Dark Matter more like Baryons

April Fools is over; I'm staying dead serious for the rest of the year. The most serious things in the months before the first LHC results are dark matter searches high and low. Here is another idea what they might find.

The most popular scenario for dark matter assumes that it consists of weakly interacting massive particles (WIMPs) who were once in thermal equilibrium. In the early hot and dense universe such a particle can efficiently annihilate into familiar particles like photon or electrons, and in this way dark matter is kept in equilibrium with the the rest of the cosmic plasma. The equilibrium ceases to hold when the temperature T of the universe falls below the dark matter particle mass M. In that regime, the number of dark matter particle very quickly decreases - as an exponential $e^{-M/T}$ - and at some point dark matter freezes out: there isn't enough dark matter particles around that they could find each other and annihilate. The surviving particles float around in the universe playing hide and seek with astronomers and physicists alike.

The WIMP scenario is nice and robust but it sheds little light on the surprising fact that the present abundanceof dark matter $\Omega_{DM}$ is very close to that of the ordinary matter who is today dominated by the baryon (proton and neutrons) abundance $\Omega_{B}$. After WMAP data we are confident that the ratio $\Omega_{DM}/\Omega_B$ is roughly five. Of course, one can always cook up the parameters of the WIMP model such that this constraint is satisfied, but nevertheless the proximity of $\Omega_B$ and $\Omega_{DM}$ is intriguing. It may suggests that baryons and dark matter have a common origin. But baryons are definitely NOT a cold relic!

In fact, we don't know for sure what is the origin of baryons in our universe but we have a bunch of ideas that go under the name of baryogenesis. The general idea is that the very early universe contains an equal number of baryons and antibaryons, but at some point in its evolution the fundamental interactions in the plasma produce a tiny $10^{-10}$ asymmetry between matter and antimatter. Once the temperature falls below the baryon mass most of the baryons and anti-baryons annihilate with each other and turn into the sea of photons, leaving only the small unpaired $10^{-10}$ fraction of baryons. These are the protons and neutrons that make galaxies and stars today.

Is it conceivable that dark matter originates in a similar fashion? That is to say, the early universe contains dark matter and anti dark matter particles which almost completely annihilate away leaving only the small asymmetric fraction? Can the dark asymmetry and the baryon asymmetry have the common origin? The answer to these questions is yes, and the first practical realization I'm aware of is due to David B. Kaplan in early nineties. In that model, the dark matter particle carries a charge under an additional U(1) global symmetry who, much as the U(1) baryon symmetry, has a mixed anomaly with the electroweak SU(2) gauge symmetry. Because of the anomalies, non-perturbative electroweak interactions that are effective in the early universe violate both the baryon number and the dark matter number. Then, if some conditions are satisfied, the electroweak phase transition generates the baryon and the dark asymmetries roughly of the same order. At the end of the day on obtains the relation $\Omega_{DM}/\Omega_B \sim m_{DM}/m_{proton}$ and the experimentally measured ratio is recovered if the dark matter particle's mass is around 5 GeV.

Kaplan's original model is long gone for several reasons, but the idea is still floating in the backchannels of model building. The most recent approach in the context of supersymmetry was made by David E. Kaplan et al (David E. Kaplan is a more recent version of David B. Kaplan with more features). In that model, there's no new quantum number invented especially for the dark matter particle; instead, it carries the lepton (or baryon in another version) quantum number. Furthermore, the model does not rely on electroweak baryogenesis but rather it assumes that the the B - L asymmetry is generated at high energies (for example by leptogenesis). That asymmetry is later redistributed between baryons and dark matter by higher-dimensional interactions. When these interactions fall out of equilibrium, dark matter asymmetry is frozen in and one again ends up with $\Omega_{DM}/\Omega_B \sim m_{DM}/ m_{proton}$. All that remains is to find 5-15 GeV dark matter in the sky, or in colliders or by direct detection...