There are several ways to search for WIMPs based on their interactions with standard model particles: production at the Large Hadron Collider, scattering in underground direct detection experiments, indirect detection of the products of annihilating dark matter, and discovery of dark stars. I will discuss each of these in turn.
5.1. Production at the Large Hadron Collider at CERN
At the Large Hadron Collider (LHC), protons are accelerated to 13 TeV. Two beams travel in opposing directions around a 27 kilometer long ring, and then collide in several detectors. The two general purpose detectors ATLAS and CMS were built with the goal of discovering the Higgs, discovering SUSY and dark matter, and discovering the unknown. The first goal of finding the Higgs boson, the last missing piece of the standard model of particle physics, was successful as of July 2012 and immediately led to a Nobel Prize for Higgs and Englert. The other goals have as yet been elusive.
SUSY dark matter particles could manifest at the LHC in a variety of ways. A possible signature would be missing transverse energy as the dark matter particle leaves undetected, together with jets of particles created during the decay chain of SUSY particles emerging from the collision. Such a signature has not yet been seen, leading to ever higher bounds on SUSY particle masses. The minimal supersymmetric standard model (MSSM) has 105 free parameters. If one makes some simplifying assumptions that unify all fermion masses m1/2 and all scalar masses m0 at a high scale, then in the resulting constrained minimal supersymmetric model (CMSSM, or MSUGRA), only five parameters remain. The experimental results are often quoted in the context of this CMSSM/MSUGRA. For example, Fig. 6 illustrates the bounds from ATLAS on the supersymmetric parameter space. The remaining parameter space is being pushed to above the TeV scale. However, it is important to note that these bounds apply only to the MSUGRA/CMSSM.
 |
Figure 6. Bounds on MSUGRA/CMSSM from 8 TeV ATLAS data. The remaining allowed parameter space is above the lines. |
The LHC will never be able to kill even minimal supersymmetry. [48] Even in the MSSM, a 25 GeV neutralino currently survives as a possibility. [47] If the LHC sees nothing, SUSY can survive. It may be at high scale. Or, it may be less simple than the assumption that all scalars and all fermions unify at some high scale; e.g. the non-universal Higgs model (NUHM) or the non-universal gaugino model (NUGM).
SUSY particles may be discovered at the LHC as missing transverse energy plus jets in an event. In that case one knows that the particles live long enough to escape the detector, but it will still be unclear whether they are long-lived enough to be the dark matter. Thus complementary astrophysical experiments are needed. Proof that the dark matter has been found requires astrophysical particles to be found, via the other prongs of the dark matter search techniques.
5.2. Direct Detection Experiments
Direct detection experiments take advantage of the large number of WIMPs in the Galaxy. A WIMP travels through the detector, scatters off of a nucleus, and deposits a small amount of energy that may be detected The experiments are extraordinarily difficult and the progress has been impressive: the count rates are less than one count/kg/day and the energy deposited is O(keV).
The history of dark matter direct detection began with the ideas and theoretical calculations in the 1980s. In 1984 Drukier and Stodolsky [49] proposed neutrino detection via weak scattering off nuclei. Then Goodman and Witten [50] turned the same approach to dark matter detection. Drukier, Freese, and Spergel [51] first included a Maxwellian distribution of WIMPs in the Galaxy, computed cross sections for a variety of candidates, and proposed the idea of annual modulation to identify a WIMP signal. In another paper we further studied the idea of using annual modulation, not only for background rejection but also to tease out a signal even in the presence of overwhelming noise; [52] this is the technique used by the DAMA experiment described below. For reviews, see Refs. 53, 54, 55, 56, 57.
The text in the subsequent few paragraphs outlines dark matter direct detection and is taken from my review paper with Lisanti and Savage. [57] When a WIMP strikes a nucleus, the nucleus recoils with energy E. The differential recoil rate per unit detector mass is
 |
(2) |
where nχ = ρχ / mχ is the number density of WIMPs, with ρχ the local dark matter mass density; f(v, t) is the time-dependent WIMP velocity distribution; and [dσ / dq2] (q2, v) is the velocity-dependent differential cross-section, with q2 = 2 M E the momentum exchange in the scatter. The differential rate is typically given in units of cpd kg−1 keV−1, where cpd is counts per day. Using the form of the differential cross-section for the most commonly assumed couplings, to be discussed below,
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(3) |
where σ(q) is an effective scattering cross-section and
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(4) |
is the mean inverse speed, with
 |
(5) |
The benefit of writing the recoil spectrum in the form of Eqn. (3) is that the particle physics and astrophysics separate into two factors, σ(q) and ρχη(vmin, t), respectively. It is traditional to define a form-factor corrected cross-section
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(6) |
Here σ0 is the scattering cross-section in the zero-momentum-transfer limit and F2(q) is a form factor to account for the finite size of the nucleus.
Two types of interactions are most commonly studied. In spin independent (SI) interactions, the scattering is coherent and scales as the atomic mass squared, A2. The SI cross-section can be written as
 |
(7) |
where µp is the WIMP-proton reduced mass. The SI cross-section grows rapidly with nuclear mass. The explicit A2 factor arises from the fact that the contributions to the total SI cross-section of a nucleus is a coherent sum over the individual protons and neutrons within.
Spin dependent (SD) scattering is due to the interaction of a WIMP with the spin of the nucleus and takes place only in those detector isotopes with an unpaired proton and/or unpaired neutron. The SD WIMP-nucleus cross-section is
 |
(8) |
where GF is the Fermi constant, J is the spin of the nucleus,
 |
(9) |
where ⟨ Sp ⟩ and ⟨ Sn ⟩ are the average spin contributions from the proton and neutron groups, respectively, and ap (an) are the effective couplings to the proton (neutron) (these need not be the same).
The dark matter halo in the local neighborhood is most likely dominated by a smooth and well-mixed (virialized) component with an average density ρχ ≈ 0.4 GeV / cm3. The simplest model for this smooth component is often taken to be the standard halo model (SHM) [51, 52] of an isothermal sphere with an isotropic, Maxwellian velocity distribution and rms velocity dispersion σv. The SHM is written as
 |
(10) |
and 
(v) = 0
otherwise. Here,
 |
(11) |
with z ≡ vesc / v0, is a normalization factor and
 |
(12) |
is the most probable speed, with an approximate value of 235 km/s (see Refs. 58, 59, 60, 61).
Our early work [51, 52] used this Maxwellian dark matter distribution. Although there has been concern that the velocity distribution of the dark matter might deviate significantly from Maxwellian, Refs. 62, 63, 64 showed that results obtained for dark matter with a Maxwellian profile are consistent with those obtained when baryons are included in dark matter simulations, though there is as yet possible disagreement for the high velocity tail. We concluded that the Maxwellian approximation is a perfectly good approximation when comparing results of dark matter experiments to data.
We also showed [51] that the dark matter signal should experience an annual modulation (for a review, see Ref. 57.) As the Sun orbits around the Galactic Center, Earth-based detectors are effectively moving into a “wind” of WIMPs. The WIMPs are moving in random directions in the Galaxy, and the Sun's motion creates (on the average) a relative velocity between us and the WIMPs. On top of that, because the Earth is moving around the Sun, the relative velocity of the Earth with the WIMP wind varies with the time of year. Thus the count rate should modulate sinusoidally with the time of year, peaking in June and with a minimum in December. We predicted that the annually modulating recoil rate can be approximated by
 |
(13) |
with |Sm| ≪ S0, where S0 is the time-averaged rate, Sm is referred to as the modulation amplitude, ω = 2π / year and t0 is the phase of the modulation. Since typical backgrounds do not experience the same annual modulation, this effect can be used to tease the signal out of the background. [52]
These first papers convinced experimentalists that they would be able to build detectors sensitive enough to search for WIMPs. The detectors must be placed deep underground in order to filter out cosmic rays, in underground mines or underneath mountains. The first experimental effort to search for and bound WIMP dark matter was Ref. 65. Now, 30 years later, direct detection searches are ongoing worldwide, in US, Canada, Europe, Asia, and the South Pole, see Fig. 7.
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Figure 7. Underground dark matter laboratories worldwide (courtesy of M. Tripathi and M. Woods). The CanFranc underground laboratory in Spain is missing from the figure. |
Of all of these experiments, only one, the Italian DAMA experiment, [66] has positive signal. They use NaI crystals in the Gran Sasso tunnel under the Apennine Mountains near Rome. The signal they have is the annual modulation we predicted for the WIMP signal. [51, 52] DAMA has observed exactly this annual modulation with the correct phase, see Fig. 8. Indeed DAMA has 10 years of cycles corresponding to a 9 σ detection of modulation.
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Figure 8. DAMA data (including DAMA/LIBRA) has a 9 σ detection of annual modulation consistent with WIMPs. [66] |
Now the question is, have they detected dark matter? Unfortunately they have not released the data for others to study. In addition, no experiment other than DAMA has found any signal at all. Indeed the null results from other experiments place strong bounds on the WIMP elastic scattering cross section. Naively it might seem that the other experiments rule out the DAMA results as being due to WIMPs. Yet, this may not be true, because all the detectors are made of different materials. DAMA is the only experiment to date that uses NaI crystals. For example, LUX [67] and XENON [68] are made of xenon while CDMS (and SuperCDMS) [69] is made of germanium, which are far heavier nuclei than the components of DAMA's NaI crystals. To compare the different experiments, theoretical input is required. For example, if one assumes the scattering is SI so that the cross section scales as A2, one can then plot the different experiments as in Fig. 9 in the cross section/ WIMP mass plane. DAMA signals could be due to roughly 10 GeV WIMPs if the scattering is with Na atoms, while the signal would be due to 80 GeV WIMPs if the scattering were off of iodine atoms. The higher mass region is in severe conflict with bounds from other experiments, while the lower mass region also appears to be ruled out. However, if one abandons the A2 assumption then this comparison plot is no longer valid. For all known theoretical assumptions it is hard to reconcile the positive results of DAMA with the negative results of other experiments. Perhaps uncertain nuclear physics may be responsible. [70, 71] Many alternate explanations to the discovery of DM have been proposed (e.g. radon contamination, muons, etc.) but all have been shown to be wrong. The reason DAMA remains so interesting is that there is no other known explanation of the annual modulation they are seeing.
 |
Figure 9. Spin independent scattering bounds from direct detection experiments as shown, as well as regions compatible with DAMA data, in the SI elastic scattering cross section vs. WIMP mass plane. Plot taken from Particle Data Book 2015 (PANDA-X and LUX bounds need to be updated). |
What is needed are further experimental tests using the same detector material as DAMA (NaI crystals) but in a different location. These experiments are now taking place: SABRE, [72] COSINE-100 [73] (KIMS has joined with dark matter-ICE [74]), and ANAIS. [75] Thus in the next five years there should be either confirmation of DAMA or it will be ruled out.
I also wanted to mention a new idea we have for dark matter direct detection using DNA (see Fig. 10). We proposed [76] to use nanometer thin sheets of gold (or other material) with ∼1060 strands of DNA attached. When a WIMP hits the gold sheet, it knocks a gold atom forward into the DNA. The gold atom then severs whatever DNA strands it hits. The broken strand of DNA then falls down and is collected. The DNA has been carefully constructed to have a well-known sequence of bases (A,G,C...). Using well known biological techniques (PCR and sequencing), the location of the break can be identified. Thus the track of the recoiling gold nucleus can be reconstructed. Since the distance between the bases in the DNA strand is nanometer in size, this technique provides a nanometer tracker. Once the track of the gold nucleus is known, since the WIMP traveled in roughly the same direction, the direction that the WIMP came in from is also known. This idea thus provides a directional dark matter detector. The importance of this is as follows. It allows clear proof of dark matter discovery. We expect ten times as many counts when the detector is pointing into the direction of the WIMP wind than when it is pointing in the opposite direction. This head/tail asymmetry would be hard to explain with any background. Additionally, both the annual and daily (due to Earth's rotation) variation of the signal would be detectable and would give superb background rejection. In the long run, a directional detector would allow the discovery of where the WIMPs are in the Galaxy and how they are moving.
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Figure 10. DNA based Dark Matter Directional Detector. A WIMP hits the nanometer-thin gold plate, knocks a gold atom into the hanging strands of DNA. Whenever the gold atom strikes a DNA strand, the strand breaks and is collected. Since the base sequence of the strands is controlled, sequencing the broken strand allow the location of the break to be identified. Hence the DNA serves as a tracker with nanometer accuracy. Since the WIMP travels in roughly the same direction as the gold atom, the detector discovers the direction the WIMP came from. |
A second radically new idea we have proposed for dark matter detection is “nanobooms”. [77] The WIMP sets off a very small explosion when it deposits heat in the detector. For example, the detector might consist of thermites. Then the WIMP's energy deposit would cause the exothermic reaction between a metal and a metal oxide to take place, i.e., there is a small explosion, which can then be detected acoustically, optically, or more likely via gas expansion.
The next five years stand to lead to tests of the DAMA annual modulation signal and a confirmation or refutation of WIMP discovery as well as progress in directional sensitivity.
WIMP annihilation in today's universe takes place wherever there is an overdensity of WIMPs. The final products of WIMP annihilation are neutrinos, e+/e− pairs, and photons. All three of these are being looked for in detectors. Promising places to look are the Galactic Center, dwarf galaxies, clusters of galaxies, [78] and in the case of neutrinos, the Earth and the Sun. The first papers suggesting the latter neutrino searches were by Silk et al. [79] in the Sun; and by Freese [80] as well as Krauss, Srednicki and Wilczek [81] in the Earth. As yet no signal of neutrinos due to WIMP annihilation in the Sun or Earth [82] has been found in the IceCube/DeepCore detectors at the South Pole.
The AMS experiment on board the International Space Station has found an excess of positrons. [84] However, this excess is not likely to be due to WIMP annihilation. A combination of two papers has shown that such an explanation is extremely unlikely. First, the work of Lopez, Savage, Spolyar, and Adams [85] pointed out that such a positron excess would predict also gamma-rays from dwarf galaxies, which are not seen in the Fermi Gamma Ray Space Telescope (Fermi-LAT) data. They used the bounds on gamma-rays from dwarfs in Fermi-LAT data to show that all WIMP annihilation channels are excluded as explanations of AMS data except one (via a mediator to four muons). This latter channel was further examined by Scaffidi et al. [86] Second, the Planck satellite examined the effects such an excess would imply for the CMB and ruled out a large swath of parameter space. [87] The work of Ref. 85 using Fermi-LAT data to rule out a DM explanation of the AMS positron excess was placed on the arXiv a month prior to the Planck bounds. It is far more likely that the AMS positron excess is due to pulsars or other point sources than due to WIMP annihilation.
Of great interest over the last few years has been Fermi-LAT's discovery of a gamma-ray excess towards the Galactic Center. Hooper and Goodenough [88] pointed out that it could be from the annihilation of a 40 GeV WIMP. More recent studies of cosmic ray backgrounds have widened the possible range of masses [89] and therefore SUSY explanations of this excess. [90] However, studies [91] have shown that a point source explanation (e.g., pulsars) is at least as likely as a dark matter explanation. Though tantalizing, a dark matter explanation of this gamma ray excess will be hard to prove as there is much astrophysical competition at the Galactic Center.
To summarize the current status of WIMP searches, there is possible evidence for WIMP detection already now, but none of it is certain. The direct detection experiment DAMA has found annual modulation of its signal that would be compatible with a WIMP origin. However, other experiments have null results in conflict with DAMA's result. Since the experiments are made of different detector materials, further tests of the same material as DAMA are now taking place around the world and will result in confirmation or refutation in the next five years.
As far as indirect detection of WIMP annihilation products, the positron excess seen by AMS likely has a different origin than WIMPs. The gamma-ray excess seen from the direction of the Galactic Center by the Fermi Gamma Ray Space Telescope is compatible with a WIMP origin but other astrophysical explanations are at least as likely.
Theorists are looking for models in which some of these results are consistent with one another, given a WIMP interpretation. What will it take for us to believe dark matter has been found? We need a compatible signal in a variety of experiments made of different detector materials and all the parties agree.