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In M. Veltman's Diagrammatica, appendix E, one can find the full Standard Model lagrangian. Some sectors (e.g fermion-Higgs and weak sectors) contain so-called Higgs ghosts $\phi^+,\phi^-$ and $\phi^0$.

Are Higgs ghosts Faddeev-Popov ghosts?

If so,

why does the Higgs field, not being a gauge field, yield Faddeev-Popov ghosts?

If not,

in which sense are they ghosts?

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1 Answer 1

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The Higgs ghosts are not Faddeev-Popov ghosts. (For starters, the Faddeev-Popov ghosts in the standard model are Grassmann-odd, while the Higgs ghosts are Grassmann-even.)

The Higgs ghosts are Goldstone bosons for the spontaneously broken part of the electroweak symmetry $SU(2) \times U(1)$, which, popularly speaking, get eaten by the massive gauge bosons $W^{\pm}$ and $Z$ via the Higgs mechanism. They are ghosts in the sense that they are not physical fields but rather gauge-dependent artifacts.

The Higgs ghosts are not so-called bad ghosts, which would have wrong sign in their kinetic terms, yield negative norm states & break unitarity.

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