Light-Phonon Technique

Phonon and light detector are paired in a detector module and are read out simultane-ously. When a particle interaction in the target crystal happens, two coincident signals are measured - one from the phonon and one from the light detector. The fraction of these two signals depends on the type of interaction and, therefore, this effect allows an active background discrimination.

The fraction of energy deposited in the absorber and transformed into phonons is mea-sured by the thermometer of the phonon detector. As the relative amount of deposited energy transformed into phonons is nearly independent of the interacting particle, the phonon signal can be used to determine the total amount of the energy deposited very precisely².

On the contrary, the amount of produced scintillation light strongly depends on the type of interacting particle. Therefore, the light signal is used to discriminate between different types of interacting particles.

The principle can be seen in figure 2.7, where a target crystal was irradiated with a

57Coγ-source and a⁹⁰Srβ-source (left plot). The energy measured in the light channel is plotted against the energy measured in the phonon channel. Events from the electron-and γ-source, as well as the background events are located in an approximately linear band. This shows that the produced light is proportional to the energy deposited in the phonon detector. Typically, the light channel is calibrated so that this band has a slope of one. By this calibration the energy measured in the light channel is assigned with the unit keV_ee, where the subscript “ee” stands for electron-equivalent. Details on the calibration can be found in section 2.5.

In the measurement shown on the right side of figure 2.7 a neutron source was added and events in a second band, with a slope reduced by a factor of about ten, appear.

This band is formed by neutron interactions, which produce less light than a gamma with the same energy in the phonon channel.

The reason for this difference is that the particles interact differently in the crystal.

Particles that interact electromagnetically, like electrons and gammas, transfer energy on the electrons of the crystal atoms. A small fraction of this energy is transformed into scintillation light. Neutrons instead, mainly deposit energy on the oxygen nuclei, which themselves recoil in the crystal afterwards and, thereby, produce a lower amount of light. The produced scintillation light differs even for different nuclei in the way that the heavier the nucleus, the less light is produced [66]. This effect is called light quenching and is exploited in CRESST to distinguish different interaction types.

Light Yield - Energy Plane

The discrimination parameter used in CRESST is thelight yield LY. The light yield of an event is defined as the energy measured in the light channelLdivided by the energy measured in the phonon channelEp:

LY := L

E_p. (2.2)

2The fraction of energy escaping the crystal as scintillation light can even be taken into account in order to make the measured energy independent of the particle type [64].

Energy in phonon channel [keV] Energy in phonon channel [keV]

Energyinlightchannel[keVee]

Figure 2.7: Both plots show the energy measured in the light detector against the energy measured in the phonon detector. In the measurements shown on the left the detector was irradiated with a⁵⁷Coγ-source and a⁹⁰Srβ-source. The electron- andγ-events, as well as the background events, appear in one band. The light channel is calibrated so that this band has a slope of one. In the measurement on the right side a neutron source was added. The neutron events appear in another band with a smaller slope. Image taken from [65].

The common way to illustrate CRESST data is in thelight yield - energy plane where the different event populations appear in roughly horizontal bands. Figure 2.8 shows a light yield - energy plot with data of the module named TUM40 operated in the latest data taking phase of CRESST-II phase 2. Due to the calibration scheme, the main background, consisting of electron and γ-events, appears around a light yield of 1.

The other bands have reduced light-yield according to theirquenching factor QF. A precise measurement of the quenching factors was performed in a dedicated experiment by irradiating a cryogenic detector with a fast neutron beam produced by an accelerator [68]. Although an energy dependence of the quenching factors is observed over the total measured energy range, for energies of 10–40 keV they can be approximated as constant values. These values are summarized in table 2.1. A description of the energy dependence for electron-recoils is given in appendix B. More details on the quenching factors can be found in e.g. [68, 69].

The upper and lower 90 % boundaries of the oxygen and tungsten nuclear recoil bands are drawn in black and red in figure 2.8, respectively. Thus, they enclose the region where the central 80 % of the respective events are expected. The calcium recoil band, which is located between the oxygen and tungsten band, is not drawn for reasons of clarity.

The two-channel detection enables an active discrimination on an event-by-event basis. However, the capability of this discrimination depends on several aspects. Back-ground and signal can only reliably be discriminated where the bands are clearly sep-arated. At low energies the different bands overlap and events inside one band can no more be attributed to a single event type. As the width of the bands is mainly given by the resolution of the light detector, the light detector determines the discrimination

Figure 2.8: Data of the detector module TUM40 operated during CRESST-II phase 2 illus-trated in the light yield - energy plane. The measured events are drawn as blue dots. The electron andγ-background appears in a roughly horizontal band around a light yield of 1. The lines correspond to the 80 % boundaries of the oxygen (black) and tungsten (red) recoil bands.

The calcium band, lying between the oxygen and tungsten band is not shown for clarity. Ad-ditionally the region of interest for dark matter search is marked in yellow. Image taken from [67].

power of the different bands.

Moreover, the event-by-event discrimination requires, that signal and background are expected to appear in different bands. While this is true for the dominant background due to electrons and gammas, this is not the case for neutrons. As mentioned before, neutrons scatter off nuclei like expected for dark matter and, thus, are a very dangerous background.

Due to kinematic reasons, neutrons mainly interact with oxygen nuclei. Depending on the mass of the dark matter particle, the dominant scatter partner changes. In the following the aspects, that determine the distribution of detectable dark matter recoils, are discussed.

Target Nuclei for Dark Matter Particles

As discussed in section 1.4 the expected dark matter particle-nucleus scattering cross-section scales asA² with the mass numberA of the target nucleus. Thus, in CaWO₄, consisting of tungsten (AW≈184), calcium (ACa ≈40), and oxygen (AO ≈16), dark matter is expected to mainly scatter off tungsten nuclei.

However, due to the finite energy threshold of the detector, interactions with an energy deposition below threshold cannot be detected. Therefore, it is necessary to

particle type QF e⁻,γ 1 O-recoils 0.112 Ca-recoils 0.0594

W-recoils 0.0172

Table 2.1:The quenching factors (QF) for CaWO₄in the energy region of 10–40 keV. Although a tiny energy dependence is observed, in this energy region it is valid to approximate the quenching factors as constants. Values taken from [68].

consider the number of detectable counts, i.e. the counts with an energy deposition above threshold.

In the case of a heavy dark matter particle (above ∼ 30 GeV/c²) the majority of detected events is expected to be tungsten scatters, as heavy particles can transfer energy efficiently to a heavy tungsten nucleus. Thus, it is possible to only consider the tungsten band in the analysis [70]. If there is neutron background, a possible dark matter signal could be discriminated, since neutrons and dark matter scatters appear mainly in different bands.

However, a lighter dark matter particle is only able to transfer a lower amount of energy to a heavy nucleus. This energy may be below the energy threshold and therefore not detectable, whereas the energy they can transfer to a calcium or oxygen nucleus might still be in the detectable range. The amount of detectable recoil events depends on the mass of the dark matter particle and on the energy threshold of the detector.

In figure 2.9 the number of detectable recoil events for an energy thresholds of 0.3 keV (solid lines) and 10 keV (dashed lines) for dark matter particle masses of 0.5 to 1000 GeV/c² are shown in black. Additionally, the respective number of the counts recoiling on each nucleus are drawn in colors.

For both thresholds the fraction of tungsten events dominates for higher masses.

However, below a certain mass, dark matter particles cannot transfer an energy above the threshold energy to a tungsten nucleus and then calcium and oxygen recoils dom-inate. This mass depends on the threshold and is at ∼3 GeV/c² for a threshold of 0.3 keV and∼17 GeV/c² in case of a detector with a threshold of 10 keV.

In summary, this shows that it is beneficial to consider all nuclear recoil bands for dark matter search, as this not only increases the number of detectable events but, in addition, extends the range of detectable dark matter particles to lower masses.

Therefore, in CRESST all three nuclear recoil bands are taken into account for the dark matter analysis [67].

Another important aspect that was already mentioned in section 1.4 and is shown also in figure 2.9 is the advantage of a low energy threshold. A lower energy threshold does not only allow to detect lighter dark matter particles but additionally increases the amount of detectable events for all masses.

Figure 2.9: Number of counts above threshold for dark matter particle masses of 0.5 to 1000 GeV/c²with an energy threshold of 0.3 keV (solid black) and 10 keV (dashed black). The fraction of events for each nucleus is shown in colors. Image taken from [71].