Massless particles must be stable

Supersymmetric Dark Matter Candidates

Research report 2007 - Max Planck Institute for Physics

Theoretical Astroparticle Physics (Dr. Raffelt) (Dr. habil. Georg Raffelt)
MPI for Physics, Munich

The particle-physical identity of dark matter is one of the great mysteries of our universe. Its solution can be linked to a previously unproven fundamental spacetime symmetry: supersymmetry. In many supersymmetric extensions of the Standard Model of elementary particle physics, the lightest supersymmetric particle cannot decay and is therefore a very promising candidate for dark matter. The lightest neutralino, which already appears in the minimal supersymmetric model, can be identified as such a candidate in the indirect and direct search for dark matter and via the production at future accelerators. Gravitino, the super partner of graviton, also provides a possible explanation of dark matter as the lightest super particle possible. It cannot be detected in the direct or indirect search for dark matter, nor can it be produced directly on accelerators. The investigation of the decay of long-lived charged particles at future accelerators could, however, enable an experimental proof of gravitino. The upcoming experiments at the CERN Large Hadron Collider can thus become a central key to understanding our universe.
The identity of dark matter is one of the greatest puzzles of our universe. Its solution may be associated with supersymmetry which is a fundamental space-time symmetry that has not been verified experimentally so far. In many supersymmetric extensions of the Standard Model of particle physics, the lightest supersymmetric particle cannot decay and is hence a promising dark matter candidate. The lightest neutralino, which appears already in the minimal supersymmetric model, can be identified as such a candidate in indirect and direct dark matter searches and at future colliders. As the superpartner of the graviton, the gravitino is another candidate for the lightest superparticle that provides a compelling explanation of dark matter. While it will neither be detected in indirect or direct searches nor be produced directly at accelerators, the analysis of late-decaying charged particles can allow for an experimental identification of the gravitino at future accelerators. In this way, the upcoming experiments at the CERN Large Hadron Collider may become a key to the understanding of our Universe.


Numerous astrophysical and cosmological observations indicate that our universe consists of approx. 73% dark energy and approx. 22% dark matter. These components of the universe cannot be explained by the particles that have so far been discovered and investigated in particle physics experiments. So there is only about 5% of the energy content of our universe in the form of the known particles (Fig. 1a). With future particle accelerators - such as the almost completed Large Hadron Collider (LHC) at the CERN research center in Geneva (Fig. 1b) - however, it could be possible in the next few years to produce and identify new particles and thus also the fundamental building block of dark matter.

The fundamental particles discovered so far and their behavior in experiments are very successfully described by the standard model of elementary particle physics. Based on the quantum field theory, this model describes three of the four fundamental forces: the electromagnetic force, the weak force and the strong force. The fourth force, gravity, is much weaker in the experimentally accessible energies than the previously mentioned. It is described by Einstein's general theory of relativity, the connection of which with quantum theory is still one of the greatest challenges in theoretical physics.

Observations of the gravitational fields of galaxies and galaxy clusters indicate the existence of dark matter. For example, the high rotational speed of visible matter in the outer arms of spiral galaxies (Fig. 2a) or the high relative speed of galaxies in galaxy clusters hints at gravitational fields that are much stronger than the gravitational fields one would expect based on the visible ordinary matter. The large accumulation of matter in a galaxy cluster can also act as a gravitational lens that provides distorted images of the galaxies behind (Fig. 2b). The extent of these distortions can only be explained with gravitational fields, the strength of which is far greater than that expected from visible matter. Galaxies and galaxy clusters must therefore largely consist of matter that neither absorbs nor emits light: dark matter.

According to current knowledge, dark matter plays a particular role in the formation of the large-scale structure in the universe (Fig. 2c) play a central role. Even the tiny temperature fluctuations in cosmic microwave radiation (Fig. 2d), which are measured very precisely by satellite and balloon experiments, can be convincingly explained if one assumes the existence of dark matter. Analyzes of these temperature fluctuations enable an exact determination of the proportion of dark matter in the total energy of the universe. In fact, the temperature fluctuations in the cosmic microwave radiation characterize the density fluctuations in the early universe, which were the starting point for the later formation of galaxies and galaxy clusters. Computer simulations - based on the initial conditions from the analyzes of cosmic microwave radiation - provide valuable insights into the formation of cosmic structures. Assuming that dark matter consists of particles with negligible velocities, these simulations show a picture (Fig. 2c) that corresponds very well with the observed distribution of the galaxies.

Since dark matter neither absorbs nor emits visible light and electromagnetic radiation with other wavelengths, its components must be electrically neutral. In addition, they must either be stable or have a lifespan that cannot be far below the age of our universe. With a shorter lifespan, a large part of dark matter would already have decayed today. However, this refutes the effects of dark matter, which were also observed in the Milky Way and in nearby spiral galaxies.

Among the known particles of the standard model of elementary particle physics, only the neutrinos have the basic properties of dark matter: They are stable, electrically neutral and are subject only to weak force and gravity. The so-called neutrino oscillations, which were clearly demonstrated only a few years ago, also show that neutrinos have a mass. However, this mass is so small that the speed of the neutrinos must have been very high in the young universe and also later. Under the assumption that dark matter consists of the established neutrinos, it is not possible due to these high speeds to understand the formation and existence of the observed structures in our universe. In the standard model of elementary particle physics, there is no particle that can explain dark matter in agreement with the observations.

Supersymmetric extensions of the standard model of elementary particle physics

If one calculates the strength of the standard model forces for energies that are many orders of magnitude above the energies that are reached at particle accelerators, then one finds that the different coupling strengths approach a common value with increasing energy. This behavior can be an indication of the union of the three Standard Model forces into one superordinate force. However, if one assumes the validity of the Standard Model up to the unification energy scale, then one encounters the so-called hierarchy problem: It turns out that the 'natural' order of magnitude of the mass of the so-called Higgs particle expected on the basis of quantum effects is far above the range which is obtained indirectly in precision calculations from the data from experiments at particle accelerators. Such precision calculations are part of the research activities at the MPI for Physics.

In the standard model, the Higgs particle is responsible for the masses of the fundamental particles and is therefore a central component. So far it could not be observed directly. It can therefore be assumed that the energy required for its production could not be achieved at the previous particle accelerators. The still outstanding direct evidence of the Higgs particle is therefore one of the main reasons for the construction of the LHC at the CERN research center in Geneva. In the coming years, this particle accelerator will advance into an energy range previously unattainable in laboratory experiments.

A particularly elegant solution to the hierarchy problem results in supersymmetrical extensions of the standard model. Supersymmetry is a fundamental spacetime symmetry between elementary particles with different spins, i.e. between the matter particles and the exchange particles that convey the forces, which are the building blocks of the underlying quantum field theory. If this symmetry is realized in nature, then there must be more than one Higgs particle, and each of the established standard model particles must have a supersymmetric partner. In the case of the Higgs mass, the quantum effects of these new particles compensate for the quantum effects of the standard model particles. This mass can then naturally lie in the range expected from the precision considerations.

Interestingly, supersymmetry doesn't just solve the hierarchy problem. Due to the new particles postulated by supersymmetry, the coupling strengths of the three standard model forces when extrapolating to high energies behave in such a way that they actually meet at a point at the point of union, which is not the case within the framework of the non-supersymmetrical standard model. This behavior underpins the hypothesis of the union of the three standard model forces into one superordinate force. Like the Higgs particles, the super partners of the Standard Model particles have so far only been predicted on the basis of theoretical considerations. The existence of these particles has not yet been proven experimentally. But here, too, hopes will be made for discoveries at the LHC.

Super symmetric dark matter

If the supersymmetry is realized in nature, then it is assumed - also due to the observed stability of the proton - that supersymmetric processes respect a discrete symmetry, the so-called R-parity. The associated quantum number differentiates between the Standard Model and the Higgs particles, the one just R-parity (+1) and their super partners who have a odd Have R parity (-1). A process only receives R-parity if the product of the R-parities of the particles in the initial state is equal to that of the particles in the final state.

It follows from the required preservation of R-parity that the disintegration of a super partner always has to result in another super partner. Since the masses of decay products must always be below the mass of the decaying particle due to energy-momentum conservation, this implies that the lightest super partner - even if it is significantly heavier than the established standard model particles - does not decay if R-parity is preserved can. So the lightest super partner will be stable. If it was produced in the early universe, it could still be in abundance today. An electrically neutral lightest super partner is therefore a very promising candidate for dark matter.

In fact, supersymmetric extensions of the Standard Model very naturally provide such dark matter candidates. These include the lightest Neutralino and Gravitino. In the following, these still hypothetical particles, their properties and detection options are described in more detail.

The lightest Neutralino

The neutralinos are super particles that consist of mixtures of the electrically neutral super partners of the Higgs particles, the photon and the so-called Z boson. Like neutrinos, they are only subject to weak force and gravity. If the neutralinos exist, then they have to be orders of magnitude heavier than the neutrinos, since they have not yet been detected in particle accelerators. This motivates the classification of a neutralino as a Weakly Interacting Massive Particle (WIMP).

The temperatures immediately after the Big Bang may have been orders of magnitude higher than the mass of the neutralinos. At such high temperatures, all Standard Model particles, the Higgs particles and their super partners could be produced efficiently. The primordial densities of these particles may therefore have been so high that a thermal equilibrium between production and destruction processes prevailed. The frequency of each individual type of particle was then comparable to that of the photons in this hot epoch. However, as the universe expands, the temperature decreases. At temperatures below the mass of a particle, the density of this type of particle becomes very small very quickly. There is no longer enough thermal energy available to be able to continue producing these particles. The heavier a particle is that is in thermal equilibrium, the earlier its density decreases rapidly. The density of the lightest neutralino also decreases sharply until the point in time when the temperature is a fraction of its mass. At this point the density of the neutralinos and the other super partners is so low that a neutralino can practically no longer find a reaction partner for an annihilation process. Such a further super partner is necessary, because due to the preservation of the R parity, super partners can only be produced or destroyed in pairs. If the probability of Neutralino annihilation processes is negligible, then the lightest Neutralino decouples from the thermal plasma, so that the number of this type of particle in the universe (almost) no longer changes.

With computer programs today one can very precisely calculate the decoupling of the lightest neutralino in the early universe and from this its current frequency. The results show that the density of neutralinos today can actually correspond to the observed density of dark matter. In addition, the speed of the neutralinos decoupled from the thermal equilibrium is negligible. Assuming that the lightest neutralino is the fundamental building block of dark matter, the formation and existence of the observed structures in our universe can be well understood. So it could be an accumulation of the lightest neutrals that make up the majority of the mass in galaxies and galaxy clusters.

Three mutually complementary methods are being pursued to experimentally verify this theoretically appealing picture: indirect search, direct search and accelerator production.

The indirect search searches for signals from Neutralino destruction processes. It is expected that in regions of the universe in which the concentration of dark matter is above average, such as in galaxies, neutralino annihilation processes still occasionally take place today. Although these processes do not have a great influence on the neutralino abundance, standard model particles should be emitted in this reaction. These standard model particles can have a high energy and thus lead to energetic cosmic rays (Fig.3a) that should be observable near and on earth. It is possible that such cosmic rays have already been observed by the satellite-based experiment EGRET (Energetic Gamma Ray Experiment Telescope). In interpreting the observed spectrum, however, the challenge is to filter out signals from neutralino annihilation processes, which also depend on the exact distribution of the invisible dark matter, from the complicated background of other sources of high-energy rays. The GLAST space telescope (Gamma-Ray Large Area Space Telescope) will provide new data on this in the future. Also in so-called Cherenkov telescopes, such as H.E.S.S. (High Energy Stereoscopic System) or MAGIC (Major Atmosspheric Gamma Imaging Cherenkov), in which the MPI for Physics is involved (Fig. 3b), signals from Neutralino annihilation processes should be observable.

The direct search searches for signals from neutralinos from their collision with atomic nuclei. As dark matter, neutralinos should also surround the earth with such a frequency that they occasionally encounter atomic nuclei despite their weak interactions. Since the mass of the neutralinos is so large, the core experiences a significant recoil, which leads to a minimal increase in temperature in the material surrounding the core (Fig. 3c). The challenge is to distinguish the recoils caused by the neutralinos from those caused by other particles. Promising methods for this are used e.g. in the experiments CDMS (Cryogenic Dark Matter Search), CRESST (Cryogenic Rare Event Search with Superconducting Thermometers) and EDELWEISS (Experience pour Detecter Les WIMPs En Site Souterrain).To shield from interfering standard model particles, these experiments are located under several hundred meters of rock, which, however, can be penetrated by the weakly interacting neutralinos without any problems. The MPI for Physics is involved in the experiment CRESST, which is located in the Gran Sasso underground laboratory (Fig. 3d).

Heavy, only weakly interacting particles have been produced and investigated with the help of particle accelerators for around 20 years. Short-lived Z bosons, which are the heaviest particles observed so far and are subject to weak force and gravity alone, have already been produced in large numbers. The probability of producing neutralinos should be similar, provided the energies at the particle accelerators are high enough. It is therefore quite possible that neutralinos will be generated in the proton-proton collisions at the LHC in the next few years (Fig. 3e). While a Z boson can be detected via its decay and the resulting visible decay products, a stable, lightest neutralino leaves no trace in the particle detectors and can therefore only be detected with the help of energy-momentum conservation. This requires an extremely precise measurement of the traces of the additionally produced standard model particles, which are also used in the ATLAS experiment which is still under construction (Fig. 3f) should be achieved with the participation of the MPI for Physics. From a theoretical point of view, the mechanism that leads to neutralino production at the accelerator must also be very well understood. This is a subject of current research also at the MPI for Physics.

The Gravitino

The gravitino is the super partner of the graviton, which is the exchange particle of gravitation and as such is not part of the standard model of elementary particle physics. The interactions of the Gravitino are, like those of the Graviton, sensitive to the energies of the interaction partners. The strength of these interactions is also given by the very small Newtonian gravitational constant. In fact, the probability of the interaction of a Gravitino in the laboratory is so small that a Gravitino cannot be produced directly at particle accelerators, even if its mass is in the energy range that is already accessible. The fact that no Gravitino could be detected on accelerators therefore does not allow any conclusions to be drawn about the Gravitino mass. If the Gravitino is viewed as a dark matter candidate, it is assumed, however, that it is the lightest existing super partner and thus lighter than the standard model super partner, which also includes the lightest neutralino discussed above. Due to the extremely suppressed interactions and the unknown mass, the Gravitino can be classified as an Extremely Weakly Interacting Particle.

It must be emphasized here that the gravitino - in contrast to the massless graviton - can only have a mass because at low energies the supersymmetry cannot exist as an exact, but only as a so-called spontaneously broken symmetry. In the case of an exact supersymmetry, the masses of the superpartners would have to be identical to those of the associated standard model particles. However, this can be ruled out, since superpartners at particle accelerators have not yet been observed. In fact, the value of the gravitino mass is directly linked to the so-called refraction scale of supersymmetry, i.e. the energy scale above which the supersymmetry can again be viewed as a perfect symmetry, and is therefore of fundamental importance in supersymmetric theories.