RE: Particle physics lectures - demystifying the Higgs boson (the theory context) by lemouth

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science · @lemouth · Sep 10 '16

Let me give more details here.

Gauge symmetries implies that your basic Standard Model equation (the Lagrangian) is symmetric under the related symmetry transformation. It is turned into itself. 

Now, once you consider the mass terms to be added to this Lagrangian to feature the particle masses, these terms turn out not to be invariant under the symmetry transformation. The only option is thus to forbid them. And we have the problem for the modelling of the masses in the Lagrangian. Particles are massive and not massless.

So how to introduce the masses?The idea is to add a new field, the Higgs field, that interacts (in a gauge symmetric way) with all the other particles. Once the gauge symmetries are broken, the interaction of the Higgs field with the elementary particles will imply that the particles will become massive. 

Some of the degrees of freedom included in the Higgs field (3 out of the 4) will be absorbed by other particles to get their masses. One of these degrees of freedom is still there after the breaking of the electroweak symmetry. This is the Higgs boson that has been observed.

Is it clearer?

👍 justtryme90

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@christymonty · Sep 10 '16

I will have to brush up on my particle physics but for now it's as clear as mud.

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@lemouth · Sep 10 '16

Well, the answer is more technical. You should start with the post above and maybe I could then help ^^

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@justtryme90 · Sep 10 '16 (edited)

Yes, okay. Masses are not derived from the higgs boson, they are a function of particles interacting with the higgs field. The higgs boson is just one component of the higgs field.

I am still trying to give my self a simple way of understanding it in my head. This is interesting, but dense information for me :)

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@lemouth · Sep 10 '16

Difficult to say without entering deeply into the equations. I should not have used the world field... Well now it is too late... ;)

The Standard Model is a quantum field theory. Which means, you have strictly speaking only fields that interact with each other, and the field are the fundamental objects of the theory. The particles can be more seen as arising from the fields. And the Higgs boson arise from the Higgs field. 

You may ask what is going on with the three other degrees of freedom of the Higgs field. A massless vector boson like the photon has two degrees of freedom, and a massive one like the W^+, W^- or Z bosons have three. We need to render three bosons massive... Then the count is right.

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