Theory of Fundamental Interactions

This is an introductory course on electroweak and strong interactions for students of the fifth year. It will take place in the first trimester. An introductory part will be devoted to general properties of gauge theories and to the spontaneous breaking of a continuous symmetry. 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: Dirac equation, second quantization, basics of Feynman diagrams.

Reference Program (A.Y. 2005-2006)

The standard model of electroweak and strong 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 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
asymptotic freedom of strong interactions

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. 2005-2006)

[3/10/2005:] General discussion about the plan of the lectures

Part A

Electroweak Theory

[4/10/2005] Classical action for a non-abelian gauge theory: the covariant derivative [PS/15.1,15.2,15.4]
[5/10/2005] Kinetic term for gauge fields [PS/15.1,15.2,15.4] Exercise 1 Exercise 2 Exercise 3
[10/10/2005] Short discussion about quantized non-abelian gauge theories: gauge fixing and Faddeev-Popov terms; spontaneous breaking of a continuous global symmetry: an example [O/20.2,PS/11.1]
[11/10/2005] The Goldstone theorem: general case at the semiclassical level; examples: SO(n)->SO(n-1), the chiral symmetry of strong interactions.
[12/10/2005] The abelian Higgs model [O/20.4], the unitary gauge Exercise 4; low-energy effective lagrangian for pions.
[17/10/2005] Bosonic sector of the electroweak theory [O/21.2-O/21.4] Exercise 5 ; Weinberg angle, vector boson masses.
[18/10/2005] The Higgs particle and its decay into a vector boson pair [O/24.1]. Fermionic sector of the electroweak theory: representations and covariant derivatives; charged and neutral currents [PS/20.2].
[19/10/2005] Decay probability of the muon [O/3.2]. Exercise 6 The Fermi constant.
[24/10/2005] Low-energy effective lagrangian for the weak interactions. Solar neutrinos at Superkamiokande: computation of the elastic cross-section for neutrino-electron scattering [O/22.1-22.2]. Exercise 7
[25/10/2005] Properties of the Z boson: partial widths and cross section for fermion pair production at LEP. The number of neutrinos [O/23.2-23.3].
[26/10/2005] Precision tests of the standard model. The running of alpha.
[7/11/2005] Precision tests of the standard model. Leading corrections in the electroweak observables.
[8/11/2005] Precision tests of the standard model. The top and Higgs masses. Yukawa interactions and fermion masses [O/21.7].
[9/11/2005] The lagrangian in the basis of mass-eigenstate fermions; the mixing matrix V; number of physical parameters; absence of flavor changing neutral currents; absence of flavor changing from Higgs interactions [PS/20.3]. Symmetries of the standard model; baryon number and individual lepton numbers as classically conserved charges from the renormalizability requirement; P and C violation; violation of CP from a complex V [PS/20.3].
[14/11/2005] Neutrino masses; Dirac and Majorana masses. Short review of the present knowledge about neutrino masses and lepton mixing angles from oscillations experiments.
[15/11/2005] Constraints on the parameters of the Cabibbo-Kobayashi-Maskawa mixing matrix.
[16/11/2005] Mixing and mass difference in the B systems; sketch of the computation of the box diagram.
[21/11/2005] Anomalies: global and local symmetries. Anomaly as a quantum effect. Anomaly of the axial current in QED. Anomalies in non-abelian gauge theories. Absence of gauge anomalies in the Standard Model: constraint on fermion electric charges.
[22/11/2005] Anomalies of baryonic and leptonic currents in the Standard Model; conserved combinations. Implications for the baryogenesis.
[23/11/2005] The decay width of a neutral pion into two photons. Anomaly of the axial neutral isovector current in QCD + electromagnetism. Effective action for pseudoscalar mesons + electromagnetism and its completion to reproduce the anomaly.
[28/11/2005] Asymptotic freedom of QCD. Scale of QCD interactions: dimensional transmutation.
[29/11/2005] Gauge coupling unification; W and Z boson production at a proton-antiproton collider.
[30/11/2005] The Higgs particle: experimental limits; Higgs production at LHC via gluon-gluon fusion.

References

[PS] An Introduction to Quantum Field Theory
by M. E. Peskin and D. V. Schroeder
1995, Addison Wesley
[O] Leptons and Quarks
by L. B. Okun
North-Holland 1982

To prepare the examination

Answer to the questions contained in the following subsections

Last modified: October 2005 - (feruglio@padova.infn.it)

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