Corso di LABORATORIO ANALISI DATI (a. a. 2018-2019)

Laurea Magistrale - Anno II - Indirizzo Fisica Nucleare e Subnucleare

Professor: Alexis Pompili

Program of the course

Suggested textbooks for the theoretical part of the course:
- Cowan (ediz. 1998)
- Metzger (ediz. 2010)

Copyright: all the material of this course could be used only under permission of the author
        (pompili AT ba.infn.it) and with proper acknowledgment.

In order to connect to the virtual machine hosted at ReCas and dedicated to the course ("pompilicorso"):
- from a Unix/Linux machine : ssh -Y [username]@212.189.205.223 [to be changed soon]
- from a Windows (<10) machine you need to freely download (from https://sourceforge.net) :
  Xming X Server for Windows and /Xming-fonts/7.7.0.10 to be able to use Emacs)

For any problem with the VM please contact giacinto.donvito AT ba.infn.it (and put A.P. in cc)

PRACTICAL CLASS 0

Introduction to the Operting System UNIX/LINUX

- Commands' review
- Tutorial
- Recipes

Introduction to the editor EMACS

- Commands/I
- Commands/II

Introduction to the light editor VI

- Commands

Introduction to ROOT : Introduction to the use of ROOT and exercises to begin with

Further material about the introduction to ROOT

Lezioni introduttive by Alfio Lazzaro: Lez.-1 , Lez.-2 , Lez.-3.
Further introductive material:
- Tutorial-1(by Manchester University)
- Tutorial-2(by Andrea Rizzi)
Online ROOT Manual

PRACTICAL CLASS 1

Histogramming within ROOT

(Operations, Absolute and Relative Normalization, Stacked Plots, Data-Monte Carlo comparison)

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)

PRACTICAL CLASS 2

Exercise on Hypothesis Testing (with ROOT)

In this exercise you will deal with a ROC curve application with the purpose to compare the rejection power
of two different algorithms. The physics case is taken by the study about the use of the impact parameter
of the leptons in the Higgs "golden" decay channel H→ZZ(*)→4leptons.

For the description of the code (ROOT macro) and the procedure: Esercitazione-2(pdf)

PRACTICAL CLASS 3a

Introduction to RooFit

Introductive material: quick-manual(by W.Verkerke)
Lessons by W.Verkerke @ the BaBar Analysis School (2008): Lez-1 , Lez-2 , Lez-3.
Online : RooFit manual.

First Maximum Likelihood Fit with RooFit

In this exercise you will learn how to fit an invariant mass distribution (ψ'→μ+μ −) by using RooFit;
the PDF has both a signal and a background components.

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.

PRACTICAL CLASS 3b

Refine the fit previously performed:

Firstly add the bin-by-bin pulls as a method of doing some goodness-of-fit.
Secondly let us use a (single-sided) Crystal-Ball function instead a Gaussian to describe the radiative tail.

For the description of the code (ROOT macro) and the procedure: Exercise-3b.

PRACTICAL CLASS 4

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.

PRACTICAL CLASS 5

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).

PRACTICAL CLASS 6

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.

PRACTICAL CLASS 7

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.

Copyright: all the material of this course could be used only under permission of the author
        (pompili AT ba.infn.it) and with proper acknowledgment.

ESERCITAZIONE 3

Interpolazione con metodo Maximum Likelihood di una distribuzione esponenziale
di tempo proprio di una particella che decade (parametro=vita media).
Si riproduce la Fig.6.2 del testo di Glen Cowan; vettore di dati e codice-base by Glen Cowan.

Per la descrizione del codice (macro di ROOT) e della procedura: Esercitazione-3(pdf)

ESERCITAZIONE 4

Interpolazione di una distribuzione di massa invariante (D0->Kaone+Pione) con ROOT.
PDF con componenti di fondo e di segnale. Normalizzazione implementata "manualmente".

Per la descrizione del codice (macro di ROOT) e della procedura: Esercitazione-4(pdf)

Interpolazione di una distribuzione di massa invariante (PsiPrime->2muoni) con ROOFIT.
PDF con componenti di fondo e di segnale. Normalizzazione automatica.

Per la descrizione del codice (macro di ROOFIT) e della procedura: Esercitazione-5(pdf)

Introduzione preliminare a ROOFIT

Materiale introduttivo: quick-manual(by Wouter Verkerke)
Lezioni by Wouter Verkerke alla BaBar Analysis School (2008): Lez-1 , Lez-2 , Lez-3.
Manuale online : Manuale di ROOFIT

ESERCITAZIONE 5bis

Raffinamento dell'interpolazione fatta nell'esercizio 5. Goodness-of-fit mediante bin-by-bin pulls.
Uso della funzione Crystal Ball per descrivere "code radiative".
Traccia dell'esercizio con introduzione alla CB; soluzione con confronto fra interpolazioni.

ESERCITAZIONE 5ter

Questa esercitazione si riferisce alla traccia d'esame per il corso 2014-2015.
La ripropongo come esercitazione preparatoria all'esame (da svolgere a casa e discutere a lezione).

Interpolazione della distribuzione di massa invariante muon+ muone- pione+ pione-. Traccia dell'esercizio.

ESERCITAZIONE 6

Generazione di una distribuzione secondo il modello segnale+fondo [dove il segnale e' una voigtiana
(BW convoluta con una funzione gaussiana di risoluzione sperimentale) e il fondo ha un'andamento esponenziale]
e successiva interpolazione mediante Unbinned Maximum Likelihood fit (in Roofit): Esercitazione-6.

Per fissare il seme del generatore casuale si veda la Nota Aggiuntiva.

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