Standard Model

This is an introductory course on electroweak and strong interactions for students of the fourth year. It will take place in the second semester. The course is addressed to all students (both theoreticians and experimentalists) aiming at

understanding the present description of electroweak and strong interactions in terms of a consistent quantum field theory
knowing the reasons of the great success of the so-called standard model, its theoretical foundations and the crucial experimental tests of its properties.
knowing why, despite the overwhelming experimental confirmations, the standard model is considered unsatisfactory and why theorists are seriously considering alternatives.

The presentation will be kept at an introductory level, but I expect that the students are already familiar with the content of Theoretical Physics and Physics of Fundamental Interactions: Dirac equation, second quantization, basics of Feynman diagrams. Non-abelian gauge theories and spontaneous symmetry breaking will be shortly reviewed in the first lectures.

Additional Material

GGI lectures on the theory of fundamental interactions - Aspects onf Neutrino Physics
by F. Feruglio
Online version
(Firenze 12-18 January 2015)
Notes on Lepton Universality
by Andraz Lipanje

Reference Program (A.Y. 2017-2018)

The standard model of electroweak interactions is a very successful theory, verified at a high degree of precision in almost all its different sectors by a large number of experimental data accumulated over the last thirty years. In the first part of this course, we review the construction of the theory and we point out its most significant properties:

absence of gauge anomalies
existence of massive gauge vector bosons
breaking of flavour symmetries and origin of quark and lepton masses
absence of flavour changing neutral currents
CP violation
conservation of B-L

We will discuss the most relevant processes for a quantitative test of the model:

Flavour changing and CP violating transitions
precision tests at the Z peak and elsewhere
Search for the Higgs boson

Effective Program (A.Y. 2017-2018)

[27/2/2018:] General discussion about the plan of the lectures

[28/2/2018] Classical action for a non-abelian gauge theory; Lagrangian for QCD; Bosonic part of the electroweak theory.
[6/3/2018] Bosonic part of the electroweak theory. Spontaneous breaking of the electroweak symmetry. The Brout-Higgs-Englert mechanism. Masses and interactions in the unitary gauge.
[7/3/2018] Fermions and their gauge interactions.
[13/3/2018] Effective Field Theories. Derivation of the Fermi Lagrangian from the Electroweak one. Muon decay.
[14/3/2018] The solar neutrino problem. Neutrino electron scattering. Yukawa coupling for one generation.
[20/3/2018] General Yukawa Lagrangian for three fermion generations. Decay width of Higgs into a fermion-antifermion pair.
[21/3/2018] Accidental symmetries. Baryon and Lepton number. Discrete symmetries C, P and CP. Wolfenstein parametrization of the mixing matrix for quarks.
[27/3/2018] Formalism of neutrino oscillations in vacuum.
[28/3/2018] Lepton mixing matrix from neutrino oscillation data; Dirac neutrino masses; neutrino masses from the dimension 5 Weinberg operator.
[4/4/2018] Recap of lepton mixing matrix. Chiral symmetry of the QCD Lagrangian. Spontaneous breaking of the chiral symmetry. Isospin symmetry and SU(3) symmetry.
[10/4/2018] Determination of the elements of the quark mixing matrix; V_ud and superallowed nuclear beta decays; V_us and semileptonic decays of K mesons; semileptonic decays of B mesons and V_cb, V_ub. Unitarity relation |V_ud|^2+|V_us|^2+|V_ub|^2=1.
[11/4/2018] Universality of weak interactions in the Fermi theory. Universality of weak interactions in the Standard Model. Computation of the width of the charged pion leptonic decay. Tests of lepton universality.
[17/4/2018] General formalism for meson-antimeson mixing. Survey of experimental results.
[18/4/2018] Evaluation of the mass splitting in the B0d system; box diagram; GIM mechanism.
[24/4/2018] Properties of the Z boson. LEP legacy. Partial decay widths of the Z boson.
[2/5/2018] Physics at the Z pole.
[15/5/2018] Continuous symmetries of the classical and quantum theory. Axial current in QED.
[16/5/2018] Triangle diagram. Absence of gauge anomalies in the SM. Anomalies of the B and L numbers.
[22/5/2018] Beyond the trees: introducing loops. Dimensional regularization.
[23/5/2018] Vacuum polarization in QED. The photon propagator.
[29/5/2018] Charge renormalization. Running of alpha.
[30/5/2018] The electron vertex function. Alpha and the electron g-2. The muon g-2: a harbinger for new physics?
[21/5/2018] Search of the Higgs boson at LEP, Tevatron and LHC. Cross-section for Higgs production at LHC from gluon-gluon fusion.

Some topics for the written part of the exam

[T]=Tree-level; [L]=1-loop

[T] Decay width of the Higgs boson into a WW or ZZ pair, for the unrealistic case mH > 2 mZ.
[T] Cross-section of antineutrino-electron scattering, for e and muon antineutrinos.
[T] Given a unitary matrix V (an explicit numerical example will be provided), extract mixing angles and CP violating phase in the Particle Data Group parametrization.
[T] Neutrino oscillation probability in vacuum in the general case of N generations.
[T] Decay width of W boson into a fermion-antifermion pair and its dependence on the final state masses.
[T] Decay width of Z boson into a fermion-antifermion pair and its dependence on the final state masses.
[T] Differential and total cross-section of electron-positron collision into a fermion-antifermion pair at a center-of-mass energy close to the Z boson mass.
[T] Forward-backward asymmetry of electron-positron collision into a fermion-antifermion pair at a center-of-mass energy close to the Z boson mass.
[T] Leptonic decay widths of charged D and B mesons.
[L] Mass difference in B-Bbar system, from the computation of the box diagram.
[T] Cross-section of electron-positron collision into Higgs and Z.
[L] Anomalous magnetic moment of the electron.
[L] Cross-section for gluon-gluon into an Higgs boson.