Displaced tracks as a signal of dark matter co-annihilation: a case study using inert doublet model at $e^+e^-$ collider

The universe is filled with a mysterious substance called dark matter. We cannot see it, touch it, or smell it, yet we know it is there because its gravity holds galaxies together and bends the path of light. It makes up about a quarter of everything in existence, but despite decades of searching, no experiment has ever caught a single particle of it. Scientists have tried to find it by listening for it to bump into atoms deep underground or by looking for the flash of light it might make when it crashes into other dark matter particles in space. So far, these efforts have come up empty. This silence has led researchers to consider a different possibility: perhaps dark matter is not a single, lonely particle, but part of a hidden family. In this scenario, dark matter might have heavier, charged relatives that are almost the same weight but slightly different. If these relatives exist, they could help explain how much dark matter we see today, but they would also leave behind a very specific, strange signature if we could catch them in a machine.

A team of physicists has recently explored how to find these hidden relatives using a future type of particle collider. They focused on a specific theory called the Inert Doublet Model, which suggests that dark matter is a neutral particle that is nearly identical in weight to a charged partner. Because their weights are so close, the charged partner cannot decay into the dark matter particle easily. Instead, it lives for a surprisingly long time before it finally breaks apart. When it does break, it releases the dark matter particle and a tiny, slow-moving piece of debris. In a normal particle detector, this would look like a charged particle that travels a short distance, suddenly stops, and vanishes, leaving behind a faint, soft track that ends abruptly. This is known as a "disappearing track." The researchers simulated how this would look in a future electron-positron collider, a machine that smashes electrons and their antimatter counterparts together at incredibly high energies. They found that if these hidden particles exist, this specific type of machine would be the perfect place to spot them, offering a much clearer view than current experiments can provide.

The team began by mapping out the rules of their model to ensure it matched what we already know about the universe. They checked that the particles they proposed would produce the correct amount of dark matter observed in the cosmos and that they would not have been detected by previous experiments. They identified four specific scenarios, or "benchmark points," where the particles would have masses ranging from about 560 to 1,200 times the mass of a proton. In these scenarios, the difference in weight between the dark matter and its charged partner is very small, often less than the weight of a single atomic nucleus. This tiny difference is crucial because it forces the charged particle to live longer than usual. The researchers calculated that for these specific masses, the charged particle would travel anywhere from a few centimeters to nearly a meter inside the detector before it decayed. This distance is long enough to be measured but short enough to happen inside the tracking equipment.

To see if these particles could be found, the researchers simulated millions of collisions at a future collider with an energy of 3 tera-electronvolts. They watched for the specific event where a pair of these charged particles is created and then travels through the detector. As the charged particle moves, it leaves a trail of signals, much like a plane leaving a contrail. However, because the particle eventually decays into invisible dark matter and a very soft, slow-moving piece of debris, the trail suddenly stops. The researchers set up a digital filter to look for these specific "kinked" or "disappearing" trails. They required the trail to start a certain distance from the center of the collision and to end within the detector's inner layers. They also checked that the angle at which the trail bent or stopped was sharp enough to be real and not just a random glitch in the machine.

The results of their simulation were promising. For the lightest of their four scenarios, they predicted that with one year of data collection, the machine would see nearly 1,000 of these disappearing events. Even for the heaviest scenario, where the particles are harder to produce, they still expected to see dozens of clear signals. The study showed that the ability to find these particles depends heavily on the exact difference in their weights. If the difference is too small, the particles live too long and escape the detector before they decay. If the difference is too large, they decay too quickly, vanishing before they can travel far enough to be noticed. The sweet spot lies in a narrow range where the particles travel just far enough to be caught by the sensors. The researchers also noted that the background noise from the machine itself would be very low in this type of collider, making it much easier to spot these rare events compared to the noisy environment of current large colliders.

The study concludes that searching for these disappearing tracks is a powerful way to test the idea of a hidden dark sector. While the researchers did not build a physical detector or run a real experiment, their detailed simulations show that if these particles exist, a future electron-positron collider could find them. The method relies on the unique behavior of particles that are almost, but not quite, the same weight. By looking for a charged particle that takes a few steps and then vanishes, scientists could finally catch a glimpse of the dark matter family. The work highlights that the next generation of particle physics experiments should be designed to look for these subtle, long-lived signals, as they might hold the key to solving one of the biggest mysteries in science.