Thanks for the questions! I am pleased to provide answers!
Even though I did not grasp the plot properly, I assume it takes care of interaction of nucleus that might happen with other stuff, say neutrinos and dark matter would have it's own characteristic signature. I guess that's what you meant?
I did not want to add too many details on the plot in order to only stress the essence of it. In fact, it represents the parameter space of a given model for a fixed dark matter mass. The y-axis corresponds to the dark matter electric dipole (that can be tuned to any value) and the x-axis to the mass difference between dark matter and a second, instable, dark state (that decays into dark matter).
To make a long story short, those are the two parameters that are left in this model, as soon as the dark matter mass has been fixed.
From there, we can calculate predictions for what should be visible in current experiments and verify that we do not violate any experimental bounds. This excludes the grey area of the parameter space.
In the next step, we can evaluate how waste would yield potentially observable signals. After assuming that the idea has been concretised experimentally and some capabilities for the corresponding experiments, we get the three coloured lines.
If nature is realised according to the model under consideration and if the parameter setup lies above the coloured lines, then dark matter will be found.
Does it clarify?
On a slightly unrelated note this question came to my mind. Do we even know that dark matter flows through earth or earth passes through some region full of dark matter? How would we ensure that dark matter interaction would occur here on earth?
We know the distribution of dark matter in the galaxy. If you assume dark matter exists in the first place, then there is a density of dark matter around us of 0.02 solar mass per cubic parsec. See for instance here for some recent results.
To put some funny numbers in perspective, this means that there are about 1000 tons of dark matter in the Sun.
I hope this helps! Feel free to come back to me if needed!