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5

Strong, Weak, and Higgs "forces" are a metaphor to mollify the public; these are short-range interactions, and lack long-range effects of the electromagnetism or gravity type. An implicit conceptual "bridge" through electromagnetism is implied, to help non-HEP physicists find their bearings. It routinely confuses laymen, and might as well ...

3

This is indeed a very confusing question and I have spent a lot of time parsing the literature looking for an answer. The references I found most useful are section 3 of the paper by Harlow and Ooguri, a set of lectures notes, and a study of SSB in superconductors(1) by van Wezel and van den Brink. Below, I summarize my current understanding; any comments ...

2

Depending on what quanta dark matter truly is made of, the Higgs boson may or may not be able to decay into those quanta. Being further nit-picky, at colliders, where the Higgs boson can be studied, dark matter may or may not be produced, the collider experiment will never be able to tell whether a new particle has a long enough lifetime to be the ...

1

Just to augment @ChiralAnomaly's answer with some algebra, we can compute a squared mass$$\frac{\partial^2V}{\partial\phi\partial\phi^\ast}=4\lambda\phi^\ast\phi-\mu^2$$for each solution of $\frac{\partial V}{\partial\phi}=0$. If $\mu^2\ge0$, $|\phi|^2=\frac{\mu^2}{2\lambda}$; if $\mu^2<0$, $\phi=0$. In both cases\frac{\partial^2V}{\partial\phi\partial\...

1

People often use the name "mass term" for a quadratic term in the lagrangian. That careless habit comes from free field theories, where it really is a mass term. But in general, the theory's physical predictions are determined by the whole theory, not just by one term in the lagrangian. The mass of the Higgs particle is real and positive. It's not ...

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