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.

A disclaimer follows:

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.

That said, here are four question together, as I have been with no internet connection for a full week, so this series lagged behind a bit. Also, the two last problems are connected to each other. Note that the second problem requires some writing, but one needs to be very concise.  Also note that problem 4 is tougher than the rest for the average particle physicist, but this is in the spirit of a large set of problems, in an exam where time is limited and no student is expected to solve everything perfectly...

1 - What is the threshold for antiproton creation in the reaction pp->X at a fixed-target experiment ?

2 - Discuss the Altarelli-Parisi equations and their importance for particle physics measurements

3 - Let x_1 and x_2 be uncorrelated measurements, sampled from Gaussian PDFs with known variances sigma_1 and sigma_2, of the same physical quantity x. Using error propagation, show that the weighted mean μ* = (x1/sigma_1^2 + x2/sigma_2^2) / (1/sigma_1^2 + 1/sigma_2^2)  is the estimator of x with the smallest variance.

4 - Suppose you have a measurement x_1 of a physical quantity x, with a variance sigma_1^2=1.0. Assume x_1 is sampled from a Gaussian PDF. You are offered to improve the knowledge of x by performing a second Gaussian measurement x_2 with variance sigma_2=4.0 and taking the weighted mean of the two. You can choose to perform the second measurement with one of two different instruments, both of which provide a measurement of x with variance sigma_2=4.0. The first measurement will have a 50% correlation with x_1; the second one will have a correlation of 75%. 
Compute the variance of the weighted average and explain which method you should choose.