Changes between Version 1 and Version 2 of EWUCL
 Timestamp:
 04/06/12 16:33:02 (8 years ago)
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EWUCL
v1 v2 21 21 * SU(2)''L x U(1)''Y : fermion representations and interactions. The problem of gauge boson masses and unitarity violation. 22 22 * Spontaneuous symmetery breaking (Goldstone theorem, Abelian Higgs model, Unitarity) 23 * SU(2)''L x U(1)''Y  >U(1)_EM23 * SU(2)''L x U(1)''Y > U(1)_EM 24 24 * Chiral Anomalies 25 25 … … 58 58 59 59 * Fermi effective field theory of weak interactions 60 1. Consider the %$\pi \to \ell \nu_\ell $% decay. Calculate the decay rate in the case of a pseudoscalar currentcurrent interaction. Determine the width for the decay of %$\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$%.60 1. Consider the $\pi \to \ell \nu_\ell $ decay. Calculate the decay rate in the case of a pseudoscalar currentcurrent 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 $e^ + \nu_\mu \to \mu^ + \nu_e$. 63 63 64 64 * EW interactions : SU(2) x U(1) 65 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 nonlinearly realized (=massive W,Z but not Higgs).66 1. Calculate $W^+ W^ \to W^+ W^$ scattering amplitude and its behaviour at high energy when the gauge symmetry is nonlinearly realized (=massive W,Z but not Higgs). 67 67 68 68 * 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.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 71 72 72 II Part … … 84 84 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 email to F.M. to get running access. 85 85 86 * [ :SimpleKinematics:Kinematics at the LHC]: single particle quantities.87 * [http ://cp3wks05.fynu.ucl.ac.be/twiki/bin/view/Physics/WAsymm DrellYan] : Study the rapidity asymmetry at the Tevatron.88 * [ :HiggsPheno:Higgs] : Higgs phenomenology at hadron colliders.89 * [ :X:New resonances]: Discover new resonances at the LHC.86 * [wiki:SimpleKinematics Kinematics at the LHC]: single particle quantities. 87 * [https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/WAsymm DrellYan] : Study the rapidity asymmetry at the Tevatron. 88 * [wiki:HiggsPheno Higgs] : Higgs phenomenology at hadron colliders. 89 * [wiki:X New resonances]: Discover new resonances at the LHC. 90 90 91 91 … … 96 96 97 97 98