[Physics] How the Higgs field exist if the Higgs boson is unstable


I understand from the internet that the Higgs particle is highly unstable! It decays as soon as it is created. If it is so unstable, how one can say that the Higgs field exist? Just like, if photons are unstable, there won't be electromagnetic field. I cannot imagine a field whose particle is highly unstable. Also, it is said that the mass depends up on how the matter interact with this higgs field. If the higgs bosons are highly unstable, how matter can interact with those unstable higgs bosons?

Best Answer

A field and a particle are two different concepts and it is well that one should separate them.

A field can be classified as a scalar field, a vector field, a spinor field or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or a tensor, respectively. For example, the Newtonian gravitational field is a vector field: specifying its value at a point in spacetime requires three numbers, the components of the gravitational field vector at that point. Moreover, within each category (scalar, vector, tensor), a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators respectively.

We are in quantum mechanics when we are talking of the Higgs field.

The Higgs boson or Higgs particle is an elementary particle in the Standard Model of Particle physics. Its main relevance is that it is the smallest possible excitation of the Higgs field

The field in quantum mechanics is defined via operators.

So it is two separate concepts. The Higgs field exists from low to high energies, but it is only at high energies that the Higgs boson can be on mass shell and subsequently decay. The Higgs boson is not a gauge boson, it does not define the interactions possible within the standard model between particles, as the photon, W and Z or the gluons do. It is a manifestation of the underlying field everywhere, when the energy available allows it, and the vacuum expectation value of this field is 246 GeV..

Particles acquire mass through the symmetry breaking mechanism of the Higgs field, not interacting with the Higgs boson/particle which is just a manifestation that had to exist if the symmetry breaking model is correct.

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