Higgs vacuum expectation value imples what energy density?

In summary, the Higgs field has a vacuum expectation value of 246 GeV, which sets the scale for other particle masses induced by the Higgs. The expectation value of the Hamiltonian is not the same as the vacuum expectation value, and the energy scale is adjusted so that the energy of the vacuum at this point is zero.
  • #1
johne1618
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I understand that the the Higgs field has a vacuum expectation value of 246 GeV.

I think that means that the expectation of the Hamiltonian energy operator applied to the vacuum state is 246 GeV.

What does this imply for the energy density of the Higgs field in the vacuum (i.e. in Joules / m^3) ?

John
 
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  • #2
johne1618, As you say, the vacuum expectation value of the Higgs field is v = 246 GeV. It serves to set the scale for the other particle masses induced by the Higgs, for example mW = ½vg where g is one of the weak coupling constants. But it's not the expectation value of the Hamiltonian. The Higgs term that appears in the Hamiltonian and Lagrangian is a quartic, V(φ) = μ2φ*φ + λ(φ*φ)2, where φ = v is the point at which V is a minimum. But regardless, we adjust the energy scale so that the energy of the vacuum at this point is zero.
 

1. What is the Higgs vacuum expectation value?

The Higgs vacuum expectation value is a fundamental property of the Higgs field, which is a quantum field that permeates all of space. It is the value of the Higgs field in its lowest energy state, also known as the ground state.

2. How does the Higgs vacuum expectation value relate to the Higgs mechanism?

The Higgs vacuum expectation value is crucial to the Higgs mechanism, which is responsible for giving particles their mass. The interaction of particles with the Higgs field through the Higgs vacuum expectation value is what gives them mass.

3. What does the Higgs vacuum expectation value imply?

The Higgs vacuum expectation value implies the existence of the Higgs field and the Higgs mechanism. It also helps explain why particles have mass and why the weak nuclear force has a short range.

4. What is the energy density of the Higgs vacuum expectation value?

The energy density of the Higgs vacuum expectation value is not well-defined as it is an expectation value rather than an actual physical quantity. However, it is related to the energy scale at which the Higgs field breaks its symmetry, which is approximately 246 GeV.

5. How does the Higgs vacuum expectation value impact the search for new physics?

The Higgs vacuum expectation value is a crucial parameter in our understanding of the Standard Model of particle physics. Any deviations from its expected value could indicate the presence of new physics beyond the Standard Model. Therefore, it is an important quantity to study and measure in particle physics experiments.

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