CFU

6

Length

14 Weeks

Semester DD

First

Introduction, particles and forces. Mandelstam variables, Fermi's golden rule, Lorentz invariant phase space, two-body decays, cross section. Klein-Gordon equation, Dirac equation, probability density and covariance. Solutions to the Dirac equation for an electron at rest. General solutions of the Dirac Equation, Antiparticles and its spinor, normalisation of the wavefunction. Spin and Helicity. Interaction by particle exchange, time-ordered 2->2 matrix element, Feynman diagrams, examples and algebra of matrices. Parity operator, Range of forces, Yukawa potential, QED matrix element for electron-tau scattering, Feynman rules for QED. QED as a perturbative theory, Spin sums in e+e- to mu+mu- annihilation, the e+e- to mu+mu- cross section and its Lorentz-invariant form, examples of application of the Feynman rules. Chirality Operator, Charge Conjugation. Electron-proton elastic scattering: Rutherford, Mott, Rosenbluth formulae, Form factors. Electron-proton inelastic scattering at high-Q2 (DIS), Bjorken scaling and Callan-Gross relation, Electron-quark scattering. Quark-Parton Model, Parton Density Functions, Valence and Sea quarks, electron-proton scattering at HERA. Symmetries and Conservation laws, SU(2) flavour symmetry, 2 and 3 quarks combinations in SU(2), Light quark (ud) baryons and mesons. SU(3) flavour symmetry, Gell-Mann matrices, Ground state light quark (uds) Mesons and Baryons, Hadron mass and constituent mass. Local gauge invariance in QED and QCD, Colour in QCD, colour confinement, Meson and Baryon colour wavefunctions, Gluons, quark-gluon and gluon-gluon interactions, Hadronisation and jets, hadroproduction in e+e- collisions. Running coupling constants in QED and QCD, Asymptotic freedom. Colour factors. Hadronic collisions and Drell-Yan. Jet production in hadronic collisions. Rapidity and pseudorapidity, Drell-Yan process, Parity in QED and QCD matrix elements, Parity Violation in weak-interactions. V-A structure of the weak interaction, Chiral properties of V-A, W boson propagator, Fermi theory, Helicity in pion decay and evidence for V-A, lepton universality of the electroweak coupling. (Anti)Neutrino-quark scattering, neutrino-nucleon cross sections, CDHS experiment. Neutrino mass and flavour eigenstates, Neutrino oscillations in 2 and 3 families, Phenomenology of neutrino experiments. CP violation in neutrino mixing, PMNS matrix, Neutrino oscillation experiments and determination of the PMNS parameters and masses. Quark mixing in weak interactions, Cabibbo angle and GIM mechanism, CKM matrix and its representations. Neutral kaons system. Kaon oscillations, CP violation in oscillations and decays. B and B_s oscillations, B factories. W boson decay width and branching ratios. Electroweak SU(2)_L gauge structure, Neutral current, Electroweak unification, the Z boson. Breit-Wigner resonance, Z production cross section in e+e- collisions, measurements of Z boson mass and width, Z FB asymmetry and weak mixing angle, the LEP collider, W boson mass and width. Decay rate of the top quark, top quark production at hadronic colliders, Higgs boson and its discovery.

LEARNING OUTCOMES:

The course aims at giving the student a solid understanding of the physics of elementary particles, starting from the experimental observations and with an emphasis on the most recent research themes. A simplified treatment of Feynmann diagrams gives the student the possibility of performing simple calculations of cross sections and decays. The mechanisms of production and decay of the W, Z, Higgs particles are presented alongside the experimental consequences. The phenomenon of oscillations and CP symmetry violation in various particles is described quantitatively. Furthermore, the phenomenon of neutrino oscillations is discussed in some detail.

KNOWLEDGE AND UNDERSTANDING:

The student will acquire a comprehension of the formal structure of quantum electrodynamics and chromodynamics, of the electroweak theory and the related experimental measurements. He will have a knowledge of the Feynmann rules required to perform calculations of cross sections and decays at leading order. The student will acquire the basic knowledge related to the role and importance of precision tests of the Standard Model, of the neutrino oscillations and the measurements of CP violation.

APPLYING KNOWLEDGE AND UNDERSTANDING:

At the end of the course the student will be able to combine together the elements required to perform the computation of processes mediated by strong and electroweak interactions, recognising the level of approximation and execute simple calculations of particle cross sections and decay. He will also be able to connect the theoretical formulation of an interaction with the experimental measurements, including from latest generation experiments.

MAKING JUDGEMENTS:

The student must be able to independently perform bibliographic searches, connecting the experimental activities and the theoretical frameworks. The student must be able to recognise and judge the role played by the current and future experimental measurements with respect to the need of new theories beyond the Standard Model.

COMMUNICATION SKILLS:

The student must be able to illustrate analytically the role that past experimental observations had on the formulation of the Standard Model, with particular regard to the observational limits. The student must be able to summarise quantitatively the results of the modern experimental campaigns, in the framework of the elements that characterise the Standard Model.

LEARNING SKILLS:

The student must be able to move comfortably and autonomously towards further studies in the latest areas. The student will acquire the elements needed to pursue studies at doctoral level or further specialisation Master level.