In this exercise you will learn, starting by a given rootuple of histograms, how to get the plots in Fig.4 (or Fig.6)
in the CMS paper JINST 7 P10002 (2012).
To understand the physics content (muon reconstruction and identification at CMS) please study the pagg. 6-14.
For the description of the code (ROOT macro) and the procedure: Esercitazione-1(pdf)
For the description of the code (ROOT macro) and the procedure: Esercitazione-2(pdf)
For the description of the code (ROOT macro) and the procedure: Exercise-3(pdf).
For the theory behind fitting with MINUIT (the minimization engine of RooFit)
[Unbinned ML fit, Binned ML fit, Extended ML fit] have a look at the addendum
Exercise-3a.
Here is additional follow-up material about MIGRAD, HESSE, MINOS functions in MINUIT.
For the description of the code (ROOT macro) and the procedure: Exercise-3b.
This exercise is a variation on the previous one.
It has been given as an Exam in 2014/15.
Here is proposed as an exercise to start in the classroom and finish at home.
Here you are asked to fit the signal of ψ' decaying into μ+μ −π +π −.
Check the mass resolution with respect to the previous signal of ψ' decaying into 2 muons
and appreciate how much it enhances with two more tracks (pions) constrained to come from the decay vertex.
Here you can find the outline of this Exercise-4(pdf).
Here is proposed as an additional exercise for home the Exam given in 2016/17.
In this exercise we fit the signal of a φ→K+K −
(diKaon invariant mass obtained by selecting B0s→J/ψ φ in a
in a part of CMS data). In this case the experimental mass resolution (~ 1.3MeV from CMS Monte Carlo) is
smaller than the natural width of the φ (~ 4.3MeV).
Therefore the signal must be fitted with a Voigtian (it is a non-relativistic Breit-Wigner convoluted with
an experimental resolution gaussian).
For the description of the code (RooFit macro) and the procedure: Exercise-5(pdf).
Generation of a distribution according to a signal+background model and subsequent fit by means of an UML fit
(with RooFit) [the signal is a Voigtian (BW convoluted with a gaussian resolution function)
while the background is given an exponential behaviour].
For the description of the code (RooFit macro) and the procedure: Exercise-6(pdf).
To be able to set the seed of the random generator please see this Additional Note.
Here you can find a follow-up: supplementary material.
Here we "re-discover" (check) that the MINOS error is equivalent to the 1σ uncertainty from the Profile Likelihood Ratio.
For the description of the code (RooFit macro) and the procedure: Exercise-7(pdf).
Here you can find a follow-up about the Profile Likelihood Ratio: supplementary material.