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We all know that in particle physics the vacuum state is the state with no real particles. Unless the vacuum has the least energy with particles, because the degenerate vacuum, lowest energy state lays on a continuum of states related to each other by a rotation, and a local maximum in energy lays at the vacuum state. This false vacuum is assumed for the Higgs field.

Real particles are excitations of the field around the zero energy state. Which in the case of the Higgs field is already a state with Higgs particles.

So what is the state of the Higgs particle in the zero energy state? Do the Higgs scalars just reside in the massless quarks and leptons? And if we excite the vacuum, by delivering energy and momentum, emerges a real Higgs because all vacuum Higgs particles are "busy" to give mass? So it's not needed for that anymore if we produce one?

So, is the zero vacuum Higgs virtual or real? I mean, the zero vacuum for an electron contains virtual electrons too.

What's the difference between an free electron interacting with the zero photon field (anomolous magnetic moment, interaction with photon quantum bubbles, loops), and an electron interacting with the non-zero Higgs field? Are there besides the Higgs vacuum bubbles (loops) other features defining the zero energy state?

MatterGauge
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Do not confuse the concept of a field in the quantum field theory of particle physics, the standard model, with the particles that creation and annihilation operators create and annihilate on those fields.

All the elementary particles in the table have their corresponding fields.

elem

The fields extend over all space time , electron fields, quark fields .. and that is true for the Higgs field . That is why, once the Higgs field was postulated in order to have the Higgs mechanism of symmetry breaking, the standard model predicts a Higgs particle, which was searched for and a candidate was found in the LHC experiments.

Virtual particles are part of the Feynman diagram method of calculating interactions for particle physics, and are just a mathematical formalism that allows keeping track at vertices of quantum numbers. See this answer for virtual particles.

anna v
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  • Yes, I know. It could be that the virtual field is real just as well. But just not observable, apart from its effects. And the quantum vacuum (though not directly observable, since observing implies a real particle) is a means for interaction. Real particles coupling to it (and virtuals too for that matter). But thats not the question here. I ask what's the difference with ordinary virtual particles in the vacuum. – MatterGauge May 22 '22 at 14:57
  • Higgs loops (virtual higgs particlescould exist if the quantum numbers are correctly done. There are no loops if there are no incoming or outgoing real particles . The vaccum loops are corrections to the first order feynman diagrams. In other theories , like QCD on the lattice calculations, the term "viftual" has no meaning. – anna v May 22 '22 at 17:51
  • "the term "viftual" has no meaning." It doesn't indeed. ;) Virtual just means not on mass shell. Real is on mass shell. Loops in a Feynman diagram refer to real but virtual particles. The vacuum is quantum bubbled. What about the Higgs vacuum with particles? What kind of particles are these? Also vacuum bubbles? – MatterGauge May 22 '22 at 18:01
  • The zero energy state of the Higgs field is a state with particles present. This state is a different state from, say, an electron field with zero energy, which is the electron vacuum field. So what kind of particles are the Higgs particles present in the lowest energy state of the Higgs field, if not the kind of virtual Higgs field states present in, say, a zero energy electron field? The free electron, for example, couples to the virtual photons, leading to an anomalous magnetic moment. – MatterGauge May 22 '22 at 18:58