Changes between Version 3 and Version 4 of EWUCL


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Timestamp:
Mar 6, 2013, 1:31:18 PM (11 years ago)
Author:
Mathieu Buchkremer
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  • EWUCL

    v3 v4  
    4646
    4747   * S. Weinberg, A Model of Leptons, Phys.Rev.Lett.19:1264-1266,1967.
    48    *
    4948
    50 Nice suggested readings about the low energy limit of the electroweak theory (Mathieu) :
     49Suggested readings about the low energy limit of the electroweak theory (Mathieu) :
    5150
    5251   * L. B. Okun, Leptons and Quarks, pp. 9-21.
    5352   * M. Maggiore, A Modern Introduction to Quantum Field Theory, pp. 195-218.
    5453
    55 === Exercises ===
     54
     55
     56=== Exercises (2013) ===
    5657
    5758I Part
    5859
    5960   * Fermi effective field theory of weak interactions
    60       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 $.
    61       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.
    62       1. Calculate the scattering amplitude for $e^- + \nu_\mu \to \mu^- + \nu_e$.
     61      1. Consider the $\pi \to \ell \nu_\ell $ decay. Compare the decay rate predictions in the cases of a $V-A$ and of a pseudoscalar current-current interactions. 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 $.
     62      2. 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.
     63      3. Calculate the scattering amplitude for $e^- + \nu_\mu \to \mu^- + \nu_e$.
    6364
    6465   * EW interactions : SU(2) x U(1)
    65       1. Derive the Feynman rules for the self interactions of the W,Z,photons.
    66       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).
     66      1. Derive the Feynman rules for a SU(N) Yang-Mills theory. Apply your results to determine the self interactions of the W,Z,photons in the SU(2) x U(1) Standard Model.
     67      2. Estimate the total width of the $W$ and $Z$ gauge bosons. What conclusions can you draw on the number of (light) neutrino flavours ? [P&S Problem 20.2, p. 728]
     68      3. 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).
    6769
    6870   * Higgs mechanism
    69       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.
    70       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.
     71      1. Determine the Feynman rules of the Abelian Higgs Model. 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.
     72      2. Check that the Higgs contribution in $W^+ W^- \to W^+ W^-$ is exactly what is needed to cancel the bad behaviour at high energy.
     73      3. Use the Goldstone Boson Equivalence Theorem to evaluate the top quark width at Leading Order. Evaluate the effect of the bottom quark mass on the final result. What are your expectations for the ratios $h_{W}=-1:h_{W}=0:h_{W}=+1$ ?
    7174
    7275II Part
    7376
    74 * *
     77* TBA *
    7578
    7679=== Final Projects ===
    7780
    78    * Calculate the total width as a function of the mass, for a SM Higgs [P&S, pag. 775]
     81   * Calculate the total width as a function of the mass, for a SM Higgs [P&S Final Project, "Decays of the Higgs Boson", p. 775]
    7982   * 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.
    8083   * 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.
     84   * Consider a gauge theory with the gauge group SU(5), coupled to a scalar field $\Phi$ in the adjoint representation. Assume that the potential for this scalar field forces it to acuire a nonzero vev. Two possible choices are $\langle \Phi \rangle =A$ Diag$(1,1,1,1,-4)$ and $\langle \Phi \rangle =B$
     85Diag$(2,2,2,-3,-3)$ . For each case, work out the spectrum of gauge bosons and the unbroken symmetry group [P&S Problem 20.1, p. 728].
     86   * ...
    8187
    8288=== EW Phenomenology at colliders ===