Complex Scalar Dark Matter with a Vector-Like Quark and Lepton: Precision, Flavor, and HL-LHC

The universe is filled with matter we can see and touch, from the stars above to the atoms in our own bodies. Yet, astronomers know that this visible stuff makes up less than a quarter of the cosmos. The rest is an invisible substance called dark matter, which holds galaxies together through its gravity but refuses to interact with light or ordinary matter in any way we can easily detect. For decades, physicists have proposed many different candidates for what this hidden substance might be, ranging from heavy, slow-moving particles to exotic fields. One of the most popular ideas is that dark matter consists of Weakly Interacting Massive Particles, or WIMPs, which would occasionally bump into normal atoms, though so rarely that we have yet to catch one. To find them, scientists build massive detectors deep underground and scan the skies for signals of dark matter particles colliding with each other, but so far, the results have been silent.

In this context, a team of researchers has proposed a specific, minimal version of a new theory to explain what dark matter could be and how it might hide from our current experiments. They suggest that dark matter is not a single, lonely particle, but part of a small, hidden family. This family includes the dark matter particle itself, which is a complex scalar, a type of field that has a specific mathematical structure allowing it to be stable. To keep this family together and prevent the dark matter from decaying into ordinary particles, the theory relies on a hidden symmetry, a rule that ensures the lightest member of the group remains safe. The theory also introduces two new types of heavy particles that act as bridges between the dark world and our own: a heavy quark and a heavy lepton. These new particles are "vector-like," meaning they behave differently from the familiar particles in the Standard Model of physics, allowing them to have mass without breaking the fundamental rules of how forces work.

The researchers set out to see if this specific family of particles could explain the amount of dark matter we observe in the universe today while also surviving the strict tests of modern physics. They performed a detailed calculation of how these new particles would interact with the known world. They looked at how the heavy quark and lepton would influence the behavior of rare particles called mesons, which are made of a quark and an antiquark. These mesons can change their identity in ways that are extremely rare in our current understanding, and any new heavy particles would leave a fingerprint on these changes. The team also examined how the new particles would affect the magnetic properties of electrons and muons, and how they might cause different types of charged particles to transform into one another, a process that has never been seen in nature. Finally, they checked how these particles would behave in the high-energy collisions of the Large Hadron Collider, the world's most powerful particle accelerator.

The study found that this model is viable, but only within a very narrow range of possibilities. The new heavy particles cannot be too light, or they would have already been detected by experiments looking for rare particle decays or changes in magnetic properties. Specifically, the heavy quark must weigh at least about 1.5 TeV, and the dark matter particle must be heavier than 1.0 TeV. If these particles were lighter, they would have caused too many rare events that experiments have already ruled out. The researchers also determined that the connection between the dark matter and the Higgs boson, the particle responsible for giving other particles mass, must be incredibly weak. If this connection were stronger, the dark matter would have been caught by sensitive underground detectors that look for dark matter bumping into atomic nuclei.

Despite these tight restrictions, the model offers a clear path for future discovery. The team calculated that the High-Luminosity Large Hadron Collider, an upgraded version of the current accelerator that will operate in the coming years, has the potential to find these heavy particles. If the dark matter particle weighs around 1.1 TeV and the heavy quark weighs about 1.6 TeV, the upgraded collider could produce them in sufficient numbers to be seen. The signal would appear as jets of heavy quarks or pairs of electrons accompanied by a large amount of missing energy, which would indicate that invisible dark matter particles were created and flew away undetected. The researchers also noted that while current searches for dark matter in space, looking for gamma rays produced when dark matter particles annihilate, do not yet rule out this model, future observations could provide further clues.

The work highlights a delicate balance in the search for new physics. The proposed family of particles is just heavy enough and just weakly interacting enough to have evaded detection so far, yet it is within reach of the next generation of experiments. By combining constraints from the behavior of rare particles, the precision of magnetic measurements, and the limits of underground detectors, the researchers have carved out a specific region of possibility where this new physics could exist. This approach demonstrates how different branches of physics, from the study of tiny particle decays to the collision of massive beams, work together to narrow down the search for the invisible universe. If the upgraded collider finds these particles, it would confirm that the dark sector is more complex than a single particle, revealing a hidden family that interacts with our world in subtle but detectable ways.