amount. This finding is critical because it means that simply knowing how the proton behaves at low energies is not enough to predict what will happen in a high-energy collider. The specific arrangement of heavy quarks matters immensely, and measuring the resolved radiation could be the key to distinguishing between different theories of how these particles interact.

The implications of these findings extend to how scientists design their searches for new physics. If researchers rely on the old, simplified models, they might look for signals in the wrong places or with the wrong expectations. The study shows that to accurately predict what a collider will see, one must carefully separate the signals from the intact proton from those where the proton breaks apart. An intact proton leaves a clean signature, while a broken proton creates a messy background. The paper argues that these two types of events cannot be described by a single, universal formula. Instead, they require distinct calculations that account for the proton's shape and the specific quark flavors involved. By doing so, physicists can better understand the "flux" of particles radiating from the beam and design experiments that are sharp enough to catch the faint signals of these elusive axion-like particles.

Ultimately, this work refines our understanding of the proton not just as a target, but as a source. It moves the field away from treating subatomic particles as simple points and toward a more nuanced view where their internal complexity dictates the outcome of high-energy collisions. The results suggest that the path to discovering new particles lies in paying close attention to the details of hadron structure. The massive suppression of the elastic signal and the extreme sensitivity of the resolved signal to heavy quark configurations mean that future experiments must be incredibly precise. The study provides the necessary theoretical tools to make these predictions, ensuring that when the next generation of colliders turns on, scientists will know exactly what to look for and how to interpret the data they find.