# Changes between Version 4 and Version 5 of EWUCL

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Timestamp:
03/06/13 13:32:33 (7 years ago)
Comment:

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Unmodified
 v4 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. 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. 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 $h_{W}=-1:h_{W}=0:h_{W}=+1$ ? 3. Use the Goldstone Boson Equivalence Theorem to evaluate the width of the top quark at Leading Order. Evaluate the effect of the bottom quark mass on the final result. What are your expectations for the ratios $h_{W}=-1:h_{W}=0:h_{W}=+1$ ? II Part * TBA * * *TBA* === Final Projects === * 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. * 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 $\langle \Phi \rangle =B$ Diag$(2,2,2,-3,-3)$ . For each case, work out the spectrum of gauge bosons and the unbroken symmetry group [P&S Problem 20.1, p. 728]. * 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 $\langle \Phi \rangle =B$ Diag$(2,2,2,-3,-3)$ . For each case, work out the spectrum of gauge bosons and the unbroken symmetry group [P&S Problem 20.1, p. 728]. * ...