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Electroweak interactions 2011


  • Jean-Marc Gerard
  • Fabio Maltoni


This course aims at providing a first introduction to the standard model of electroweak interactions. The prerequisites include Introduction to Particle Physics, Quantum Field Theory I and II, and Relativistic Quantum Mechanics. The course will be divided in two parts, for a total of 22.5 hours (4 ECTS).


I Part : SU(2)_L x U(1)_Y, the gauge boson sector

  • Experimental evidence on weak interactions
  • Fermi theory of weak interactions : applications and limitations
  • Gauge symmetries : Abelian and non-Abelian groups
  • SU(2)_L x U(1)_Y : fermion representations and interactions. The problem of gauge boson masses and unitarity violation.
  • Spontaneuous symmetery breaking (Goldstone theorem, Abelian Higgs model, Unitarity)
  • SU(2)_L x U(1)_Y -> U(1)_EM
  • Chiral Anomalies

II Part : Flavor dynamics

  • Custodial symmetry
  • Fermion masses : Yukawa interactions
  • Mixing in quark sector : theory and phenomenology
  • CP violation
  • Mixing in the lepton sector : neutrino mixing, ...


Further reading:

  • An introduction to quantum field theory, M. Peskin and D. Schroeder [P&S]. Chapters 15, 20, 21.

Original papers:

  • S. Weinberg, A Model of Leptons, Phys.Rev.Lett.19:1264-1266,1967.

Nice suggested readings about the low energy limit of the electroweak theory (Mathieu) :

  • L. B. Okun, Leptons and Quarks, pp. 9-21.
  • M. Maggiore, A Modern Introduction to Quantum Field Theory, pp. 195-218.


I Part

  • Fermi effective field theory of weak interactions

1 Consider the $ \pi \to \ell \nu_\ell $ decay. Calculate the decay rate in the case of a pseudoscalar current-current interaction. Determine the width for the decay of $\tau \to \pi \nu_\tau $ using as an input the experimental width of $\pi \to \ell \nu_\ell $. 1 Consider the $\mu^- \to e^- {\bar \nu_{e}} \nu_\mu$. Calculate $|M|^2$ using the Fierz trick (problem 3.6 of [P&S]) to turn the matrix element squared into a single trace. Consider the decay of a polarized muon. Find the angular distribution of the outcoming electron. 1 Calculate the scattering amplitude for $e^- + \nu_\mu \to \mu^- + \nu_e$.

  • EW interactions : SU(2) x U(1)

1 Derive the Feynman rules for the self interactions of the W,Z,photons. 1 Calculate $W^+ W^- \to W^+ W^-$ scattering amplitude and its behaviour at high energy when the gauge symmetry is non-linearly realized (=massive W,Z but not Higgs).

  • Higgs mechanism

1 Calculate the scattering $H \gamma \to H \gamma$ in the Abelian Higgs model. Verify that the Goldstone boson contribution is equivalent to the propagation of a massive photon in the internal lines. 1 Check that the Higgs contribution in $W^+ W^- \to W^+ W^-$ is exactly what is needed to cancel the bad behaviour at high energy.

II Part

  • *

Final Projects

  • Calculate the total width as a function of the mass, for a SM Higgs [P&S, pag. 775]
  • Extend the SM to include a mass for the neutrino's. Consider the two possibilities, Dirac and Majorana. Present and discuss the main differences between the phenomelogy of these two kinds of neutrino's.
  • Consider the simple extension of the Higgs sector, where two weak doublets are present. Discuss the various possibilities of giving mass to bosons and fermions, the relation with SUSY, custodial symmetry and the main differences in collider phenomenology.

EW Phenomenology at colliders

Here is a list of exercises that can be "solved" using Software.MadGraph. To do so register at and send an e-mail to F.M. to get running access.