As explained in the first installment of this series, these questions are a warm-up for my younger colleagues, who will in two months have to pass a tough exam to become INFN researchers. In fact, now that the application period has ended, I can say that there have been 718 applications for 58 positions. That's a lot, but OTOH any applicants starts off with a one-in-12.4 chance of getting the job, which is not so terribly small. 

A disclaimer is attached at the bottom of this post.
And now for questions number 10, 11, and 12. As always, your tentative solutions and / or comments are welcome in the comments thread below.
10. Succinctly describe a method to search for dark matter particles.

11. Estimate the ratio between the cross section of hadron production and the cross section of muon pair production in electron-positron annihilations, at the following center-of-mass energies: 2 GeV, 6 GeV, 12 GeV.

12. Draw the energy distribution of electrons emitted in the decay of muons at rest, and explain the features you sketched.


I offer these questions as a self-test of one's knowledge in particle physics. I am not part of the INFN selection committee. I have no connection to the selection committee, nor any insider information on how the exam will be structured. All I know about it is what is contained in the official call, available to everybody. I do have some previous experience with INFN selections of researchers, but this needs not be relevant for this year's selection.