Kinetic Equilibrium between SIMP Dark Matter and Radiation via Internal Bremsstrahlung

The universe is filled with a mysterious substance called dark matter. We know it is there because its gravity holds galaxies together and bends the light of distant stars, yet it does not emit, absorb, or reflect any light. While we have measured exactly how much of this invisible stuff exists in the cosmos, we still do not know how it came to be. In the standard story of the early universe, dark matter particles were once abundant and hot, but as the universe expanded and cooled, they stopped interacting with each other and "froze out," leaving behind the steady population we see today. This process usually relies on pairs of particles colliding and vanishing into lighter energy. However, a specific class of dark matter candidates, known as strongly interacting massive particles, behaves differently. These particles are heavy and bump into each other with great force, often requiring three or four of them to collide at once to change their numbers. For this scenario to work, the particles must not only reduce their numbers but also get rid of their excess heat energy, or they would simply bounce back together instead of disappearing.

A team of researchers at the International Centre for Theoretical Physics Asia-Pacific has proposed a new way for these particles to cool down and settle into their current state. In their study, they suggest that instead of the usual method of bouncing off a sea of radiation to lose heat, these dark matter particles can shed their energy by emitting a nearly invisible, lightweight particle during their collisions. They call this process internal Bremsstrahlung, a mechanism where the act of scattering itself produces a burst of radiation that carries away the kinetic energy. This idea solves a long-standing problem in the theory of strongly interacting dark matter. Previously, scientists believed that for particles to stay cool enough to freeze out correctly, they had to constantly scatter off radiation. But this requirement created a mathematical conflict: the same physics that allowed them to cool down also forced them to annihilate too quickly, leaving almost no dark matter behind. The new mechanism breaks this deadlock by allowing the particles to lose heat without triggering that dangerous over-annihilation.

To test this idea, the researchers built a specific model based on a hidden sector of physics that mimics the strong nuclear force but operates in the dark. In this model, the dark matter particles are like dark pions, which are heavy, composite particles. They interact with each other through a heavy, short-lived messenger particle, similar to a dark version of a rho meson. When two dark pions collide, they can briefly form this heavy messenger, which then decays back into two pions while simultaneously shooting out a light, ghostly particle called a dark axion. This axion acts as the radiator, carrying away the heat generated by the collision. Crucially, the researchers designed the rules of their model so that the dark pions cannot talk directly to the axion, nor can they easily turn into axions in pairs. This ensures that the only way for the particles to lose energy is through the specific three-to-two collision process that reduces their numbers, while the heat is siphoned off by the axion emission.

The team ran detailed computer simulations to see if this setup could produce the right amount of dark matter we observe today. They tracked the temperature and density of the dark particles as the universe cooled, solving complex equations that describe how these populations evolve over time. Their results showed that when the dark axion is light enough and the interaction between the particles is strong enough, the system maintains a perfect balance. The dark pions stay in thermal equilibrium with the axion radiation bath, allowing them to dissipate energy efficiently. This keeps them cool enough to continue the number-reducing collisions until the universe expands enough that the particles finally freeze out. In their simulations, this process successfully yields the exact density of dark matter observed in the cosmos for particle masses in the range of tens to hundreds of GeV, a scale that is accessible to future experiments.

The study also explored what happens if the connection between the dark pions and the axion is too weak. If the particles stop exchanging heat too early, they retain too much kinetic energy, which causes them to bounce apart rather than annihilate, leaving behind too much dark matter. Conversely, if the connection is strong enough to last until the very end of the freeze-out process, the model works perfectly. The researchers found that there are two distinct ways this can happen. In one scenario, the particles cool down and stop interacting with the axion radiation just as they stop annihilating, a timing that matches the traditional view. In the other, the cooling process lasts longer, allowing the particles to settle into a stable state even if the annihilation stops earlier. Both paths lead to the correct amount of dark matter, suggesting that nature has more than one way to arrange this cosmic puzzle.

This work does more than just offer a new calculation; it opens a door to a broader class of theories. The mechanism described here relies on a general structure where dark matter particles interact with radiation only through heavy, intermediate states, rather than through direct contact. This structure avoids the mathematical contradictions that have plagued previous models. The researchers note that while their specific example uses dark pions and axions, the same logic could apply to other types of dark matter, such as dark vector particles, provided they interact with a heavy scalar partner and a light pseudoscalar partner. By showing that kinetic equilibrium can be maintained without dangerous side effects, this study suggests that strongly interacting dark matter is a viable and robust candidate for the invisible mass that shapes our universe. The findings remain theoretical, grounded in simulations and mathematical consistency, but they provide a clear and compelling path forward for understanding how the dark sector cooled and settled into the quiet state we observe today.