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Let me answer your questions, albeit slightly indirectly. We start with a local $U(1)$ symmetry, i.e. a gauge symmetry, for a Lagrangian describing a scalar, $\phi$, and a gauge boson $A_\mu$. You write global. A global symmetry requries no gauge bosons, because its continuous parameter $\epsilon\neq\epsilon(x)$ commutes with derivatives $\partial_\mu$. The ...

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First, to be clear on what the graph is showing: as a function of the possible mass of the Higgs, it plots the fraction of Higgs bosons that will decay via each individual channel. Before we knew the mass of the Higgs boson, a plot like this one was useful for identifying the best channels to look at to detect the Higgs in various mass ranges. For example, ...

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Unfortunately I cannot comment to ask you for more details. What exactly do you mean 'equilibrium point at -V'? Is this the potential, $V(\phi^* \phi)$, or the VEV, $v$ ? Is it the fact that we put $$\mu^2 < 0$$ where $$V(\phi^* \phi) = \mu^2 (\phi^* \phi) + \frac{\lambda}{4}(\phi^* \phi )^2$$ that is bothering you? The Vacuum Expectation Value ...

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I'll only address your first question here. To start off with a sidenote, I think the idea that mass is a fundamental property of a particle has been on shaky ground ever since Einstein showed the equivalence of mass and energy. I can hardly imagine it took very long for people to come to the conclusion that mass cannot be a fundamental property of ...

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I don't have enough reputation to leave this as a comment, but this Youtube video by Sean Carroll answers your question very well. https://www.youtube.com/watch?v=RwdY7Eqyguo

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You must also take in account the diagram where a muon is the intermediate state, although it is not dominant. This particle will connect the two Higgs vertices.

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This isn't a complete answer to your question, just two comments on two specific points that came up that were too long for a comment: WRT the Higgs having a spatially varying background because of inhomogeneities in the universe: It's important to keep in mind that the Higgs field is VERY MASSIVE when it has a nonzero VEV (as it does in the universe ...

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An obvious difference between the two ways of thinking about it you mention is that in the case of the Higgs mechanism, there is an observable particle excitation of the field associated with it, which was found recently. Furthermore it should be noted that the Higgs mechanism only concerns the mass generation of some elementary particles. The mass of ...

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