Direct Searches

As stated above, ’direct search’ experiments probe the ’direct’ interaction of dark matter particles with detector material. Astrophysical considerations (f.i. the measurement of the number of tracer stars as a function of the distance perpendicular to the galactic disc at the position of the earth, Weber and de Boer [2010]) give an astrophysical mo-tivation for the presence of dark matter at the position of the earth with a density of

∼0.3 GeV/cm³. Figure 3.2 show examples of Feynman diagrams for the interaction of Kaluza-Klein and supersymmetric particle dark matter candidates with matter. Con-sider a dark matter particle interacting f.i. via the diagrams in fig. 3.2 with quarks in a detector on earth. The dark matter particle as well as the interacting quark are both elementary particles, the interaction is thus elastic and energy is transferred between the two particles. In the rest frame of the detector, the atomic nucleus in which the quark is embedded will thus in general receive energy from the collision. The experimental task of direct particle dark matter search experiments is to measure this energy transfer and discriminate it from background events.

Background events can be caused by all sorts of standard model particles that enter the detector and interact with its material. For instance cosmic rays and particles produced in the interaction of cosmic rays with the earth atmosphere (for example muons) are candidates for particles that generate background events. Direct dark matter search experiments have to install their detectors in underground laboratories (f.i. the XENON

Figure 3.2: Example tree level Feynman diagrams relevant for the direct detection of Kaluza-Klein (upper two plots) and supersymmetric (lower two plots) parti-cle dark matter. The upper two plots (taken from Servant and Tait [2002]) show the t-channel Higgs exchange and the s-channel exchange of a first KK quark mode for the interaction of the first KK mode of the hypercharge bo-son B⁽¹⁾ with a quark in a detector material. The lower two plots (taken from Jungmann et al. [1996]) show the t-channel exchange of the two CP even Higgs particles of the MSSM and the s-channel squark exchange of a neutralino interacting with a quark in a detector material. The diagrams in-dicate the phenomenological similarity of Kaluza-Klein and supersymmetric dark matter particles.

3.2 Experimental Situation experiment is operated in the Gran Sasso massive with∼3.5 km water equivalent shield-ing) to suppress cosmic ray background. Also natural radioactivity in the environment or the detector itself generates particles that lead to background events. Electrons andγ -rays from radioactive decays in the vicinity of the detector or the detector material itself interact typically with the electrons of the material, in contrast to particle dark matter which interacts with the nucleus. It is thus desired to discriminate between electronic and nuclei interactions in the detector. Protons, neutrons and α-particles generated in radioactive decays interact with the nuclei of the detector material and have to be sup-pressed by ultra-clean materials, shielding and active vetos on charged particles. The main background is in fact currently due to neutrons as they are electrically uncharged and mimic the behavior of particle dark matter interactions. It is evident that a very detailed understanding of the background is needed to perform a successful direct search for particle dark matter.

Currently there are O(20) direct detection experiments running. The suppression of background events is in all cases technically highly non-trivial and the concrete methods depend on the experimental approach, i.e. the detector medium and the detection prin-ciple. Most of the currently operating experiments aim to measure the nuclear recoil in a WIMP-quark interaction where typically∼1 keV energy is transferred for a∼10 GeV WIMP mass by measuring one or two of the following three quantities.

• When a WIMP scatters on a nucleus which is part of a solid state detector (typically germanium or silicon), phonons are excited and in turn the temperature of the detector increases. The increase in temperature can be measured with typically highly advanced techniques (f.i. the measurement of electrical resistance changes of either a highly doped semiconductor whose resistance-temperature curve is very steep or the operation of a superconductor on the turning point between super-and normal conducting state). It is obvious that the detector must be cooled to nearly absolute zero temperature and this temperature must be kept stable over a science run, i.e. typically many months.

• In certain liquid (f.i. xenon) and solid state (f.i. NaI doped with thalium) materials, a nucleus can induce the emission of scintillation light if it is hit by a WIMP and thus recoiling (see Chepel and Araujo [2012]). The principle is also used for the detection of high energy neutrons in nuclear physics. The scintillation light can be measured by optical detectors (f.i. photomultipliers). It is not necessary to cool down the detector for the use of this effect and thus large detectors can be realized.

• The∼1 keV recoil of a nucleus hit by a WIMP can induce a band gap transition of valence electrons in semiconductors, typically germanium (band gap ∼0.7 eV) or silicon (band gap∼1.2 eV). Free electrons that can be generated by recoiling nuclei after a WIMP collision are employed in liquid noble gas (typically xenon or argon) detectors, see Chepel and Araujo [2012]. Either the charges in the conduction band or the free electrons can be electronically detected.

As stated, current direct detection experiments use typically two distinct detection prin-ciples in coincidence to increase the discrimination power of signal from background.

The quantity that is directly measured by direct detection experiments is the number of recorded events or the event rate respectively. The event rate is supposed to con-tain a fraction of signal events from WIMP interactions among background events. In practice, the WIMP-nucleon scattering cross section is either inferred from a significant signal measurement or an upper limit on the cross section is derived. A distinction is made between the ’spin dependent’ and the ’spin independent’ WIMP-nucleon cross section. Consider the Feynman diagrams in fig. 3.2. The exchange of a scalar Higgs boson between a WIMP candidate and a quark will lead to a spin independent or scalar interaction. On the other hand, the exchange of fermions depends on the relative spin of WIMP and quark and leads in general to a spin independent (scalar and possibly vec-tor) and a spin dependent (axial vecvec-tor) contribution. Note that vector interactions are helicity suppressed for Majorana fermions such as supersymmetric neutralino WIMPs but not for Kaluza-KleinB⁽¹⁾. For more information on the direct detection cross sec-tion see Servant and Tait [2002] and Jungmann et al. [1996] or Bertone et al. [2005] for Kaluza-Klein and supersymmetric WIMPs respectively. The spin independent WIMP scattering cross section is roughly proportional to the number of nucleons squared but the spin dependent cross section is only proportional to the total nucleon spin (see Jung-mann et al. [1996]). Experiments are therefore typically much more sensitive to the spin independent WIMP scattering cross section (only a material with large atomic number has to be chosen) than to the spin dependent cross section (nuclear spins tend to be small due to spin pairing between nucleons).

To derive a statement on the WIMP-nucleon scattering cross section based on the number of detected signal events in a direct detection experiment it is necessary to input among information on the scattering kinematics and nuclear form factors (which are measured) also astrophysical parameters. Most important are the local dark matter density and the velocity distribution of WIMPs in the detector. Both parameters are subject to intensive discussions. The local dark matter density is in general assumed to be ∼0.3 GeV/cm³, however, the error on this quantity is sometimes argued to be∼10% (Weber and de Boer [2010]) or∼1% (Catena and Ullio [2010]). The WIMP velocity distribution is (usually) taken to be a Maxwell-Boltzmann distribution,f(v)∼1/v_RMS³ exp(−(v−v₀)²/(2v²_RMS)), wherev₀∼220 km/s is the velocity of the earth moving around the galactic center and v_RMS = v₀/√

β where β ∼ 1−2 depends on the WIMP density distribution in the galactic halo via the Jeans equation (see Peter [2011]). The underlying assumption of a Maxwell-Boltzmann velocity distribution is strictly speaking only valid for a collision-less ideal gas with constant density and pressure and thus already intrinsically assumes a specific, i.e. constant, WIMP density distribution. Computer simulations predict, however, that the WIMP density is increasing towards the center of galaxies and thus deviations from a Maxwell-Boltzmann distributions for the WIMP velocity. The influ-ence of this effect can be significant (factor 0.2−6, Baushev [2011]) but depends on the detector properties, see also Peter [2011], Kuhlen et al. [2010]. Figure 3.3 summarizes the current experimental status of direct detection searches with respect to the spin independent WIMP-nucleon scattering cross section. The signal detections by CoGeNT and DAMA are in obvious conflict with the upper limits of most notably XENON100.

The measured DAMA signal is compatible to two different regions in the parameter

3.2 Experimental Situation

Figure 3.3: Current status of spin independent WIMP-nucleon cross section measure-ments as a function of the WIMP mass. The results of different experimeasure-ments are shown (colored) together with predictions of supersymmetric models (grey). Closed colored lines indicate significant detections (CoGeNT and DAMA). The figure is taken from Aprile et al. [2011]. Note that the plot does not contain the hint for a positive signal (∼3σ) reported from CDMS-II (CDMS Col. [2013]) for a WIMP mass of∼8.6 GeV with a spin independent cross section of∼1.9·10⁻⁴¹cm².

space plotted in fig. 3.3. One of the allowed regions is in the vicinity to a region allowed by the CoGeNT detection. Especially the DAMA signal which is the annual modula-tion of the WIMP-nucleon scattering rate while the earth is moving around the sun is highly significant (overall∼9σ detected over 7 annual cycles, Bernabei et al. [2010]) and carefully checked for systematics (Bernabei et al. [2000]). A theoretical explanation of this effect and the non detection in other experiments is challenging, mainly ’inelastic’

dark matter is currently discussed (see f.i. Smith and Weiner [2001]). The inelastic dark matter scenario assumes the WIMP to have intrinsic degrees of freedom (f.i. through a higher Kaluza-Klein state or mixed supersymmetric states) and absorb energy if the in-teraction momentum transfer is large enough. In this way the XENON100 measurement (typically sensitive to∼40 keV recoil energies) and the DAMA measurement (typically sensitive to∼3 keV recoils) can be made compatible. However, much more detailed in-vestigations and independent cross checks are necessary to reach conclusive statements in this issue. Not shown in fig. 3.3 are predictions of spin independent cross sections for Kaluza-Klein WIMPs which are typically∼10⁻⁴⁶cm² (see Servant and Tait [2002]).

The figure shows that direct detection experiments and especially XENON100 are start-ing to constrain the supersymmetric WIMP parameter space but do not yet reach the necessary sensitivity to constrain Kaluza-Klein models.