# Changes between Version 1 and Version 2 of EWUCL

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Timestamp:
04/06/12 16:33:02 (8 years ago)
Comment:

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Unmodified
 v1 * 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 * SU(2)''L x U(1)''Y -> U(1)_EM * Chiral Anomalies * 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 %$e^- + \nu_\mu \to \mu^- + \nu_e$%. 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). 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. 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 Here is a list of exercises that can be "solved" using Software.MadGraph. To do so register at http://madgraph.hep.uiuc.edu and send an e-mail to F.M. to get running access. * [:SimpleKinematics:Kinematics at the LHC]: single particle quantities. * [http://cp3wks05.fynu.ucl.ac.be/twiki/bin/view/Physics/WAsymm Drell-Yan] : Study the rapidity asymmetry at the Tevatron. * [:HiggsPheno:Higgs] : Higgs phenomenology at hadron colliders. * [:X:New resonances]: Discover new resonances at the LHC. * [wiki:SimpleKinematics Kinematics at the LHC]: single particle quantities. * [https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/WAsymm Drell-Yan] : Study the rapidity asymmetry at the Tevatron. * [wiki:HiggsPheno Higgs] : Higgs phenomenology at hadron colliders. * [wiki:X New resonances]: Discover new resonances at the LHC.