286. Nambu-Goldstone dark matter

This is a guest post by Yu Nakayama from the University of California, Berkeley. Dmitry.

First of all, I’d like thank Dmitry for giving me this opportunity to post a guest blog on our hottest paper about Nambu-Goldstone Dark Matter (arXiv:0902.2914). This is based on the collaboration with M. Ibe, H. Murayama, and T.T Yanagida. You know, last year Nambu got his Nobel prize for his discovery of the spontaneous breaking of the global symmetry and associated massless scalar fields (Nambu-Goldstone boson). The main idea of our paper is to use this Nambu-Goldstone boson as a candidate for dark matter, in the context of the supersymmetric extension of the standard model.

A surprising fact about our universe is 96% of the total energy is dark. Dark simply means we don’t know its origin, but we certainly know it’s not conventional matter such as hydrogen, helium, electron, photon and so on. If it were originated from these, we could’ve seen it! Within this 96%, 74% is the so-called dark energy, also known as Einstein’s biggest mistake in his life time. The remaining 22% is the so-called dark matter, and this dark matter is what this blog is all about.

The number 22% comes from the recent WMAP data. WMAP is a satellite experiment collecting all the information about the cosmic microwave background of the universe and study its fluctuation around the thermal Plank distribution. More recent experiments such as ATIC, PPB-BETS (balloon experiments) show the existence of a bump in a GeV energy region of flux in cosmic rays. The most exciting interpretation of the excess is the annihilation and/or decay of the dark matter with a mass in a TeV range. It is remarkable that it explains simultaneously the anomalous excess of flux in PAMELA experiments.

So, we know that our universe is filled with the non-baryonic dark matter. And naturally, we come up with a question: what is this dark matter? Can we explain the origin of the dark matter as well as its density in the current universe? Is it anything to do with the particle physics? The answer to the last question is probably yes. The number 22% may have something to do with new particles at TeV scale. Not coincidentally, this scale is nothing but the energy scale we are looking for at LHC!

While astrophysicists launch satellites and balloons from the earth to catch cosmic rays, experimental particle physicists dig a very long tunnel (27 kilometers) under the city of CERN, to set up a huge accelerator called LHC. The accessible energy is TeV. In other words, this accelerator is a giant microscope whose resolution is meter. We collide protons inside the tunnel and see what happens. I cannot tell what happens, but we believe the collision will produce new species of particles, and the best candidate I can imagine is the supersymmetric parter of the standard model particles (and Higgs, of course).

If you have new particles at TeV scale, they may be good candidates for the dark matter under the condition that they only weakly interact with our known particles. The dark matter candidate in the context of the supersymmetry has a long history, and it is a well studied subject. Basically, we have two possibilities: one is to use the lightest supersymmetric particle (LSP), and the other often overlooked is to use stable composite “baryons” in a dynamical supersymmetry breaking sector. The former case, however, implies the masses of the gluino and squarks are much larger than a TeV range, which causes serious problems in discoveries of supersymmetry particles at the LHC. The latter case predicts most likely the mass of the dark matter to be in at least about 30 TeV, and accordingly, it seems difficult to explain the dark matter with a TeV mass.

Furthermore, we cannot use the LSP scenario in our favorite gauge mediation because it is the gravitino that is the LSP here and the constraint on the gravitino dark matter is severe. In addition, PAMELA does not see any proton flux, which cannot be explained in the conventional LSP scenario because the final states of LSP annihilation can be protons!

This is a challenge for the supersymmetry phenomenology. We were all excited that the dark matter is natural in supersymmetry scenario, but now the new data have forced us to realize that the supersymmetry life is not so easy as originally expected. We have a dilemma, but we’re happy because this is a chance to pin down various possibilities.

After the appearance of the data, many theoretical physicists try to solve the dilemma within the former LSP scenario with partial success. We, on the other hand, have taken a look at the latter possibility: the dark matter is a hidden sector “baryons”. The name “baryons” may need explanations here: it doesn’t refer to the conventional baryonic charge (say, proton has charge 1), but it just refers to a global symmetry or charge in the hidden sector (say, proton has charge 0). This approach is intriguing because the nature of the dark matter can tell us the structure of the hidden supersymmetry breaking sector! In the LSP scenario, in contrast, the hidden sector is just a black box, and we cannot tell any difference there. Maybe, we will find the supersymmetry breaking sector in the sky before we find the supersymmetric parter of our standard particles under the ground.

How does our scenario work? As I pointed out earlier, without any further assumptions, the dark matter predicted in the hidden “baryon” scenario has mass of order 30-100 TeV. There is nothing wrong about it if we neglected the recent cosmic ray data, but if we consider the data seriously, this approach seems in contradiction. Now, the idea to overcome this contradiction is to identify the hidden “baryon” dark matter with the (approximate) Nambu-Goldstone boson of the global symmetry breaking in the hidden sector. In this way, we can explain the “small” mass of the dark matter compared with the naively expected value. When a global symmetry is broken down to its subgroup , the Goldstone theorem suggests the emergence of the massless boson that lives in the coset space . Since the Nambu-Goldstone boson may possess a non-trivial charge under , we can obtain a good candidate of the (nearly) massless stable particle! This is what we needed in our hidden “baryon” dark matter scenario: we need small mass to explain the cosmic ray data, and we need a stability (global charge) to use it as a dark matter.

Let me explain how our hidden “baryon” dark matter decays into other particles to explain the observed dark matter density as well as the recent astrophysical experiments. Our discussion in the paper is based on a concrete model, where you can compute everything from scratch without dynamical assumptions, but here, as a review blog, I’d like to convey the essence of our construction by simply presenting relevant spectra of the supersymmetry breaking hidden sector.

Our hidden sector has an R-symmetry, which is spontaneously broken, so the lightest particle in the hidden sector is the R-axion. Then, the next lightest particle is the (approximate) Nambu-Goldstone boson. This Nambu-Goldstone boson is our dark matter. In addition, the R-axion has a superpartner (we call as flaton in the paper): the flaton acquires a mass from the supersymmetry breaking 1-loop corrections. All the other particles are much heavier than these naturally light particles from the symmetry (or symmetry breaking).

One problem to have such lighter dark matter than the natural supersymmetry breaking scale is that the annihilation cross section is too suppressed. So, we cannot explain the observed dark matter density of the universe from the hidden sector baryons. It remains too much today! This is related to the difficulty of explaining recent astrophysical data from the hidden “baryon” dark matter scenario. The natural mass scale to explain the observed dark matter density is 30-100 TeV. To avoid the problem, we attempt to adjust the mass of the flaton to just twice that of the dark matter “baryon”. In this case, thanks to S-channel resonance from the intermediate flaton, the annihilation rate of the dark matter will be enhanced to explain the observed dark matter density.

Is this resonance assumption natural? We need tuning of parameters at this point, but this also explains the so-called boost factor in the dark matter annihilation. The boost factor is the factor difference between the naively expected cross section in the zero temperature universe and what appears in the actual thermal universe. Our resonance assumption naturally leads to the boost factor of order , consistent with the cosmic ray experiments. Fine-tuning is not a bad thing, especially when you can explain two things at a time. Of course, it is totally a matter of taste which explanation is more important than the other. But this is until everything will become clear when the new experiments reveal the nature. We will eventually see whose bets are right.

Our scenario also gives a clue to the puzzle at PAMELA experiments: they don’t see any excess of proton flux. In our case, the hidden “baryon” dark matter annihilates first into R-axion, and then decays to electrons or muons. We cannot produce protons here because R-axion is simply lighter than protons. So, all in all, our scenario is quite successful in explaining the new data.

In this blog, I tried to explain the gist of our work without using any equations. Clearly, I had to restrict myself to basic assumptions and the main results without giving any detailed computation. But I hope the readers found the hidden dark baryon dark matter scenario is an alternative attractive possibility.
To close this blog, let me come back to Nambu. He got his Nobel prize for the invention of Nambu-Goldstone boson among other things. Have we found his boson in nature? Not yet, in the realm of high energy particle physics! Maybe the first Nambu-Goldstone boson will be our hidden “baryon” dark matter. Of course, then, we will discover supersymmetry at the same time. This is what we want: “killing two birds with one Goldstone“.