# Changes between Version 1 and Version 2 of ElectroWeak

Ignore:
Timestamp:
03/20/12 16:04:32 (8 years ago)
Comment:

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### Legend:

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 * Halzen and Martin * [http://cp3wks05.fynu.ucl.ac.be/twiki/pub/Physics/EWUCL/smcom.pdf An introduction to the SM], by Giovanni Ridolfi. * [https://cp3.irmp.ucl.ac.be/projects/madgraph5/wiki/UCL/smcom.pdf An introduction to the SM], by Giovanni Ridolfi. * [http://arxiv.org/abs/0705.4264 The Standard Model of Electroweak interactions], by A. Pich. * [http://www.people.fas.harvard.edu/~hgeorgi/weak.pdf][Weak Interactions], by Howard Georgi. * 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. * [http://cp3wks05.fynu.ucl.ac.be/twiki/bin/view/Physics/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. * [http://cp3wks05.fynu.ucl.ac.be/twiki/bin/view/Physics/HiggsPheno Higgs] : Higgs phenomenology at hadron colliders. * [[http://cp3wks05.fynu.ucl.ac.be/twiki/bin/view/Physics/X New resonances]: Discover new resonances at the LHC. * [https://cp3.irmp.ucl.ac.be/projects/madgraph5/wiki/cs/SimpleKinematics Kinematics at the LHC]: single particle quantities. * [https://cp3.irmp.ucl.ac.be/projects/madgraph5/wiki/cs/WAsymm Drell-Yan] : Study the rapidity asymmetry at the Tevatron. * [https://cp3.irmp.ucl.ac.be/projects/madgraph5/wiki/cs/HiggsPheno Higgs] : Higgs phenomenology at hadron colliders. * [[https://cp3.irmp.ucl.ac.be/projects/madgraph5/wiki/cs/X New resonances]: Discover new resonances at the LHC.