The goal of the course is to illustrate the theoretical and observational foundations of the Standard Model of ElectroWeak and Strong Interactions. An elementary knowledge of Quantum Field Theory and of Feynman diagrams is required.
21/10/2016: General Introduction. Why we need gauge theories I (phenomenology): QED with the electron and the muon, universality of photon couplings, absence of flavor transition and of mu -> e gamma. Why we need gauge theories II (theory): Gupta-Bleuer quantisation (review), the scalar photon, the risk of unitarity violation, scalar photon decoupling from the Ward Identities.
24/10/2016: Non-Abelian gauge theories (review). Gauge kinetic term and the counting of gauge couplings; why we need a compact group. The SU(2) gauge theory: charged W bosons, Feynman rules for fermion and boson couplings. Spontaneous symmetry breaking (review): Exact, Approximate and Spontaneously broken symmetries; non-linear (non-homogeneous) representation of spontaneously broken symmetries.
28/10/2016: Towards the SM: SU(2) with Higgs doublet or triplet. The SM SU(2)XU(1): the Q=T3+Y formula, the Higgs doublet and the unbroken U(1), gauge kinetic terms and gauge couplings. How to find the Z boson and photon fields, the Weinberg angle and the electic charge, from symmetries. The Higgs covariant derivative, the role of pseudo-Goldstones and the Unitary Gauge, counting degrees of freedom. The complete gauge-plus-Higgs Lagrangian: IVB masses and Higgs-IVB couplings, the rho=1 relation, Higgs and IVB self-couplings. The Higgs mass as a new parameter.
04/11/2016: Chiral Spinors. Explicit solutions of the Dirac equation and the particle content of a massless chiral spinor. Chirality and helicity. Discrete symmetries (C and P) acting on spinor fields and on fermion bilinear operators.
07/11/2016: Quarks and Leptons: quantum numbers and covariant derivatives, charged and neutral currents and Feynman rules. Discrete symmetries in the SM and in generic gauge theories.
11/11/2016: Polarised W boson decay, breaking of P and C and conservation of CP. Effective Field Theories: the general concept and a simple example.
14/11/2016: Fermi theory: brief review, the decay of the muon and the determination of the Fermi constant. The tau lepton decay. Neutrino-electron scattering and e+e- to mu+mu-: the evidence for neutral currents, vector and axial coupling measurements, a first determination of the Weinberg angle and the prediction of the W boson mass.
18/11/2016: The problem of singularities in the presence of unstable particles. The Breit-Wigner formula. Z-boson pole physics at LEP: Z-boson mass and width, an accurate determination of the Weinberg angle, Forward-Backward asymmetry and its physical origin in terms of polarised amplitudes. Measuring the number of (active and light) neutrinos.
21/11/2016: Quark masses and mixings: the Yukawa Lagrangian and its diagonalisation, the VCKM matrix, the condition for CP conservation, the hint for a third family.
25/11/2016: Global unbroken symmetries in QFT (scalar example): conserved currents and charges, charge operator and its action on fields and states, the invariance of the S-matrix and of operators matrix elements. An SO(2) example: explicit form of the charge in the free theory, the matrix element of the current between one-particle states.
28/11/2016: The QCD theory and its symmetries: the strong CP problem, one/two/three flavours QCD, the octet of mesons.
02/12/2016: Flavor transistions in the Fermi Lagrangian. The charged pion decay to lepton and neutrino. Lepton mass suppression from chirality of the interaction and angular momentum conservation. Muon versus electron decay. The charged kaon decay, fK=fpi and a first determination of the Cabibbo angle. The pi+ to pi- e+ ve decay and a second determination of the Weinberg angle.
05/12/2016: The K0-K0bar system: mass-degeneracy from strangeness conservation and CPT, charged Weak interactions as the sole source of splitting, the CP symmetry and its implications on the Kaons decays, the effective Hamiltonian, oscillations and decays.
09/12/2016: Kaon mass-splitting from an effective operator, the calculation in the SM and the GIM suppression, a first estimate of the charm quark mass. High-energy QCD as a free theory of partons, hadron production from e+e- and the concept of inclusive reactions, comparison with observations.
12/12/2016: Deep inelastic scattering: kynematical variables Q, x and y; the hadronic tensor and its parametrisation with form factors; form factors computed in the approximation of point-like proton; Bjorken scaling.
16/12/2016: Deep inelastic scattering in the parton model: the concept of parton distribution functions; cross-section computed; Callan-Gross relation.
19/12/2016: Cross-sections at hadron colliders: the general formula and the W production from proton-proton collisions. Neutrino masses: absense of neutrino masses in the minimal SM; right-handed neutrinos and Dirac neutrino masses; the Weinberg operator and Majorana neutrinos; lepton number symmetries and their violation, mu to e gamma and neutrino-less double-beta decay.
Evaluation Exercises Last modified: October 2017 - (andrea.wulzer@unipd.it) Back to the homepage
Previous Academic Years
2012/2013
2013/2014
2014/2015
2015/2016