ps9 - their masses in terms of the gauge couplings and any...

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Physics 509: Relativistic Quantum Field Theory Problem Set 9 Due Friday, 16 December 2011 30. Alternative Standard Model In this problem, we pose an alternative to the standard model, in which the Higgs boson (as opposed to the actual Higgs field of the standard model, which transforms as an SU (2) W doublet with hypercharge 1/2) transforms in a triplet representation of SU (2) W with hypercharge 1. Aside from that, the content is the same as for the standard model. a) Construct a tree level potential which permits spontaneous symmetry breaking of SU (2) × U (1) U (1) gauge summetry. Derive the masses of the W and Z bosons. Perform your analysis at tree level. b) What is the low energy spectrum of scalars and gauge bosons? Give the fields and
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Unformatted text preview: their masses in terms of the gauge couplings and any parameters you have defined in your potential. c) In the usual standard model, the ratio of the masses of the Z and W bosons is M Z /M W = 1 / cos θ W , where θ W is the weak mixing angle (i.e. tan θ W = g 1 /g 2 ). In our alternative model, is there a value of the Higgs expectation value such that the ra-tio of masses satisfies this relation? State two measurements which can distinguish this spectrum from the conventional standard model ones. d) Construct all possible renormalizable Yukawa interactions in the non-standard model. Which fermions, if any, get a mass? 1...
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