The Daily Physics Problem - 10, 11, 12

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. 

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.

Disclaimer:

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.


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Tommaso Dorigo

Professor Tommaso Dorigo is an experimental particle physicist, who works for the INFN at the University of Padova, and collaborates with the CMS experiment at the CERN LHC. He is currently a RECAT Guest Professor at Lulea University of Technology, and participates in the EIC-PATHFINDER project "PHINDER". Dorigo is the president of the USERN organization (https://usern.org), and the editor in chief of the journal "Brain, AI and cognition".  He is the author of Anomaly! Collider physics and the quest for new phenomena at Fermilab. Read more