Week 3: Direct detection of Dark Matter - adam-coogan/GRAPPA_Student_Seminar_2019 GitHub Wiki

In week 3, you will write scripts for estimating the sensitivity reach of current liquid Xenon direct dark matter search experiments, both in terms of projected upper limits as well as in reconstruction contours.

Outputs

  • Calculate the expected 95% C.L. upper limits on the WIMP-proton coupling cross-section, as function of the dark matter mass. To this end, assume that the target material is 500 kg of liquid Xenon, the recoil energy threshold is 3 keV, and the observation time is one year. Assume that the expected number of background events as well as the number of measured events is zero. Compare your predicted constraints with the latest published constraints from the Xenon-1T experiment.
  • For the above scenario, assume that 10 events are measured with recoil energies between 3 keV and 10 keV, and 5 events are measured with recoil energies between 10 keV and 20 keV. Plot 68% and 95% reconstruction contours in the WIMP-proton coupling cross-section vs dark matter mass plane.

Suggestions

  • For the first point, first estimate the 95% CL upper limit on the number of expected signal events (given zero background and zero measured events). Then express the WIMP-proton cross-section as function of the dark matter mass and the expected number of signal events. Plot results from 1 GeV to 1 TeV.
  • For the second point, calculate the number of expected events in the first and second recoil energy band in a grid that spans 10 to 1000 GeV of dark matter mass (in 20 logarithmic steps, use numpy.logspace), and in a suitable cross-section range (again 20 logarithmic steps). Calculate the corresponding chi^2 function. For a two-parameter fit to two data bins, what is the chi^2 value at the best-fit point? Use pyplot.contour to plot confidence contours, by setting the appropriate levels. If necessary, increase the resolution such that the results become reasonably stable.

References