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If the Higgs boson mediates mass interactions, do they exist in nature? Are there Higgs bosons flying around all the time? Or do they only exist for a tiny fraction of a second while they mediate mass?

As I understand it, the bosons are all mediators of interactions. We know that photons, gluons, and the W-/Z- bosons exist. Photons persist for very long durations as they speed through the cosmos. Does the Higgs/mass-mediating boson do this? I'm sort of having trouble getting a grasp on at what point the mass boson would exist and how that would work in practical fact.

Also, it's entirely possible that this is a nonsensical question based on me misunderstanding everything. :)

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You need to distinguish between the Higgs boson, that has just been discovered by the LHC, and the Higgs field.

The Higgs field exists everywhere, and it's the interaction of the Higgs field with the electroweak field that gives the W and Z bosons their mass. A different interaction of the field with fermions gives them mass, but I must admit the details of this are somewhat mysterious to me.

Anyhow, the Higgs boson is the bit left over after the Higgs field has interacted with the electroweak bosons, and it doesn't do anything except excite physicists. It's importance is that its discovery is evidence for the Higgs field rather than because of any special property of it's own. It's just an excitation of the Higgs field along the radial direction in the "mexican hat" model. Higgs bosons exist everywhere in the sense that they are created continuously in cosmic ray collisions or as virtual particles, but any individual Higgs boson rapidly decays.

But then this is true for the W and Z bosons as well. It's only the photon that has an extended lifetime.

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As I understand it, the bosons are all mediators of interactions. We know that photons, gluons, and the W-/Z- bosons exist. ... Does the Higgs/mass-mediating boson do this?

I don't think it's correct to think about the Higgs field as mediating mass.

First, do keep in mind that photons, gluons, and the weak vector bosons are quanta of gauge fields and that the Higgs field is not a gauge field, it is in fact, two complex scalar fields that form an electroweak doublet, i.e., the Higgs field carries electroweak charge.

Now, the Higgs mechanism by which the weak vector bosons gain "mass" is similar to the way a photon gains "mass" inside an electromagnetic superconductor. The Higgs field decays to a ground state which, due to the Higgs peculiar potential, makes the "vacuum" an electroweak superconductor.

The point is this: just as electric charge doesn't "mediate" mass and yet, the photon appears massive when embedded in electromagnetic superconductor, the Higgs field doesn't "mediate" mass but the weak vector bosons appear massive in the electroweak superconducting vacuum.

I believe the argument is similar for fermions although their interaction with the Higgs field is via a Yukawa interaction rather than a gauge interaction

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