I understand that the Higgs Field is everywhere, but I don't have a feel for the density, or number, of Higgs Bosons in an area - say 1 cubic metre. Is there 1 mole of HB for every mole of quark in a particular area, or perhaps 1 mole for every accelerating mole of quark? I'm looking for a general idea on this number.
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asked Jan 20, 2020 at 16:22
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3 Answers
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A quantum Higgs field is everywhere, filling up the vacuum, and normally there are no real Higgs particles to be seen--just as the quantum field of the electron is all over the place, but, in the ground state, the vacuum, there are no real electrons to be seen.
If you had energy available, 1MeV, you could "pluck" that electron field, and create an electron-positron pair; and if you had more energy, these particles would travel. Their characteristic behavior ("massive propagation") would be prescribed by their interaction with that Higgs field, without any real Higgs particles being present.
Now if you really slammed particles with energy much much more than 125GeV , the mass of a real Higgs, you could create one such, which would then decay in a fantastically short time.
So the number of real Higgs particles in a region is directly (but subtly) related to the energy density you contrive to pack in that region, but, in humdrum undisturbed vacuum, the number is zero...
answered Jan 20, 2020 at 16:44
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The natural density of Higgs bosons is zero. This is why we had to use an enormous particle accelerator to briefly create some. They quickly decayed as soon as we made them, because they are very unstable.
In the same way that you can have a static electric or magnetic field without having any photons, you can have a static Higgs field without any Higgs bosons. A Higgs boson happens, roughly, when we add a little energy to the Higgs field and make it briefly vibrate.
You may be interested in this other question about what the energy density of the Higgs field was at the beginning of the universe. (Mind-bogglingly enormous! When the field was zero!)
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$\begingroup$ What I'm trying to find is how many bosons are there when they are there. You say we use a particle accelerator to create them. In nature, how many are created when they are created. How many are created per square metre or what ever other measure is appropriate? $\endgroup$ Commented Jan 20, 2020 at 16:40
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$\begingroup$ This CERN article says that in 2017 the LHC produced three million Higgs bosons. If the accelerator operated continuously, that would be only one every 10 seconds. Each one lasted only about $10^{-22}$ seconds before decaying. So, even when we were making them, most of the time the density was zero! $\endgroup$– G. SmithCommented Jan 20, 2020 at 17:11
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$\begingroup$ thanks, that's what i was looking for. $\endgroup$ Commented Jan 20, 2020 at 17:22
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You have the usual misunderstanding of confusing the Higgs field with the Higgs boson.
In quantum field theory every elementary particle in the standard model is a field covering all space and time: an electron field, an electron neutrino field etc.
The Higgs boson is one of the elementary particles. The fields are like a coordinate system or a Lorenz invariant ether where creation and annihilation operators act on them to produce the named particle.
See this relevant answer of mine .
So there is no density of Higgs bosons. They only appear if they have real fourvectors with the mass of the Higgs.
The fields are plane wave wavefunction on which the differential creator and annihilator operators operate. The mathematical formalism give rise to the Feynman diagrams that are used to calculate crossections and decays.
