Experimental Evidence

χ

b

¯b

˜ j χ

(a) ˜b→b˜χ⁰₁ ^pp

¯ j c

(b) ˜t→c˜χ⁰₁ ^pp

¯b

˜ j χ

(c) ˜t→tχ˜⁰₁

Fig. 3.4:Pair production of squarks in association with a jetjinppcollisions and their subsequent decays. (a) Production of ˜b˜b with decay mode: ˜b → bχ˜⁰₁. (b) Production of ˜t˜t with decay mode:

˜

t→cχ˜⁰₁, and (c) the decay mode: ˜t→`^±νbχ˜⁰₁ (four body decay).

As already mentioned, SUSY is a complete theory that provides a dark matter candidate, the LSP, here the neutralino. The next section discusses the need for dark matter and alternative approaches besides SUSY that try to model it.

3.3 Dark Matter

3.3.1 Experimental Evidence

There is a number of observations from the present and past universe that point to the existence of dark matter (DM). It has been first postulated by Fritz Zwicky in 1933 to explain orbital velocities of galaxies in galaxy clusters [29]. He measured these in the Coma cluster (also called

‘Abell 1656’) and found that the amount of luminous matter is not accountable for keeping the galaxies on their orbits. The velocities measured would lead to a diffusion of galaxy clusters. In spite, Zwicky proposed the existence of a ‘dark ’component with a mass 400 times the mass of the luminous matter to keep Newton dynamics valid. The term dark refers to the property of

non-interaction with electromagnetic radiation.

Later on in the 1970s, measurements of rotation curves of spiral galaxies supported the existence of an unknown DM component [30]: the rotation curves v(r) are measured as the tangential velocity of stars moving around the galactic centre at a distance r from the centre. Measure-ments of this kind give information on the mass distributionM(r) inside a galaxy. In general, the velocity obtained by assuming gravitational force and centripetal force equal has the form

v(r)∝ s

M(r)

r . (3.11)

At large distances, where the visible mass becomes constant, the velocity should decrease as 1/√

r. Instead, in most spiral galaxies it was observed that the velocity is rather constant with increasing r (sometimes even increasing, see e. g. Ref. [41–43]). Figure 3.5 shows the measured data for v(r) for the galaxyngc4157 in red [44, 45]. The model for v(r) including a disk and a bulge component that make up the visible matter of the galaxy is shown as the green curve.

In order to resolve the discrepancy between the green curve and the data an additional dark matter halo component is introduced (then: v_tot = ^qv²_disk+bulge+v_halo² ). The model of the halo is shown in blue. The velocity vtot was fitted to the data, the fitted components are the curves shown. The dark halo mass component has to increase linearly with r to explain the data. While both Zwicky’s observations and the rotation curves of galaxies can have

alterna-40 60 80 100 120 140 160 180 200 220 240

0 5 10 15 20 25 30

rotationalvelocity[km/s]

radius [kpc]

data ngc4157 v_disk+bulge(r) vhalo(r)

Fig. 3.5: Rotation curve of the spiral galaxy ngc4157 with fitted disk+bulge component (green) and halo component (blue).

tive explanations other than DM, like modified Newtonian Dynamics (‘MOND’ theories), data from gravitational lensing cannot be explained by these alternatives. Gravitational lensing is a model independent tool to obtain mass distributions of galaxies and galaxy clusters by studying deflection of light from the gravitational potential of a foreground object. The most prominent measurement w. r. t. DM evidence is the one from the bullet cluster [46]: the bullet cluster is the result of two colliding galaxy clusters. The observation from radiative gas distributions inside the cluster point to an interaction that has taken place between the two colliding clusters since the gas is prominent in the centre. Gravitational lensing data however measures gravity

centers displaced w. r. t. the centre. MOND theories would not predict such a behaviour, instead a present DM component could explain the displacement: when the clusters collided the DM components barely interacted with each other and instead travelled undisturbed.

While these observations from the present universe are already compelling, there is an even more substantial observation from the early universe: thecosmic microwave background (CMB). The CMB is the photon radiation originating from about 380 000 years after the Big Bang. The Big Bang initiated the early phase of the hot universe where all photons and nuclei where in thermal equilibrium constantly interacting with each other. When the universe cooled down photons decoupled from the rest of the particles and began to travel freely. Therefore, the CMB is also called surface of last scattering. The latest most precise measurements of this radiation yield a temperature of T = 2.7255±0.0006 K^b[8]. The CMB is extremely isotropic supporting the model ofinflation: it is the same all over the sky, in every direction. There are only small anisotropies of the order ofµK. They are these anisotropies that reveal a lot of information about our universe. Therefore, the angular power spectrum is examined: it is the temperature differ-ence between two positions as a function of the angular separation (and not orientation, since the CMB is isotropic). Since the temperature fluctuations lie on a sphere they are expressed in a series of spherical harmonics:

∆T(θ, φ)

T0 = T(θ, φ)−T₀

T0 =^X

l,m

a_lmY_lm(θ, φ). (3.12) In Eq. 3.12,l denotes the multipole order and is connected to the angle θvia θ=π/l and thus is a measure for the distance on a spherical surface. The modesa_lm are assumed to be Gaussian and uncorrelated [47]. For an isotropic sky, all modesm are equivalent. The power spectrum is finally obtained as

Pl= l(l+ 1)C_l

2π with Cl=h|a_lm|²i. (3.13)

The power spectrum as measured by the PLANCK satellite [48] is shown in Fig. 3.6. It exhibits some striking maxima and minima. They originate from acoustic oscillations in the early uni-verse at the time of the photon decoupling. The oscillations are a product of the competing pressure and gravitational force. While the gravitational force leads to compression of dense areas the pressure leads to the exact opposite effect causing the oscillations. At the time of decoupling, these oscillations were frozen. More dense regions exhibit higher temperatures as lower density regions. The first peak in Fig. 3.6 gives information about the geometry of the universe, the second, smaller peak about the baryon density and the abundance of dark matter influences the third peak. The damping tail at high l is due to the surface of last scattering having a finite thickness where not all photons decoupled at exactly the same time. From these peaks we know that the DM is making up about 25.9% of our universe where baryonic matter only contributes∼4.9% [48]. The open question is what is: this ‘dark matter’?.

We know that DM is interacting gravitationally. It must be at most weakly interacting with SM particles, paying respect to the term ‘dark’, otherwise it likely would have been already detected. It has to be stable on a cosmological time scale (otherwise a decay would imply an exponentially small abundance of dark matter at the present) and has to have the right relic

bIt is obtained from the intensity of the black-body radiation that is the CMB.

Fig. 3.6: Measured Power Spectrum by PLANCK [48]. The overlayed curve is fitted to the data.

The underlying model is the ΛCDM theory.

density consistent with cosmological measurements. There are three different concepts for dark matter:

• Cold DM: “Cold” refers to the non-relativistic speed (v < 0.1c) of the DM particles.

Cold DM is necessary to explain large structure formation in the universe like galaxies and galaxy clusters. Cold DM can play the role of a compactor of structure. The most popular candidate for cold DM is the Weakly Interacting Massive Particle (WIMP).

Other candidates are the sterile neutrino, the axion and primordial black holes^c.

• Warm DM: “Warm” refers to the relativistic speed (0.1c < v <0.95c) of the DM particles.

These particles move too quickly to be bound to galaxies or clusters and they do not form gravitational lenses. A candidate for warm DM is also the sterile neutrino that is required in certain theories. This scenario is also favoured by some measurements of haloes of

‘satellite galaxies’ (see e. g. Ref. [49]).

• Hot DM: These DM particles travel at ultra-relativistic speeds (v >0.95c). These parti-cles are needed to explain the lensing data of the Abell cluster and in certain theories. But they are assumed to be too light to be responsible for the DM component predicted from cosmology. We already know an example for hot DM which is the neutrino as a Weakly Interacting Light Particle (WILP).

These concepts are not mutually exclusive and can coexist. However, the most favoured concept is the one that DM consists of WIMPs. WIMPs are expected to interact weakly with normal matter. The expected WIMP massesm_χ range from about 10 GeV to a few TeV. Lower masses are excluded by experiments and higher masses are excluded by cosmological considerations. It is assumed that WIMPs were in thermal equilibrium with the SM particles after inflation. This means that they were equally transforming into SM particles as SM particles were transforming

cSterile neutrinos denote heavy, right-handed neutrinos that do not couple to the Z-boson and only interact via mixing with SM neutrinos. Axions are a consequence of a spontaneously broken “Peccei-Quinn” U(1) symmetry introduced to solve the absence ofCP violation in QCD.Primordial black holesdenote black holes formed during the first second of the universe’s existence from a gravitational collapse of density fluctuations.

into WIMPs. When the universe cooled down, WIMP production was suppressed by their mass.

One speaks of a ‘freeze out’ of WIMPs at the temperature TF ' ^m₂₀^χ, when the transforming probability into SM particles fell under a certain threshold [8]. From the relic density, the present abundance of DM, it is possible to determine the interaction cross section of DM with SM particles. This indeed leads to a cross section at the weak scale which lends support to the WIMP picture for DM. A favoured WIMP candidate is the lightest supersymmetric particle, the neutralino.

If WIMPs exist, we should be able to detect them. There are three categories of WIMP search experiments:

• Direct Detection: A search for WIMP-nucleon interactions is performed: a WIMP might scatter on nuclei of detector material and thereby transfer recoil energy. This recoil energy can be measured e. g. by phonon detection. There are many experiments targeting direct DM detection such as XENON [50], CDMS [51], LUX [52], CRESST [53], etc..

All of these have slightly different materials and background suppression, are sensitive to spin-dependent or spin-independent interactions.

• Indirect Detection: A search for annihilation products of WIMP-WIMP interaction.

Space experiments detect photons/neutrinos/electrons/positrons/antiprotons and search for a feature in the energy spectrum. Experiments such as Fermi-LAT [54] and MAGIC [55]

are space telescopes. Earth based experiments are IceCube [56] or ANTARES [57].

• Pair Production: Collider searches aim at the production of WIMPs in pairs. If they really interact weakly there is a chance of producing them directly in collisions with a sufficiently high centre-of-mass energy above 2mχ. The WIMPs will escape the detector just like neutrinos and will leave a signature of missing transverse momentum.

All methods are complementary to each other. This thesis focuses on the pair production of WIMPs using the Atlasexperiment at the Lhc(see Chap. 5). This production can be depicted as shown in Fig. 3.7^d. An advantage with respect to direct detection searches is the better sensitivity to low WIMP masses, that hardly lead to a measurable recoil in a WIMP-nucleon scattering but can be produced in particle collisions. The underlying modelling of WIMPs is discussed in the following.

Fig. 3.7: Possible pair production of WIMPs at the Lhc: (a) in context of an effective field theory where the blob represents the unresolved physics, a new mediator; (b) in context of a simplified model whereA denotes the exchanged mediator with couplings g_q and q_χ to quarks and WIMPs, respectively. The mediator diagram is an example fors-channel production. In both diagrams initial state radiation is added that recoils against the invisible WIMPS.

dRotation of the time axis yields the Feynman diagrams for direct detection (90^◦) and indirect detection (180^◦).