GSS2018_Direct

This is the repository for Group 4, covering the topic of Dark Matter Direct Detection. See the main repository - GRAPPA_Student_Seminar_2018 - for more information.

In particular, for information about the scripts, see here.

Use the review/ folder for the LaTeX files for your review and the scripts/ folder for your code.

Comments on the scripts

The main code notebook looks very nice, with lots of detailed text and latex! This is exactly the kind of thing we were looking for. Here are some hints to help you along a bit:

• Your plot of the integrated velocity distribution (velocity vs. speed_integrated) looks a little odd. It looks like when you're calling speed_integrated(i, v_e, v_esc, sigma) that should be speed_integrated(i, v_esc, v_e, sigma) based on your definition of the function. Note also that speed_integrated has units of 1/v (it's not a dimensionless probability as suggested by your axis label).
• Your form factor calculation is very close. At the moment, you have m = 0.05, meaning that your nuclear mass doesn't depend on A the nucleon number! You should have something like m = 0.9315*A if you want the mass in GeV. Next, make sure everything has matching units. If you want to input a recoil energy in units of keV, then you need to multiply it by 10^-6 to get it in GeV so that it matches other things. Of course, you can use recoil energies in GeV, just make sure everything is consistent. You should also convert distances into energies using (1/GeV) = 0.1975 fm. This is very close to what you do, but just double-check. Finally, make sure that when you're multiplying q with a distance, that you're using the distance in natural units (e.g. R1_NU instead of just R1). In the end, you should find that the Xenon form factor has a first minimum around 100 keV.
• Try to make sure that your plots have the correct units (e.g. instead of just energy, you should specify keV or GeV or whatever).
• Make sure that you're making all the units match in your calculations. For example, in v_min you probably want to convert your nuclear mass into GeV, to match the DM mass (which I assume you want in GeV). Similarly, in diff_int_rate it looks like your nuclear mass is in kg, but your DM mass is in GeV. Note also that the reduced mass appearing in this differential event rate is the DM-proton reduced mass.
• In the end, you probably want your differential event rate to have units like events/kg/keV/day (which is sensible for thinking about kg-scale detectors with exposures of 100s of days. Once you make sure that all your units match (see above), work out what units you end up with in the differential event rate and work out what conversion factors you need to get it into events/kg/keV/day (here events is just a number so it's dimensionless). Note for example that the local DM density typically has units of GeV/cm^3, masses typically have units of GeV (unless you've used something different) and your integrated speed distribution probably has units of (km/s)^-1, so you may need some factors of c to get rid of that. Let me - Bradley - know if you want to check the normalisation of the rates, i.e. you could send me the differential rate at a particular recoil energy and mass and we can compare some numbers :)
• Your plots of the differential rate (plt.loglog(mDM,dRdE_test,label='E=%.2g GeV'%E)) are nice, but this is not usually how this information is presented :) Typically, you fix the DM mass and plot dRdE as a function of E. You can put curves for multiple DM masses or multiple detector targets on the same plot so that you can see how the spectrum of recoils changes with DM mass and with detector nucleus.
• Recoil energies are typically in the keV range. For example, Xenon1T can see recoils in the range of ~2 keV up to about 50 keV - see Fig. 1 of https://arxiv.org/abs/1805.12562.
• Once you have the differential rates, you can integrate over recoil energies to determine the number of signal events which are expected in a detector. Only worry about this if you have time - focus first on getting the differential recoil rates correct!

General Comments [BK 28/06/2018]

• In the introduction, 63% seems a bit small for the fraction of matter which is Dark. Shouldn't this be more like 80+% (a reference here would be good).

• In Section 2, you describe the DM distribution as 'stationary', but this should probably be 'isotropic' (i.e. the DM has not average net motion, but it is moving).

• In Eq. 3, I think there is a mistake. The two cross sections sigma_SI and sigma_SD should not add coherently in this way (i.e. I think you have squared the sum of the cross sections, which isn't correct). Please check this.

• Eq. 5 and 6 should probably appear after they are mentioned (i.e. "a normalised response function of an ensemble of spin-1/2 particles:" and then have Eq. 5, etc.) rather than appearing randomly.

• Sec. 2.2 on the velocity distribution still needs to be completed, including uncertainties on the velocity distribution and what N-body simulations (including recent hydrodynamical ones) suggest about the velocity distribution (is it a standard Maxwell-Boltzmann, or something else?)

• Section 3.1 still needs to be completed - say, 1 paragraph on 'global' estimates of the local DM density would be reasonable.

• You discuss this a little, but it might be nice to clarify that we don't know whether the spin-independent or spin-dependent cross section for DM scattering is larger (it depends on the theory). But if we assume that the SI and SD cross sections for DM-nucleon scattering are equal, then the SI cross section for DM-nucleus scattering is typically much bigger than the SD one. So all other things being equal, you perhaps expect that the SI interaction will dominate.

• You state in section 5 that all inelastic scattering is spin-dependent, but I don't think this is the case (in fact there's no reason why you can't have spin-independent scattering which is inelastic - if you have a model for it...)

• It might be good to have a paragraph/sub-section (relatively early on) discussing the annual modulation signature (i.e. why do we expect to have a modulation signature and why this is a 'smoking gun' of Dark Matter).

• You state in Sec. 5 that "A lot of the energy in any type of inelastic dark matter scattering is send out as heat in the form of phonons." However, for DM-electron scattering there should be almost no phonons - all the energy goes into the ionised electron (to first order).

• If Sec. 5.3 is the only section which talks about the 'theory' of DM electron scattering, you should probably give some more details - at least some expressions of the recoil rates, or of the minimum DM velocity required. Even if you don't go into lots of technical detail (e.g. concerning calculation of electron orbital form factors, etc.).

• In Sec. 6.1, you state that "Direct dark matter detectors measure a combination of two of them". This is not always the case, although its often advantageous as it allows you to discriminate electron from nuclear recoils.

• In Sec. 6.2 there is a paragraph which (halfway-down) says "The shape of the curves are like this due to two aspects...." this discussion (of why the limits look like they do and how the rate scales with mass and cross section) is quite general. It's an important discussion but it should probably appear in a more general context in an earlier section.

• In Sec. 6 you discuss only the principles behind how dual-phase Xenon TPCs work. In principle, this is okay - you could for example say that you're just presenting one particular example rather than going into all the technical details of all the experiments. But without this explanation it seems a bit odd to only discuss Liquid Noble TPCs. Also, why do Liquid Noble TPCs measure S1 and S2? Why not just measure S1?

• For the neutrino background, it is important to emphasise that (1) the different sources of neutrinos have different recoil spectra in the detector (due to their different energies) and (2) that neutrinos are only a problem if the spectrum looks like a WIMP spectrum - in particular, for Solar neutrinos, you only have a problem for WIMPs around 6 GeV (Solar Neutrinos do not affect limits on high mass WIMps).

• Discriminating electron from nuclear recoils is usually something you have to do anyway - first you have to convince yourself that you have nuclear recoils (which could be coming from WIMPs or neutrinos). Then you have to find a way to discriminate WIMP-nuclear recoils from neutrino-nuclear recoils.

• Make sure that when you're describing a method of going beyond the neutrino floor, you emphasise how this method works - i.e. what would the WIMP signal look like and what would the neutrino signal look like. Are these different and how does this help us distinguish the two?

• Script: Your script is much much better (the units look much better now). However, be careful in your definition of speed_integrated(v_min, v_esc, v_earth, sigma). Note that N_esc should not depend on v_min - it should just be a normalisation constant.

• Script: Again, a couple of plots comparing the recoil energy spectra for different masses/targets (overlaid on the same plot) would be good.