Cold Dark Matter and Experimental Searches for WIMPs

Seeking WIMPs in all the wrong places

The Need for Dark Matter
Extragalactic systems like spiral galaxies and clusters of galaxies exhibit mass discrepancies. The application of Newton's Law of Gravity to the observed stars and gas fails to explain the rapid observed motions. This leads to the inference that some form of invisible mass - dark matter - dominates the dynamics of the universe.

If asked what the dark matter is, most scientists working in the field will respond honestly that we have no idea. There are many possible candidates. Some, like MACHOs (Massive Compact Halo Objects, perhaps brown dwarfs) have essentially been ruled out. However, in our heart of hearts there is a huge odds-on favorite: the WIMP.

WIMP stands for Weakly Interacting Massive Particle. This is an entire class of new fundamental particles that emerge from supersymmetry. Supersymmetry is a theoretical notion by which known elementary particles have supersymmetric partner particles. This notion is not part of the highly successful standard model of particle physics, but might exist provided that the Higgs boson exists. In the so-called Minimal Supersymmetric Standard Model (MSSM), which was hypothesized to explain the hierarchy problem (i.e., why do the elementary particles have the various masses that they do), the lightest stable supersymmetric particle is the neutralino. This is the WIMP that presumably makes up the dark matter.

Cosmology, meet particle physics
There is a confluence of history in the development of previously distinct fields. The need for cosmological dark matter became clear in the 1980s, the same time that MSSM was hypothesized to solve the hierarchy problem in particle physics. Moreover, it was quickly realized that the cosmological dark matter could not be normal ("baryonic") matter. New fundamental particles therefore seemed a natural fit.

The cosmic craving for CDM
There are two cosmological reason why we need non-baryonic cold dark matter (CDM):

  1. The measured density of gravitating mass appears to considerably exceed that in normal matter as constrained by Big Bang Nucleosynthesis (BBN):
    Ωm = 6 Ωb (so Ωnot baryons = 5 Ωbaryons).
  2. Gravity is too weak to grow the presently observed structures (e.g., galaxies, clusters, filaments) from the smooth initial condition observed in the cosmic microwave background (CMB) unless something speeds up the process. Extra mass will do this, but it must not interact with the photons of the CMB the way ordinary matter does.
By themselves, either of these arguments are strong. Together, they were compelling enough to launch the CDM paradigm.

From the astronomical perspective, all that is required is that the dark matter be non-baryonic and dynamically cold. Non-baryonic so that it does not participate in Big Bang Nucleosynthesis or interact with photons (a good way to remain invisible!), and dynamically cold (i.e., slow moving, not relativistic) so that it can clump and form gravitationally bound structures. Many things might satisfy these astronomical requirements. For example, supermassive black holes fit the bill, though they would somehow have to form in the first minute of creation in order not to impact BBN.

The WIMP Miracle
From a particle physics perspective, the early universe was a high energy place where energy and mass could switch from one form to the other freely as enshrined in Einstein's E = mc2. Pairs of particles and their antiparticles could come and go. However, as the universe expands, it cools. As it cools, it loses the energy necessary to create particle pairs. When this happens for a particular particle depends on the mass of the particle - the more mass, the more energy is required, and the earlier that particle-antiparticle pair "freeze out." After freeze-out, the remaining particle-antiparticle pairs can mutually annihilate, leaving only energy. To avoid this fate, there must either be some asymmetry (apparently there was about one extra proton for every billion proton-antiproton pairs - an asymmetry on which our existence depends even if we don't yet understand it) or the "cross section" - the probability for interacting - must be so low that particles and their antiparticles go their separate ways without meeting often enough to annihilate completely. This process leaves some relic density that depends on the properties of the particles.

If one asks what relic density is necessary to make up the cosmic dark matter, the cross section that comes out is about that of the weak nuclear force. A particle that interacts through the weak force but not the electromagnetic force will have the about the right relic density. Moreover, it won't interfere with BBN or the CMB. The WIMPs hypothesized by supersymmetry fit the bill for cosmologists' CDM. This coincidence of scales - the relic density and the weak force interaction scale - is sometimes referred to as the "WIMP miracle" and was part of the motivation to adopt the WIMP as the leading candidate for cosmological dark matter.

WIMP detection experiments
WIMPs as CDM is a well posed scientific hypothesis subject to experimental verification. From astronomical measurements, we know how much we need in the solar neighborhood - about 0.3 GeV c-2 cm-3. (That means there are a few hundred WIMPs passing through your body at any given moment, depending on the exact mass of the particle.) From particle physics, we know the weak interaction cross section, so can calculate the probability of a WIMP interacting with normal matter. In this respect, WIMPs are very much like neutrinos - they can pass right through solid matter because they do not experience the electromagnetic interactions that make ordinary matter solid. But once in a very rare while, they may come close enough to an atomic nucleus to interact with it via the weak force. This is the signature that can be sought experimentally.

There is a Nobel Prize waiting for whoever discovers the dark matter, so there are now many experiments seeking to do so. Generically, these use very pure samples of some element (like Germanium or Argon) to act as targets for the WIMPs making up the dark matter component of our Milky Way Galaxy. The sensitivity required is phenomenal, and many mundane background events (cosmic rays, natural radioactivity, clumsy colleagues dropping beer cans) that might mimic WIMPs must be screened out. For this reason, there is a strong desire to perform these experiments in deep mine shafts where the apparatus can be shielded from the cosmic rays that bombard our planet and other practical nuisances.

Searches for WIMPs are proceeding apace. The sensitivity of these experiments is increasing at an accelerating rate. They already provide important constraints - see the figure:

Searching for WIMPs

This plot was generated by DMTools.

This graph shows the status of searches for Weakly Interacting Massive Particles (WIMPs). The abscissa is the mass of the putative WIMP particle. For reference, the proton has a mass of about one in these units. The ordinate is a measure of the probability for WIMPs to interact with normal matter. Not much!

The shaded regions represent theoretical expectations for WIMPs. The light red region is the original (Ellis et al.) forecast. The blue and green regions are more recent predictions (Trotta et al. 2008).

The lines are representative experimental limits. The region above each line is excluded - if WIMPs had existed in that range of mass and interaction probability, they would have been detected already. The top line (from CDMS in 2004) excluded much of the original prediction. More recent work (colored lines, circa 2008) now approach the currently expected region.

April 2011 update: XENON100 sees nada. Note how the "expected" region continues to retreat downward in cross section as experiments exclude the previous sweet spots in this parameter. This is the express elevator to hell (see below).

September 2011 update: CREST-II claims a detection. Unfortunately, their positive result violates limits imposed by several other experiments, including XENON100. Somebody is doing their false event rejection wrong.

July 2012 update: XENON100 still seeing squat. Note that the "head" of the most probable (blue) region in the figure above is now excluded.

Indeed, the experiments have perhaps been too successful. The original region of cross section-mass parameter space in which WIMPs were expected to reside was excluded years ago. Not easily dissuaded, theorists waved their hands, invoked the Majorana see-saw mechanism, and reduced the interaction probability to safely non-detectable levels. This is the vertical separation of the reddish and blue-green regions in the figure.

[Or, to quote a particle physicist, "The most appealing possibility - a weak scale dark matter particle interacting with matter via Z-boson exchange - leads to the cross section of order 10^-39 cm2 which was excluded back in the 80s by the first round of dark matter experiments. There exists another natural possibility for WIMP dark matter: a particle interacting via Higgs boson exchange. This would lead to the cross section in the 10^-42-10^-46 cm2 ballpark (depending on the Higgs mass and on the coupling of dark matter to the Higgs)."]

Though set back and discouraged by this theoretical slight of hand (the WIMP "miracle" is now more of a vague coincidence, like seeing an old flame in Grand Central Station but failing to say anything because (a) s/he is way over on another platform and (b) on reflection, you're not really sure it was him or her after all), experimentalists have been gaining ground on the newly predicted region. If all goes as planned, most of the plausible parameter space will have been explored in a few more years. (I write this in 2010. I have heard it asserted that "we'll know what the dark matter is in 5 years" every 5 years for the past two decades.)

The express elevator to hell
"We're on an express elevator to hell - going down!"

There is a slight problem with the current predictions for WIMPs. While there is a clear focus point where WIMPs most probably reside (the blue blob in the figure), there is also a long tail to low interaction cross section. If we fail to detect WIMPs when experimental sensitivity encompasses the blob, the presumption will be that we're just unlucky and WIMPs happen to live in the low-probability tail that is not yet excluded. (Low probability regions tend to seem more reasonable as higher probability regions are rejected and we forget about them.) This is the express elevator to hell. No matter how much time, money, and effort we invest in further experimentation, the answer will always be right around the corner. This process can go on forever. Is dark matter a scientific (falsifiable) hypothesis?
The existence of dark matter is an inference, not an experimental fact. Individual candidates for the dark matter can be tested and falsified. For example, it was once reasonable to imagine that innumerable brown dwarfs could be the dark matter. That is no longer true - the brown dwarf hypothesis has been falsified. WIMPs are falsifiable dark matter candidates - provided we don't continually revise their interaction probability.

The concept of dark matter is not falsifiable. If we exclude one candidate, we are free to make up another one. After WIMPs, the next obvious candidate is axions. Should those be falsified, we invent something else. (Particle physicists love to do this. The literature is littered with half-baked dark matter candidates invented for dubious reasons, often to explain phenomena with obvious astrophysics causes. The ludicrous uproar over the ATIC and PAMELA cosmic ray experiments is a good example.)

September 2011 update: Fermi confirms the PAMELA positron excess. Too well for it to be dark matter: there is no upper threshold energy corresponding to the WIMP mass. Apparently these cosmic rays are astrophysical in origin, which comes as no surprise to astrophysicists or objective astroparticle physicists.

The express elevator doesn't just go down to hell. It keeps going there over and over again.

Some perspective on scale
The inference of dark matter is based on absolute faith in the application of Newtonian dynamics to scales very different than where the they have been experimentally tested. This faith seems well placed, but the mass discrepancy occurs on scales inaccessible to laboratory experiment. The need for dark matter appears in galaxies that are 100,000,000 times larger than the solar system and on acceleration scales 100,000,000,000 times smaller than we experience on the surface of the earth. The inference of dark matter could just as well be interpreted as an indication of the failure of purely Newtonian dynamics.

Why does MOND work so well?
People have, of course, considered modifications to gravitational theory as an alternative to dark matter. It is hard to do this without breaking something else fundamental. So hard that the widespread presumption is that it is impossible. Indeed, the vast majority of modified gravity hypotheses quickly fail when confronted with astronomical data, never mind theoretical objections. For example, it is possible to exclude any modification that is simply based on changing the force law at a particular length scale.

One hypothesis to modify Newtonain dynamics, MOND, has endured for a quarter century, despite periodic claims to falsify it. (So far most, if not all, of these claims have proven to be premature or outright wrong.) More disturbing to me than the supposed failures of MOND is that it works so well. This should not happen if dark matter is the right answer. MOND has persistently had more predictive success in galaxies than have dark matter models.

The phenomenological success of MOND has some curious consequences for dark matter. Whatever the dark matter is, it has to look, smell, and act like MOND. This is no trivial feat. MOND is a simple formula connecting the observed distribution of stars and gas unique to each galaxy to the dynamics that are uniquely observed for each galaxy. There is no reference to the dark matter that is suppose to dominate the show. The baryonic tail wags the dark matter dog.

Though well established observationally, the MONDian phenomenology is widely ignored by modelers seeking to explain the pertinent data. Ignoring facts is not healthy in science.

The many failings of CDM on galaxy scales are routinely attributed to "feedback" from star formation mucking things up. On the one hand, this is legitimate: the CDM theory can accurately predict what the dark matter does, but not what the luminous matter does. Since we can only observe the latter, it is reasonable to imagine that there is more to the story than just what the CDM should do when left to itself. On the other hand, what galaxies are observed to do could hardly be less reasonable: follow the predictions of the antithesis of dark matter. In spite of enormous effort, feedback remains nothing more than a fig leaf to hide our ignorance of how things came to be so.

I have made considerable efforts to understand the observed MONDian phenomenology in terms of dark matter. I have failed. A few others have claimed to succeed. Either they are more clever than me, or more self-deluded and less intellectually honest. For some reason, I have never seen their results reproduced in the literature: the expectation for feedback keeps changing.

The problem is fundamental. We are trying to take a simple observed phenomenon, and reproduce it with a complicated feedback scheme with many free parameters. One can, of course, fit anything with such a procedure. That was the problem with epicycles. The modern situation may well be analogous: we add epicycles of feedback to make our CDM model look like MOND. But does that mean that dark matter is just the modern version of Æther? A ubiquitous, invisible substance that simply must exist...

Oh, ye seekers after dark matter, how many vain chimeras have you pursued?
Go and take your place with the alchemists.

paraphrased from Leonardo da Vinci