#
Phenomenology of the standard model of particle physics

A.Y. 2019/2020

Learning objectives

The students will learn the physics of fundamental particles and their interactions, as described by the Standard Model of elementary particles, both from the formal point of view, and from that of the experimental techniques.

Expected learning outcomes

At the end of this course, students are expected to know:

- the lagrangians of QED, QCD, the electroweak model, the physical fields and interaction terms, the computation at tree-level of cross-sections and decay widths

- the experimental foundation of QCD, that put into evidence the parton composition of the proton, the quark and gluon production, the evidence of the color

- the precision measurements of the electroweak theory, that allowed to validate the Standard Model at per mil precision

- the main characteristics of physics at hadron colliders, the experimental techniques to identify particles and jets and to measure cross sections

- the statistical techniques to extract from data measurements of quantities at a given confidence level, perform hypothesis tests, establish discovery of exclusion of new physics signals

- the predicted properties of the Higgs boson, the experimental techniques used for its discovery and the measurements of its properties

- some notions of supersymmetry, its phenomenology, and present experimental limits

- the lagrangians of QED, QCD, the electroweak model, the physical fields and interaction terms, the computation at tree-level of cross-sections and decay widths

- the experimental foundation of QCD, that put into evidence the parton composition of the proton, the quark and gluon production, the evidence of the color

- the precision measurements of the electroweak theory, that allowed to validate the Standard Model at per mil precision

- the main characteristics of physics at hadron colliders, the experimental techniques to identify particles and jets and to measure cross sections

- the statistical techniques to extract from data measurements of quantities at a given confidence level, perform hypothesis tests, establish discovery of exclusion of new physics signals

- the predicted properties of the Higgs boson, the experimental techniques used for its discovery and the measurements of its properties

- some notions of supersymmetry, its phenomenology, and present experimental limits

**Lesson period:**
Second semester

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### Single session

Responsible

Lesson period

Second semester

**Course syllabus**

Recalling previous concepts

- scalar, fermionic and vector fields

- interactions: Feynman rules, transition matrix, Fermi's golden rule, cross-sections, decay widths

- elecromagnetic interactions, scattering of charged fermions, fermionic currents

- Fermi's model of weak interactions, charged currents, unitarity violation

- abelian gauge theories, QED

- non-abelian gauge theories (Yang-Mills)

Quantum Chromodynamics (QCD)

- elastic e-p scattering: proton form factors

- inelastic e-p scattering: proton structure functions, Bjorken scaling, evidence of "partons" inside the proton

- parton distribution functions (PDF), hadronic and partonic cross-section

- quark-antiquark production at e+e- collisions, hadronic jets, sphericity and thrust, evidence of color factor

- formulation of QCD as a non-abelian gauge theory, SU(3) group, gluons as mediators of strong interaction, running of alpha_S, asymptotic freedom and color confinement

- gluon production at e+e- collisions, events with 3 jets, measurement of alpha_S

- gluons in PDFs, violation of Bjorken scaling, Altarelli-Parisi equations

Electroweak interactions

- EW interactions: symmetry group SU(2)xU(1), fermionic and vector fileds, lagrangian

- physical fields, W+,W-,Z, and photon, Weinberg angle

- the problem of masses, symmetry breaking, Higgs mechanism, the Higgs boson

Precision measurements of electroweak physics at e+e- collisions

- the e+e- --> f fbar reaction, vector and axial couplings C_V, C_A, computation of decay width, branching ratios, cross-sections

- particle identification in a detector, reconstruction of hadronic jets, identification of final states

- measurements of luminosity and cross-sections

- measurements of e+/e- beam energy

- "line hape" measurements: Z mass, decay width, cross-sections and forward/backward asymmetries, extraction of C_V, C_A

- light neutrino families counting

- identification of heavy quarks (bottom, charm), measurements of branching ratios and asymmetries for heavy quarks

- observation of W+/W- bosons in e+e- collisions, cross-section and measurement of m_W

- virtual corrections to e+e- --> Z -->f fbar reaction, sensitivity to top quark and Higgs boson loops

- search for the Higgs boson at LEP

Physics at hadron colliders

- kinematics at hadron colliders, Mandelstam variables, rapidity

- hard scattering, hadronic and partonic cross-section, PDFs, underlying event

- pros and cons of hadronic colliders vs e+e-

- luminosity measurement at hadron colliders

- physics at LHC: cross-sections of typical processes, pile-up

- structure of detectors, particle identification, jet clustering algorithms, calibration, missing transverse momentum, b-quark identification

- measures of cross-sections, efficiencies, acceptances, fiducial regions, estimation of reducible and irreducible backgrounds, control regions, unfolding experimental effects

- examples: cross-section measurements of events with one or two photons, and t-tbar events

Statistical analysis techniques

- estimators and their properties

- likelihood function, estimators based on maximum likelihood and their properties, examples, parameters of interest and nuisance parameters

- frequentist statistics, confidence interval, coverage

- the "profiled likelihood ratio" (PLR) and its statistical properties, Wilk's theorem, confidence region, handling of nuisance parameters

- Hypothesis test, test size, test power, confidence level

- Simple and composite hypotheses, test statistic, p-value, Neyman-Pearson lemma, likelihood ratio

- Background-only hypothesis test, criteria for "discovery"

- Background+signal hypothesis test, criteria for "exclusion"

- Composite hypotheses, modified PLR, criteria for discovery and exclusion, treatment of systematic effects

Higgs boson physics

- predicted properties of the Higgs boson: decay width, branching ratios, cross-sections

- Higgs production at the LHC, theoretical characteristics and experimental signatures

- discovery of the Higgs boson: observation of a resonance decaying to two photons and 4 leptons, excess of events with W+W- final state, estimation of the backgrouns, statistical significance

- observation of Higgs decaying to tau+tau-

- measurement of the Higgs mass

- measurements of cross-sections and of couplings of the Higgs boson ot other particles

- measurements of spin and parity

Some notions of supersymmetry (SUSY)

- motivations for an extension of the Standard Model

- theoretical formulation of SUSY, extension of the Standard Model

- phenomenology of the main SUSY models

- experimental results in SUSY

- scalar, fermionic and vector fields

- interactions: Feynman rules, transition matrix, Fermi's golden rule, cross-sections, decay widths

- elecromagnetic interactions, scattering of charged fermions, fermionic currents

- Fermi's model of weak interactions, charged currents, unitarity violation

- abelian gauge theories, QED

- non-abelian gauge theories (Yang-Mills)

Quantum Chromodynamics (QCD)

- elastic e-p scattering: proton form factors

- inelastic e-p scattering: proton structure functions, Bjorken scaling, evidence of "partons" inside the proton

- parton distribution functions (PDF), hadronic and partonic cross-section

- quark-antiquark production at e+e- collisions, hadronic jets, sphericity and thrust, evidence of color factor

- formulation of QCD as a non-abelian gauge theory, SU(3) group, gluons as mediators of strong interaction, running of alpha_S, asymptotic freedom and color confinement

- gluon production at e+e- collisions, events with 3 jets, measurement of alpha_S

- gluons in PDFs, violation of Bjorken scaling, Altarelli-Parisi equations

Electroweak interactions

- EW interactions: symmetry group SU(2)xU(1), fermionic and vector fileds, lagrangian

- physical fields, W+,W-,Z, and photon, Weinberg angle

- the problem of masses, symmetry breaking, Higgs mechanism, the Higgs boson

Precision measurements of electroweak physics at e+e- collisions

- the e+e- --> f fbar reaction, vector and axial couplings C_V, C_A, computation of decay width, branching ratios, cross-sections

- particle identification in a detector, reconstruction of hadronic jets, identification of final states

- measurements of luminosity and cross-sections

- measurements of e+/e- beam energy

- "line hape" measurements: Z mass, decay width, cross-sections and forward/backward asymmetries, extraction of C_V, C_A

- light neutrino families counting

- identification of heavy quarks (bottom, charm), measurements of branching ratios and asymmetries for heavy quarks

- observation of W+/W- bosons in e+e- collisions, cross-section and measurement of m_W

- virtual corrections to e+e- --> Z -->f fbar reaction, sensitivity to top quark and Higgs boson loops

- search for the Higgs boson at LEP

Physics at hadron colliders

- kinematics at hadron colliders, Mandelstam variables, rapidity

- hard scattering, hadronic and partonic cross-section, PDFs, underlying event

- pros and cons of hadronic colliders vs e+e-

- luminosity measurement at hadron colliders

- physics at LHC: cross-sections of typical processes, pile-up

- structure of detectors, particle identification, jet clustering algorithms, calibration, missing transverse momentum, b-quark identification

- measures of cross-sections, efficiencies, acceptances, fiducial regions, estimation of reducible and irreducible backgrounds, control regions, unfolding experimental effects

- examples: cross-section measurements of events with one or two photons, and t-tbar events

Statistical analysis techniques

- estimators and their properties

- likelihood function, estimators based on maximum likelihood and their properties, examples, parameters of interest and nuisance parameters

- frequentist statistics, confidence interval, coverage

- the "profiled likelihood ratio" (PLR) and its statistical properties, Wilk's theorem, confidence region, handling of nuisance parameters

- Hypothesis test, test size, test power, confidence level

- Simple and composite hypotheses, test statistic, p-value, Neyman-Pearson lemma, likelihood ratio

- Background-only hypothesis test, criteria for "discovery"

- Background+signal hypothesis test, criteria for "exclusion"

- Composite hypotheses, modified PLR, criteria for discovery and exclusion, treatment of systematic effects

Higgs boson physics

- predicted properties of the Higgs boson: decay width, branching ratios, cross-sections

- Higgs production at the LHC, theoretical characteristics and experimental signatures

- discovery of the Higgs boson: observation of a resonance decaying to two photons and 4 leptons, excess of events with W+W- final state, estimation of the backgrouns, statistical significance

- observation of Higgs decaying to tau+tau-

- measurement of the Higgs mass

- measurements of cross-sections and of couplings of the Higgs boson ot other particles

- measurements of spin and parity

Some notions of supersymmetry (SUSY)

- motivations for an extension of the Standard Model

- theoretical formulation of SUSY, extension of the Standard Model

- phenomenology of the main SUSY models

- experimental results in SUSY

**Prerequisites for admission**

Quantum mechanics, special relativity, lagrangian formalism, electromagnetic and weak interactions, cross-sections and decay widths, fundamental constituents of matter

(students are strongly encouraged to follow the courses "Interazioni Elettrodeboli" and "Fisica delle Particelle")

(students are strongly encouraged to follow the courses "Interazioni Elettrodeboli" and "Fisica delle Particelle")

**Teaching methods**

Front lectures. Students are strongly encouraged to attend.

**Teaching Resources**

- slides of the lectures, available at http://www.mi.infn.it/~fanti/Particelle3

- R. Cahn, G. Goldhaber, The Experimental Foundation of Particle Physics, Cambridge University Press (2nd edition)

- F. Halzen, A. D. Martin - Quarks and Leptons - 1984 - J. Wiley

- Griffith - Introduction to Elementary Particles - 2008 - J. Wiley

- G. Cowan - "Statistical data analysis", Oxford Science Publications

- R. Barlow - "Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences", Manchester Physics Series

- R. Cahn, G. Goldhaber, The Experimental Foundation of Particle Physics, Cambridge University Press (2nd edition)

- F. Halzen, A. D. Martin - Quarks and Leptons - 1984 - J. Wiley

- Griffith - Introduction to Elementary Particles - 2008 - J. Wiley

- G. Cowan - "Statistical data analysis", Oxford Science Publications

- R. Barlow - "Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences", Manchester Physics Series

**Assessment methods and Criteria**

The exam consists of a presentation with slides on a scientific result recently published, chosen by the student, followed by an oral discussion on a topic, chosen by the professor, among those treated during the course. The overall length of the exam is about 90 minutes.

FIS/04 - NUCLEAR AND SUBNUCLEAR PHYSICS - University credits: 6

Lessons: 42 hours

Professor:
Fanti Marcello

Professor(s)