1. Searching for Dark Matter Beyond the Neutrino Floor.
A literature review presentation by
Warren Lynch

2. Contents Introduction: Experimental evidence for dark matter
Theoretical motivation for dark matter
Direct Detection Methods
Neutrino Floor
Dark matter search methods to overcome the neutrino floor:
Increasing mass time exposure
Directionality
Annual modulation
Target complementarity
Polarizing Helium-3
Summary

3. Experimental Evidence
Mass/light ratio of galaxy clusters [1]
Gravitational rotation curves [2]
Gravitational Lensing [3]
Cosmic Microwave Background (CMB) [5]
-Baryonic matter density: ±0.0010
-Dark matter density: ±0.0057
Big Bang Nucleosynthesis [6]
Figure 1: The Bullet cluster [4]
This list includes some not all of the experimental evidence.
First measurement of this was by Zwicky in 1933: measured the mass of the COMA cluster using observations of the radial velocities of 8 if it’s galaxies and compared this to the visible light emitted from the cluster. He saw that there was much more matter than light emitting matter and states “If this is confirmed we would arrive at the astonishing conclusion that dark matter is present with a much greater density than luminous matter”.
Gravitational rotation curves -> In 1939 Babcock reported that the outer regions of the Andromeda galaxy were rotating with higher than expected velocities and In 1970 Rubin and Ford reported that rotational velocity did not drop of with distance from the galactic center of Andromeda suggesting a greater mass within and around the galaxy holding it together.
Gravitational lensing It gives a separate approach to looking for mass other than the light it emitts. Figure 1 shows an example of possible dark matter within the bullet cluster. As two clusters collide the luminous matter interact and slows down (red) and the dark matter passes through with minimal interaction (blue).
The ratio of dark matter to ordinary matter can be derived from the relative peak heights of the temperature power spectrum of the CMB. More DM more compression, more normal matter bigger bounces.
L is multipole L=10 is about 10 degrees in the sky, L=100 is about 1 degree in the sky and so on. Y axis shows temperature fluctuation but as a correlation function that shows clearer structure at smaller angular scales.
Big Bang Nucleosynthesis -> Todays relative abundance of light elements (Deuterium, Lithium, He, He3) depends on the baryonic density at the time of nucleosynthesis this Gives the density of Baryonic mass so we know that dark matter can not be baryonic as there is simply not enough of it.
Figure 2: CMB temperature power spectrum [5]

4. Theoretical Motivation
Supersymmetry (R-Parity conservation) – Lightest supersymmetric particle (LSP) [7]
Universal Extra Dimension (KK-parity) – Lightest Kaluza-Klein particle (LKP) [8]
Little Higgs (T-parity) – Lightest T-odd particle (LTP) [9]
WIMP Miracle [10]
The evidence for dark matter has led to many theoretical attempts to extend the standard model in order to incorporate missing mass.
All theories look for their lightest particle as dark matter needs to of been around since the big bang for the galaxy formation we observe today. The lightest particle can not decy due to certain conservation laws within the theories.
Supersymmetry -> LSP is the neutralino. Normal particles have R parity +1 and their supersymmetric partner particles have R parity -1.
UED -> all of the SM particles exist in the know dimensions plus one or more extra dimensions.
KK-parity ->plays an analogoues role to R parity in supersymmetry and make the LKP stable.
Little Higgs-> Similar parity conservation to SUSY and UED called T-parity. LTP is the heavy photon.
WIMP Miricle -> The dark matter particles predicted by these theories are termed Weakly Interacting Massive Particles (WIMPs) Interact gravitationally and with other matter at a scale similar to or lower than the weak force . The WIMP abundance predicted by Supersymmetry is approximately the same as the predicted dark matter density from the CMB. This coincidence is termed the WIMP Miracle and premotes the WIMP as a possible dark matter candidate.

5. Direct Detection Methods
Scintillation
- LUX (lqd), Zeplin (lqd), LZ(lqd), COSINE (crystal), DAMA/LIBRA (crystal)
Ionisation
- Drift IId (gas), DMTPC (gas), LUX (lqd), Zeplin (lqd), LZ (lgd)
Phonon vibration
CDMS/SuperCDMS (crystal), CRESSTII (crystal), EDELWEISS-II (cystal)
LHC
Figure 3: LZ two stage signal [11]
Figure 4: Crystal phonon vibration [12]
Scintillation -> A particle interaction causes a light emission that is picked up by PMTs
Ionisation -> A particle interaction ionises within a target volume which is detected as a charge signal.
Phonon vibration -> Crystal detectors that are kept at low temperature and detect a temperature increase from particle interactions within the crystal.
The LHC is another type of Direct detection but they are different from the methods listed here as the LHC tries to create dark matter and detect it rather than detect existing dark matter.
LZ-> Particle interacts inside lqd Xenon which causes scintillation and ionisation. The ionised signal is drifted via an electric field to a gas stage above the liquid where it causes a second stage scintillation. Comparison of the two signal aids in particle identification and background discrimination.
Fig. 4: An illustraion of a phonon vibration through a crystal lattice and fig 5. shows an incoming particle ioising within CS2 gas and drifting via an electric field to a charge read out.
I have listed a few current and next generation dark matter detectors that utilise the detection methods we have discussed. For a more detailed description of WIMP DM detectors and there methods please make note of the reference at the bottom.
Figure 5: Ionisation[13]
For an overview of detector techniques see [14]

6. The Neutrino Floor
Neutrino’s and dark matter candidates can not be shielded against. Only electron-neutrino interactions have been observed [15]. Future DM detectors could also conduct neutrino physics.
This poses a challenge for future detectors looking for dark matter beyond the neutrino floor as neutrinos could mimic a potential dark matter event.
Dark matter detectors are looking for a dark matter interactions with a target nucleus so it is neutrino-nucleus interactions that are of concern and this has not yet been observed [REF].
A dark matter detector sensitive to neutrinos could also conduct neutrino physics such as the study of solar neutrinos in order to learn more about the solar interior.
Figure 6: Current experimental limits (solid lines), future experimental predications (dashed lines) and the neutrino floor [16]

7. The Neutrino Floor Contributions to the neutrino floor come from [15]:
Atmospheric neutrinos produced by cosmic ray collisions with the atmosphere.
Solar neutrino’s (mostly B8) produced via the pp chain.
Diffuse Supernova Neutrino Background (DSNB).
Neutrino’s that contribute to the neutrino floor come from:
Boron-8 solar produced in the PPIII chain. Although the flux is low compared to other solar neutrino flux’s the energy is much higher, making them the most likely to produce a dark matter like signal.
Anti-neutrinos could also add to the neutrino floor they are also produced from within the earth and from nuclear reactors. However, the Geo flux is 2 orders of magnitude below that of the solar neutrino contribution and the reactor flux can be reduced to near negligible by placing the detector far from a reactor. Interesting side note to this would be that a detector placed close to a reactor could be used to monitor it (Watchman).
Cosmic ray collisions produce pion that decay to muons and electrons producing muon and electron neutrinos along the way.
The DSNB is the product of all the neutrinos produced by all supernova that have had sufficient time to reach us and produce a background on earth.
Cosmic Ray interacting with the atmosphere to producing Pions, Muons and electrons along with electron and muon neutrinos.
Figure 8: PPIII chain.
Figure 7: Cosmic ray interaction with the atmosphere

8. Mass Time Exposure 1/MT with negligible neutrino background
1/√(MT) as detector becomes sensitive to neutrino background
Constant as neutrino background begins to saturate [17]
Refers to the amount of target mass in the detector and the length of time the detector has been running.
Probably the simplest idea for searching for dark matter below the neutrino floor is to increase the detector mass and time exposure.
A detectors discovery potential depends on it’s target mass (M), run time (T) and neutrino background and scales as [REF]:
1/sqrt(MT) due to (Poisson) background subtraction being required.
Figure 4 shows an example of the neutrino backgrounds effect on a detectors discovery potential. Background subtraction can be done for low neutrino events but the detector would become saturated at a certain level of background.
In summary the neutrino floor can be probed by simply creating more massive detectors and running them for long periods of time but the trade off is low due to the sqrt term and a better understanding of the total neutrino flux would eventually be required to overcome saturation of the detector seen at high neutron event numbers.
Figure 9: Discovery limit for a 6 GeV/c2 DM particle against neutrino background [17]

9. Annual Modulation
Method for discriminating a WIMP signal from solar neutrinos.
Solar neutrino signal peaks around January 4th
WIMP signal peaks around early June
Timing difference and compression increases with cross section [18]
Figure 10: Residual modulation of DM only, neutrinos only and DM + neutrinos for two different cross sections [18]
The peak solar neutrino signal occurs around January 4th when the distance between the Earth and the Sun is smallest and a hypothetical WIMP signal would peak around early June [7]
The Neutrino + DM signal is compressed and pushed forward in time compared to the neutrino only signal. The timing difference could be used to recognise a DM signal within a neutrino background.
(Residual -> The fractional deviation of the modulated rate from the time-average).
To retrieve the timing information a high amount of statistical data would be required ( > ~ 10^4 events). This is about 1 year of running in an idealised 10 tonne low threshold Xenon detector [8].

10. Directionality
Method for discriminating a WIMP signal from solar neutrinos.
Solar neutrinos come from the Sun.
Wimps expected to come from the constellation Cygnus.
Directionality gives discrimination between the two signals.
Figure 11: Mollweide projection of the angular differential event rate for B8 solar neutrinos and for WIMPs. The events are binned into 3 equal energy regimes between 0-5 keV [19]
Top (bottom) row: Smallest (60°) difference between solar and WIMP directions with WIMP events on the left.
Bottom row: Largest (120°) difference between solar and WIMP directions with WIMP events on the right.
Although the above figure only considers 8B Neutrinos other solar neutrinos also come from the Sun and therefore, like 8B neutrinos their signals can be separated out from a potential WIMP signal using directionality. This would allow for the discovery potential of the detector to continue to scale as 1/MT rather than 1/sqrt(MT) within the solar neutrino dominated background (WIMP mass round 6GeV/c^2)
A directional detector sensitive to solar neutrinos may be able to observe the first solar neutrino-nuclei scattering and could also be used to conduct solar physics as well as search for dark matter beyond the solar neutrino floor.
Difficulty->Scaling up of a large directional TPC. Uses gas which is usually kept at low pressure so this would require a very large volume in order to be competitive with other liquid based DM detectors.
Research is on going by the CYGNUS collaboration into different types of gas mixtures, readouts and pressures that would allow for the optimisation of a large scale directional TPC.

11. Target Complementarity
Similar spectra from WIMPs and neutrinos at each particular WIMP mass and cross section [20]
The particular WIMP mass and cross section is target material dependent [20]
Comparing spectra for different target material gives discrimination.
For particular WIMP masses and cross sections the WIMP and neutrino spectra are similar. The mass and cross sections for which this occurs is target material dependant [4]. It could therefore be tested to see if combining data from different experiments using different target materials may allow for higher discrimination power between wimp and neutrino events.
Fig 8: SI is spin independent such that all the protons within the nucleus are paired with a neutron. SD-N is spin dependant such that there are an even number of protons but an odd number of neutrons and the WIMP interacts with the odd neutron. SD-P is the same as SD-N but it is the odd proton that interacts.
The SI case doesn’t show much variation this is due to the fact that both the WIMP and neutrino nuclei cross sections are proportional to an A2 factor. The most noticeable effect is on the SD-proton interaction.
Figure 12: The difference in cross section from the same wimp interaction for target material of differing atomic mass number, A. Shows results for SI, SD-N and SD-P [20]

12. Polarised Helium-3
Polarising the nuclear spin of helium-3 in the opposite direction to incoming neutrinos
Can be used to reduce solar neutrino interactions (98%) [21]
Can be polarised at high pressures using Spin Exchange Optical Pumping (SEOP) [22]
Can be polarised at low pressures using Metastability Exchange Optical Pumping (MEOP) [23]
Figure 13: Differential cross section for He-3 neutrino interactions at different angles between the incoming neutrino direction and the h-3 spin[21]
When He-3 is polarised in the opposite direction to incoming neutrinos the h-3 neutrino differential cross section approaches 0.
He3 is already a good DM target candidate -> 1kg of He3 has the same number of unpaired neutrons as 90kg of Xenon -> so much more sensitive to SD interactions. It is rare and expensive.
Good WIMP target
Detector needs to point towards the Sun.

13. Summary
If the next generation of dark matter detectors (such as LZ) fails to find dark matter then future detectors would need to investigate parameter space populated by neutrinos.
As dark matter detectors become more and more sensitive they should start to see electron-neutrino interactions and possibly neutrino-nuclei interactions for the first time. Future detectors may conduct both dark matter and neutrino physics.
Possible techniques for future detectors include: Increasing mass exposure, annual modulation, directionality, target complementarity, polarised He3 or some combination of the above.

14. References
[1] Zwicky Ref: F. Zwicky, Astrophysical Journal, Vol 86, No. 3 (1937) [2] V. Rubin & W. Kent Ford Jr, Astrophysical Journal, Vol 159, No 2 (1970) [3] T. Tommaso, P. Marshall, D. Clowe, American Journal of Physics, vol 80, iss 9, 753 (2012) [4] [5] Planck Collaboration. Astronomy & Astrophysics manuscript no. planck ‘parameters’ 2015 (2016) [6] R. Alpher, H. Bethe, G. Gamow, Phys. Rev. Lett. Vol 73. No 7. (1948) [7] G. Jungman, M. Kamionkowski, K. Griest, Phys. Reports 267, (1996) [8] H-C Cheng, J. Feng, K. Matchev, Phys. Rev. Lett. 89, (2002) [9] A. Birkedal et al arXiv:hep-ph/ v3 (2012) [10] [11] [12] [13] [14] / / /baudis_texas15.pdf [15] J. Monroe and P. Fisher, Phys. Rev. D 76, (2007). [16] [17] J.Billard, E. Figueroa-Feliciano, L. Strigari, Phys. Rev. Lett. D (2014) [18] J. Davis, Journal of Cosmology and Astroparticle Physics 03, 012 (2015) [19] A.Ciaran, J. O’Hare et al Phys. Rev. Lett D 92, (2015) [20] F. Ruppin, J. Billard, E. Figueroa-Feliciano, L.Strigari, Phys. Rev. Lett D 90, (2014) [21] T. Franarin, M.Fairbairn. Phys. Rev. D 94, (2016) [22] T. Walker and W. Happer, Rev. Mod. Phys. 69, 629 (1997) [23] F. Colegrave, L. Schearer, G. Walters, Phys. Rev. 132, 2561 (1963)