When we look around us, at all the things we can touch and see – all of this is visible matter. And yet, this makes up less than 5% of the universe.

We now know that the vast majority of matter is dark. This dark matter does not emit or reflect light, nor have we yet observed any known particle interacting with it. It is through the gravitational effect of dark matter on other matter in space that astronomers inferred its existence.

The first evidence for the existence of dark matter came as early as the 1930s^[1]. Many astronomers had been observing the motion of galaxies, and found a discrepancy with respect to their expectation that only accounted for matter that was emitting light. This was corroborated in the 70s through observations of the rotational velocity of galaxies made by Vera Rubin and collaborators.

Because of gravitational lensing, an effect related to Einstein’s general theory of relativity, matter that stands between a light source and its observer can bend the light from the source so that the observed image is distorted. From comparing the known position of the source (e.g. obtained through direct emission of visible particles from the source) to its distorted image, one can reconstruct the distribution of the matter causing the distortion. Observations of gravitational lensing also pointed to additional matter with respect to what was visible.

More recently, supercomputer simulations of the structure of our universe show that only including visible matter will not reproduce the structures that are observed in the universe, while if dark matter is included then a closer agreement is obtained between observations and simulations.

The presence of dark matter and its amount in the universe can also be inferred from the variations of temperature in the early universe. This leftover amount of dark matter is called its “relic density”, and it amounts to about 27% of the matter-energy content of the universe.

However, none of the observations or simulations involving dark matter give a clear indication of what dark matter is made of. We only know that if dark matter is a particle^[2], then it must have mass, since it interacts with other matter through the force of gravity. We can hope to understand its nature by observing rare dark matter particles and their interactions from space (where we have already seen its effects), and by trying to produce them in controlled laboratory conditions.

How particle collisions can create dark matter in a lab

Experiments at particle accelerators have revealed much about the nature of visible (ordinary) matter, starting from the first prototypes that aided the discovery of the proton and the antiproton to the recent discovery of the Higgs boson. All of the particles observed so far are part of the Standard Model of Particle Physics, describing the fundamental components of matter and their non-gravitational interactions.

The most powerful accelerator ever built is the Large Hadron Collider (LHC) at CERN in Geneva, accelerating protons and colliding them with a total energy of 13 TeV. According to Einstein’s most famous equation, E=mc², the more energy (E) the more massive particles (with a mass m) one can create (13 TeV corresponds to roughly 14 thousand times the rest mass of a proton). The hope is that at the LHC we can create massive dark matter particles by colliding known particles, in the same way we create the Higgs boson in proton-proton collisions.

Particles are regularly accelerated to very high energies in the universe in "natural" particle accelerators, such as supernovae explosions, and then collide with other particles in our atmosphere. Cosmic rays, for example, are particles that are generated in outer space and make it to Earth. However, the advantage of laboratory particle accelerators such as the LHC is that there we know the initial conditions of the collisions – namely the type and energy of the particles being collided. We can also create a large (and known) number of collisions and observe them in a controlled environment. These are essential features for detecting dark matter particles at experiments like ATLAS.

Characteristics of dark matter and consequences for detector signatures

Since dark matter is dark, it will not interact significantly with instruments made of ordinary matter. For this reason, the underlying signature of dark matter production at the LHC, used by all ATLAS searches, is the presence of invisible particles in proton-proton collisions.

One might reasonably ask how invisible particles can be observed, since they are by definition undetectable! We solve this problem with a little ingenuity. Before each collision, the protons travel along the direction of the LHC beams, and not in directions perpendicular to the beams. This means that their momenta in these perpendicular directions – their "transverse momentum" – is zero. A fundamental principle of physics is that momentum is conserved and so, after the collision, the sum of the transverse momenta of the products of the collision should still be zero. Therefore, if we add up the transverse momenta of all the visible particles produced in the collision and find it not to be zero, then this could be because we have missed the momentum carried away by invisible particles.

This happens routinely in ATLAS, in the case of physics processes involving neutrinos. We refer to this missed transverse momentum as "ETmiss". LHC searches for dark matter look for collisions with large values of ETmiss, where the dark matter is produced in association with other, visible particles from the Standard Model, such as photons, quarks or gluons (forming "jets" of particles), or electrons, muons or tau leptons. While ETmiss can be difficult to measure because it relies on accurate measurements of all the other particles in the collision, it is a powerful tool for observing dark matter.

A further requirement for the identification of dark matter particles in collisions is that the invisible particles should not decay as they travel through the ATLAS detector. In order for an invisible particle to be a candidate for the "relic" dark matter produced in the Big Bang, it should have a lifetime of at least the age of the universe – of the order of 14 billion years. Particles created in LHC collisions take about 40 nanoseconds to cross the ATLAS detector, so requiring that their lifetime be longer than this is not enough, on its own, to prove they constitute the dark matter. Complementary information from astroparticle experiments searching for relic dark matter would be required. However, it is a very good start!

It is worth noting that other particles that are connected to dark matter might also be detected at the LHC, for example new short-lived particles that can decay both into dark matter and into known matter. Observing those would be an important complement to an observation of dark matter particles from space, as it would allow us to better understand the landscape of dark matter interactions.

What could dark matter be? Theoretical hypotheses

Experimentally, there are very few indications of what dark matter might be. We can, however, make theoretical hypotheses on the nature of dark matter, which are useful to experimentalists. The theorist and experimentalist communities often collaborate, for example within the LHC Dark Matter Working Group^[3]. Theoretical models of dark matter can tell us more about how the interaction of dark matter with ordinary matter may take place. From that, we can predict what to expect in our detectors if that model were realised in nature. This is relevant for designing detectors sensitive to dark matter, and for deciding how to analyse the products of the collisions once they have been recorded. It is also useful to know what to look for, as we have to decide in real-time which collisions to save data from (this is done using the ATLAS trigger system). A solid theoretical framework for dark matter is also necessary to put LHC searches into context and to compare them with dark matter searches from other instruments.

Searches for dark matter at the LHC are commonly guided by theoretical models that would allow us to explain the relic density of dark matter with one or a few kinds of particles. A class of models that satisfies these requirements includes a dark matter particle that only interacts weakly with ordinary particles and has a mass within the energy range that can be probed at the LHC – a Weakly Interacting Massive Particle (WIMP).

Using WIMP models as our starting point for LHC searches doesn’t mean that we are bound to the idea that dark matter should be described with a single particle and a single interaction! This is especially important when you consider that the content of dark matter in the universe is five times the content of ordinary matter, and ordinary matter is described by a variety of different particles and interactions. At the LHC, we have begun our tour into possible theoretical models of dark matter^[4] hoping that the few most prominent components and interactions of dark matter will be detected first, just as the electron, proton and electromagnetic interaction were discovered before all other particles of the Standard Model.

The simplest models one can build in terms of particle content are those where the dark matter particle is added to the Standard Model. In these models, the interaction between visible and dark matter must proceed through existing particles, such as the Z or Higgs boson. This means that the Z or Higgs boson could decay into two dark matter particles^[5], in addition to their ordinary decay modes involving Standard Model particles.

These models are called “portal” models of dark matter, as known particles act as the portal between what we know (ordinary matter) and what we don’t know (dark matter). While models with a Z boson portal are fairly constrained by precision measurements, including those done at the LEP collider at CERN during the 1990s, now is the first time in the history of particles that we can study the properties of the Higgs boson in detail. We could discover whether one or more of those properties lead to a connection to dark matter.

In addition to dark matter, one can also conceive of another particle not included in the Standard Model that acts as a portal particle. These are called “mediator” particles, since they mediate a new interaction between ordinary matter and dark matter. In the simplest versions of these models, the mediator is an unstable heavy particle that is produced directly from the interaction of Standard Model particles, such as quarks at the LHC. Therefore, it must also be able to decay into those same particles, or into a pair of dark matter particles. If a model of this kind occurs in nature, we have a chance to directly discover this mediator particle at the LHC, as we would be able to detect its Standard Model decay products. Other simple models don’t have a mediator that can also decay to Standard Model particles, but instead foresee the production of dark matter particles in association with Standard Model particles that can aid the detection of the process over known backgrounds.

While these models are commonly used to interpret the results of many LHC searches in terms of dark matter, they are too simple to represent the full complexity of a dark matter theory. However, they are still useful as building blocks for more complete theories with more ingredients.

The most popular example of a more complete theory that includes a dark matter candidate is supersymmetry (SUSY). SUSY was one of the first dark matter models to be studied extensively at the LHC. An appealing feature of supersymmetry is that it also solves a stability problem of the relatively low mass of the Higgs boson and other electroweak particles of the Standard Model (around 100 GeV) compared to the Planck scale (10¹⁹ GeV), at which gravity is expected to become strong and the Standard Model must break down. Quantum field theories like the Standard Model naturally prevent such large differences in energy scale from developing, so a physical mechanism is required to generate them. SUSY models provide such a mechanism and, in many cases, predict the existence of a new stable, invisible particle - the lightest supersymmetric particle (LSP) - which has exactly the right properties to be a WIMP dark matter particle. The search for particles predicted by SUSY is a major focus of the ATLAS physics programme. If produced in LHC collisions, these particles could decay to produce a variety of Standard Model particles that can be observed in the ATLAS detector, together with two escaping LSP dark matter particles that generate the characteristic ETmiss signature discussed above.

Many other theories, of various degrees of completeness and complexity, contain dark matter particle candidates. Some of them predict new particles similar to the Higgs boson that can decay into dark matter, while others go beyond the WIMP paradigm and include mediators with extremely feeble interactions with known particles that only decay after traveling significant distances inside (or outside!) the detector, or more complex sectors of particles mirroring the Standard Model^[6]. It is important for LHC searches to cover all this ground, while also preparing for unexpected, not-yet-theorised discoveries. No stone must be left unturned!

Experimental techniques and results

ATLAS already measures many processes involving invisible particles, namely neutrinos from the Standard Model. Fig. 5 shows the results of the measurement of the number of Z bosons decaying into a pair of neutrinos (about one fifth of all Z boson decays). As shown in the diagram in Fig. 6, we use a visible object (in this case a photon) to detect the presence of invisible particles and measure their missing transverse energy, as explained in the previous section.

A very similar technique can be used for detecting the presence of dark matter particles. If we take the process in Fig. 6, replace the neutrinos with dark matter particles, replace the Z boson with a generic mediator between ordinary matter and dark matter, then we have the diagram in Fig. 7.

The detector signature of the processes shown in Fig. 6 and Fig. 7 is identical (and is shown in the event display in Fig. 8). Since we cannot distinguish the processes on a collision-by-collision basis, we have to take a different approach. We start by collecting a large number of events that have a large amount of missing transverse momentum and a highly energetic object. Then, we estimate precisely the number of expected events from Standard Model processes (called “backgrounds”), and look for an excess of additional events that could be due to dark matter processes. This kind of search is called “ETmiss+X”, where X stands for what the dark matter recoils against^[7].

So far, we have not found any excess with respect to backgrounds in this kind of search,as shown in Fig. 12 where the data agrees with the Standard Model-only prediction. Still, the journey of ETmiss+X searches at the LHC is far from over. Adding data and improving the experimental precision of future searches will enable us to search for even weaker dark matter interactions yielding processes that are still rarer than those to which we are already sensitive.

The advantage of this kind of search is that it makes no specific assumption about the nature of the invisible particles, other than that they are produced in association with a Standard Model particle. It is therefore well-suited to cast a wide net on a variety of dark matter models, as long as the model’s signature includes invisible particles and includes dark matter–Standard Model interactions. Conversely, the very large Standard Model backgrounds in ETmiss+X searches can be reduced by giving up some of their generality, for example by requiring distinctive particles (e.g. top quarks, the Higgs boson or related particles) to be produced in association with the dark matter.

The mediator particle can also decay to visible particles, leading to a peak or "resonance" in the total mass of those particles. Searches for new particles using resonances in the total mass of visible particles have led to numerous discoveries at colliders, including, most recently, the Higgs boson at the LHC. Given that the LHC is the highest-energy laboratory particle collider, the most obvious goal is to search for extremely massive particles that could not have been produced before.

Still, dark matter mediators could also appear at lower masses, escaping detection because of very low couplings to protons. This is a region where it has been increasingly difficult to perform searches due to the overwhelming Standard Model backgrounds that exceed the experiment’s data capacity if recorded in their entirety. Since background events are indistinguishable from events coming from decays of dark matter mediators, there is a risk of discarding both. Being able to detect this kind of process has provided motivation for overcoming technical limitations. All the main LHC experiments now employ data-taking techniques that allow them to retain a smaller amount of information for some events, so that more events can be recorded^[8]. These searches have not yet yielded any new particles, but improvements to the data selection and data acquisition system may bring surprises for the next LHC run.

The results of searches for invisible and visible dark matter-mediator decays bring complementary information on different parameters of dark matter models. Together, they could help to characterise the nature of a discovery. We must keep in mind, though, that these searches are interpreted in terms of the processes shown in Fig. 7, which stem from a very simple theoretical model. In this model, the only two new particles are the dark matter and the mediator of the interaction, and that may not describe the full complexity of the unknown matter in the universe.

This is why ATLAS searches target many other experimental signatures in addition to MET-X and resonance searches. For example, models including putative new Higgs bosons yield an assortment of detector signals that can be targeted by different searches. These results can be compared to see whether there are regions in the model parameter space where we haven’t yet looked and, in some cases, they can be combined to strengthen the discovery potential or constraints on dark matter models. A comprehensive summary of these kinds of searches for dark matter, as well as their connection to astrophysical searches (described in the next section), can be found in a new ATLAS paper published today (arXiv: 1903.01400).

Compared with ETmiss+X searches, detector signatures from SUSY scenarios offer the possibility to make use of some additional tricks to identify a dark matter signal from the Standard Model background.

In many models, SUSY particles are produced in pairs due to a requirement to conserve a quantity called “R-parity”^[9] (sometimes also denoted “matter-parity”). Whenever a SUSY particle decays, the resulting decay products must include exactly one lighter SUSY particle. The decay chain ends when the lightest SUSY particle, which is a candidate dark matter particle, is produced.

In contrast to many non-SUSY dark matter models, SUSY particle decays can generate many visible Standard Model particles of high energy. Hence, events containing SUSY particles can be identified by requiring these particles as well as missing transverse momentum. A further trick is to make use of constraints on the momenta of the visible particles produced in the SUSY decays coming from the high masses of their SUSY particle parents. In particular, when two visible particles are produced from two identical decay chains in a SUSY event, we can measure properties of the event which can take on much larger values than those expected in Standard Model background events. An example is shown in Fig. 10.

With the help of these tools, SUSY searches are able to set tight requirements for events with a given set of characteristics, targeting specific models. This makes them less general than ETmiss+X searches, but also less impacted by large numbers of background events.

ATLAS has not yet found evidence of SUSY LSPs, and has strongly constrained many of the models that would simultaneously solve the dark matter puzzle and provide an explanation for the low mass of the Higgs boson. Nevertheless, many SUSY variants remain interesting and the search isn’t over, as described in the dedicated feature article.

Many other searches for particles from more complex dark matter theories, e.g. those in footnote 7, are also performed in ATLAS even though we don’t cover them in detail in this article. Some of the characteristics of these particles make them behave very differently compared with the particles the LHC was built to observe. Therefore, searching for these (still well-motivated) variants of dark matter is generally more challenging and requires dedicated techniques to identify and reconstruct candidate particles that would hint at the presence of dark matter. These searches are now at the forefront of the ATLAS and LHC quest for dark matter, and have gathered at least as much interest as searches for WIMPs and their associated particles.

Connecting collider searches to astrophysical searches

Searches for dark matter at the LHC are typically searches for the production, rather than the interaction or annihilation, of potential dark matter particles. As such, data from ATLAS would not provide proof that a new particle constitutes the dark matter – the sensitivity to dark matter lifetimes is just too short (see above). Nevertheless, ATLAS data could establish consistency with the predictions of dark matter models, and within those models ATLAS can provide complementary information to the broad range of astroparticle searches for the interaction of relic dark matter particles being carried out around the world. This complementarity can be illustrated taking, for example, the simple dark matter-mediator model.

Within this model, in order for dark matter particles to be produced in pairs at the LHC, two strongly interacting quarks or gluons from the colliding protons must interact to produce the two dark matter particles (Fig. 11(b)). These same interactions could enable relic dark matter particles trapped in the Milky Way galaxy to scatter off atomic nuclei on Earth, generating the nuclear recoil signature exploited by "direct" astroparticle searches for dark matter such as XENON in Europe, LUX in North America and PANDA-X in China. Constraints from ATLAS searches can therefore be translated, albeit with assumptions on the mediator–proton and mediator–dark matter interaction, into constraints on the possible signals in those experiments (Fig. 12).

Furthermore, the same interactions also enable relic dark matter particles produced in the early universe to annihilate and create Standard Model particles (Fig. 11(a)). This leads to the signatures for dark matter sought by "indirect" dark matter search experiments – typically high-energy photons (observed by telescopes such as HESS, MAGIC and VERITAS), neutrinos (observed by neutrino telescopes such as IceCube) or anti-particles (detected by space experiments such as AMS on the International Space Station). Results from collider searches can therefore also be compared with results from those experiments.

The complementarity between recent ATLAS searches and astroparticle searches for dark matter is illustrated by Fig. 12, for the case of the simple dark matter-mediator model.

When interpreting and combining ATLAS results and those from astroparticle dark matter searches, we need to consider whether the dark matter model being tested is consistent with the observed density of relic dark matter particles. This has been measured with a precision better than 1% through observations of the cosmic microwave background by satellites like Planck. When considering a particular dark matter model, this only sets an upper limit on the amount of dark matter the model should produce. This is because, in principle, the dark matter could consist of multiple types of particles, with any one type only contributing a fraction of the amount measured by Planck.

The relic dark matter density constraint is particularly important for SUSY dark matter models, where the models can often predict more dark matter than the Planck satellite observed. Special characteristics of the model, such as closely-spaced SUSY particle masses or increased dark matter interactions, can reduce this density to values consistent with Planck observations, and searches for models with these characteristics are a high priority for ATLAS.

Outlook: where do we go from here?

• ATLAS is searching for dark matter at the LHC in synergy with other experimental collaborations, such as CMS and LHCb. LHC experiments have not yet discovered dark matter candidates from Run 1/2 data, but there is a large number of proton-proton collisions ahead. The upcoming LHC data-taking period (2021-2023, known as Run 3) is expected to more than double the current dataset, and the high-luminosity period beginning 2026 will deliver at least another factor of 10 more data. The experiments will be able to probe dark matter processes that are rarer and more challenging to reconstruct than the ones studied today. In view of the upcoming data-taking, experiments are also making use of more advanced data-collection and data-analysis techniques, such as machine learning^[10].
• Direct and indirect searches for signals of the existing dark matter in our galactic neighbourhood are important complementary strategies to LHC searches, since astrophysical experiments are able to detect relic dark matter and they are necessary to confirm that a new invisible particle discovered at the LHC could make up dark matter. We will continue the dialogue with these experiments, exchanging scientific results and perspectives, share theoretical models, and extend the discussion to the broader astrophysics community.
• Other experiments can probe dark matter models to which the LHC experiments are not sensitive, for example models where the interactions between dark matter and ordinary matter are too feeble for dark matter to be produced in collisions of known particles. These experiments are being discussed in the Physics Beyond Colliders effort that recently started at CERN.
• As one of the main outstanding questions in fundamental physics, the identification of the nature of dark matter is a key scientific driver for the future of particle physics. For this reason dark matter searches are a main focus of the discussions, including both experimentalists and theorists, which have taken place in recent initiatives to draw up roadmaps for the future of the field. While the nature of dark matter is currently still unknown, it is clear that the quest to better understand it will be a highlight of humanity’s study of the fundamental constituents of the universe for many years to come.

About the authors

Caterina Doglioni is associate senior lecturer at Lund University, Sweden, and member of the ATLAS collaboration. She searches for new phenomena in ATLAS data. One of the targets of her research are possible mediators of dark matter interactions, discoverable using non-standard data recording techniques. Doglioni has been one of the LHC Dark Matter Working Group organisers. Dan Tovey is Professor of Physics at the University of Sheffield and a renowned expert of supersymmetry, a theory which predicts – among other phenomena – dark matter particles. Tovey coordinated the ATLAS physics programme between 2016 and 2017.

Research by C. D. is part of a project that has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation program (grant agreement 679305) and from the Swedish Research Council. Research by D. T. is part of a project that has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation program (grant agreement 694202) and from the UK Science and Technology Facilities Council (STFC).

[1] For an exhaustive overview of the history of dark matter, with ideas on dark matter that date even further back in time, see Bertone and Hooper's “A History of Dark Matter” (arXiv: 1605.04909), or Bertone, de Swart and van Dongen's “How dark matter came to matter” (arXiv: 1703.00013).

[2] This piece will not discuss the possibility that scientists haven’t understood all of the details of the structure of space-time, including how gravity acts. That hypothesis is discussed in more detail in this article and its references: "Shaking the dark matter paradigm" (Symmetry magazine, 2017).

[3] For this reason, the community of theorists and experimentalists looking for dark matter at the LHC has joined forces, forming first the Dark Matter Forum and then the Dark Matter Working Group. The goal and results of those group are described here.

[4] This article does not contain an exhaustive list of models. For a graduate-level lecture series on models of dark matter see, for example, the TASI "Lectures on Dark Matter Physics" by M. Lisanti (arXiv: 1603.03797).

[5] If the dark matter mass is less than half of that of the Z or the Higgs boson.

[6] For an introduction to these kind of models see, for example, "If You Can’t Find Dark Matter, Look First for a Dark Force" (Nautilus article, 2017), "Hunting for Dark Matter’s ‘Hidden Valley’" (BNL feature story, 2016), "Voyage into the dark sector" (Symmetry magazine, 2018) and "Long-lived physics" (CERN article, 2018).

[7] For more information on the missing transverse momentum+jet search, see the 2017 ATLAS Physics Briefing "Chasing the Invisible".

[8] For more information on this kind of searches, see the 2018 ATLAS Physics Briefing "A new data-collection method for ATLAS aids in the hunt for new physics".

[9] R-parity ensures that in SUSY models protons, and hence all of the atoms in the universe, are unable to decay to other particles quickly by exchanging SUSY particles. In models without R-parity conservation, this can also be prevented. However, introducing R-parity is the simplest possibility.

[10] For more information on ongoing efforts on Machine Learning, see the DarkMachines research collective. For general perspectives on data acquisition and collection see the HEP Software Foundation.

Further Reading

• For more advanced insight into the topics in this feature article, see Dark Matter Searches at Colliders by Antonio Boveia and Caterina Doglioni (Annual Review of Nuclear and Particle Science, Vol. 68:429-459, 2018, arXiv: 1810.12238).
• The Higgs boson: the hunt, the discovery, the study and some future perspectives by Heather Gray and Bruno Mansoulie, ATLAS Feature Article (2018).
• Broken symmetry: searches for supersymmetry at the LHC by George Redlinger and Paul de Jong, ATLAS Feature Article (2017).