Standard Model and Beyond

04 Ott 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Introduction to the Standard Model. Fermi theory of beta decay, neutron decay and parity violation. W boson as a mediator, functional integral and effective theories.

06 Ott 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Non-abelian gauge theories, charged and neutral currents, hypercharge and fermion quantum numbers. Glashow-Weinberg-Salam model, generalization to extended gauge models. Chiral representations of the Lorentz group, two-component spinor formalism.

18 Ott 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

W and Z bosons and their couplings. Spontaneous symmetry breaking, scalar potential, Goldstone bosons. Higgs mechanism, breaking of gauge symmetries, gauge-goldstone mixing and Ward identity. Gauge fixing in spontaneously broken theories, unitary gauge, xi-gauges. Scalar QED, generalization to non-abelian theories, the Standard Model Higgs.

20 Ott 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Quantization of the Standard Model: Higgs and Goldstone boson couplings and propagators. The global symmetries of the Standard Model: baryon and lepton number conservation, axial charges, flavor symmetry. Accidental symmetries and effective theory, introduction to SMEFT, neutrino masses and the Weinberg operator, seesaw mechanism.

25 Ott 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

The Higgs potential, custodial symmetry and its breaking, rho parameter and gauge boson masses. Determination of the SM parameters, electroweak scheme, calculation of hadronic vacuum polarization from total hadronic cross-section.

27 Ott 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Vector and axial couplings of the Z boson. Low-energy tests of the Standard Model: determination of the gauge couplings from neutrino scattering experiments, weak contribution to electron-positron scattering, total cross-section and forward-backward asymmetry, parity violation in atomic physics and the weak charge of the atom.

03 Nov 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Precision tests of the Z couplings: LEP and SLC. Pseudo-observables and radiative corrections, improved Born approximation, effective couplings, rho parameter and effective mixing angle. Observables at the Z pole: total cross-section, forward-backward asymmetry and polarization asymmetry. Z boson partial widths, rates and asymmetries, lepton flavor universality.

08 Nov 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

One-loop corrections in the Standard Model. Vacuum polarizations, vertex corrections, and corrections to muon decay. One-loop corrections to the rho parameter, effective mixing angle, and W boson mass.

15 Nov 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Corrections to the rho parameter from loops of Higgs-gauge bosons, Goldstone boson wave-function renormalization, leading correction to rho from top loop. Indirect determination of Higgs and top masses, the electroweak fit, Altarelli-Barbieri epsilon parameters.

17 Nov 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Electroweak precision tests in models with heavy new physics, oblique corrections to vacuum polarizations: S, T, U parameters; W ,Y and their symmetries. Interpretation in the SM Effective Field Theory, ultraviolet contributions, modified Higgs couplings and infrared logarithms, renormalization and operator mixing.

24 Nov 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Soft and collinear divergences in gauge theories. Infrared singularities and collinear singularities in QED and QCD, Sudakov logarithm, definition of Sterman-Weinberg jets. Calculation of the two-jet and three-jet cross-section at LO and NLO, cancellation of divergences, total hadronic cross-section.

25 Nov 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Higgs boson decays at tree-level: partial widths into fermions and gauge bosons, Goldstone boson equivalence theorem, branching ratios as function of the Higgs mass. Loop-induced Higgs decays: partial widths into photons and gluons, dependence on top mass and heavy top limit, Higgs low-energy theorem, relation with gauge boson vacuum polarizations and beta function.

29 Nov 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Higgs boson production cross-sections at lepton colliders: associated ZH production, vector boson fusion. Collinear gauge boson radiation, effective vector approximation (EPA and EWA), splitting functions for longitudinal and transverse W bosons, Parton Distribution Functions. Calculation of VBF cross-section, energy dependence,

01 Dic 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Higgs production at hadron colliders: gluon-fusion, vector boson fusion, associated production, ttH. Modified Higgs couplings, kappa parameters and EFT. Higgs signal strengths, differential distributions, and determination of Higgs couplings. Double Higgs production, trilinear Higgs coupling, example of modified Higgs couplings in SMEFT.

02 Dic 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Non-linear realization of symmetries, CCWZ formalism. The Chiral Lagrangian, Higgsless realization of EW symmetry breaking, longitudinal vector boson scattering (pion scattering), cut-off of the chiral effective theory. The Higgs boson and unitarity in WW scattering, modified Higgs couplings and unitarity. The scalar effective potential, the naturalness problem of the EW scale.

06 Dic 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Effective potential and the hierarchy problem, EFT perspective on naturalness, natural extensions of the SM: supersymmetry and composite Higgs. Composite Higgs models, the Higgs as a pseudo-Goldstone boson, Minimal Composite Higgs SO(5)/SO(4), vacuum misalignment and EW symmetry breaking, modified Higgs couplings in composite Higgs, EW precision observables.

07 Dic 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

The Higgs potential in composite Higgs theories: gauge boson contribution, the problem of vacuum alignment, top quark contribution and fine-tuning. Fermion masses in composite Higgs, the flavor problem in technicolor models, partial compositeness. Higgs effective potential and the stability of EW vacuum in the Standard Model.

13 Dic 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

The flavor sector of the Standard Model. Flavor symmetry and Yukawa interactions, CKM matrix, physical parameters, CP violation. Parametrizations of the CKM matrix, unitarity triangle, Jarlskog invariant. Tree-level determinations of the CKM parameters: semi-leptonic flavor-changing decays, complex phases and physical CP violating observables.

15 Dic 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Tree-level determination of gamma from B -> KD decays. Meson mixing: general formalism, mass difference and CP violation. K-Kbar sysytem: K -> ππ amplitudes, epsilon and epsilon' parameters. Direct and indirect CP violation, time-integrated and time-dependent CP asymmetries. Interference between decay and mixing.

16 Dic 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Loop constraints on the CKM parameters: CP violation in the B system, S_psiK and the angle beta, B-Bbar mass difference, epsilon_K. Delta F = 2 processes in the Standard Model: CKM unitarity and the GIM mechanism, kaon mass difference and indirect determination of the charm mass, Delta F = 2 loop function.

20 Dic 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Weak effective hamiltonian, semi-leptonic and four-quark operators, tree-level and one-loop matching of four-fermion operators. Running and matching of Wilson coefficients, anomalous dimension, RG-improvement.

22 Dic 2022 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Weak effective hamiltonian for Delta F = 1 processes. Tree-level and penguin operators, semi-leptonic operators, rare meson decays. New physics scale from flavor processes, minimal flavor violation, flavor symmetries.

17 Gen 2023 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Heavy Quark Effective Theory. QCD Lagrangian in the non-relativistic limit, kinetic and magnetic operators, spin-flavor symmetry, hadron spectrum in the heavy quark limit, renormalization of heavy quark EFT. Isgur-Wise functions, meson form factors in the heavy quark limit.

19 Gen 2023 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Flavor in the lepton sector, neutrino oscillations, neutrino mass differences, PMNS matrix, mixing angles and CP violation, neutrino oscillations in matter and MSW effect. Seesaw mechanism and neutrino masses. Charged lepton flavor violation in the SM and beyond.

20 Gen 2023 (2h 00m)

Dario Buttazzo - Corso (attività didattica) - In presenza

Anomalies in chiral gauge theories, anomaly cancellation in the SM, charge quantization, anomaly cancellation for hypercharge and B-L. Unification of quantum numbers: SU(5) and Pati-Salam unification, SO(10), proton decay and other experimental constraints.