Higgs Fields?

[PhysicsisPhunGuy]

The Higgs \'mechanism\' is responsible for mass in the standard model, correct? It\'s a scalar bosonic field? So it couples to all the fermionic fields? Is there an associated gauge invariance with the Higgs field?

Any corrections/information would be appreciated.

[uequals0]

The Higgs boson shows up in the following scenario. The microscopic theory of electromagnetic and weak interactions is the electroweak theory. The Lagrangian has local SU(2)xU(1) invariance (this is then called the gauge group of the electroweak theory). The field content consists of (massless) vector fields in the adjoint representation of the gauge group (therefore, there are four of them) and two massive scalar fields (vector representation of SU(2)). Due to gauge invariance, one can transform the doublet of scalar fields from (a,b) to (0,v). Thus, there is only one *physical* massive scalar field. This is the Higgs boson.
At lower energies, the doublet of scalar fields gets a non-zero vacuum expectation value (a phase change of the vacuum) and appear to be massless in this vauum. In this vacuum, the gauge invariance is now only U(1). The gauge field of this U(1) is the photon field. The massless scalar fields become the zero helicity states of the other 3 massless vector fields...thus we have 3 vector fields each with 3 spin states. This means that they are masive vector fields. These are the W+, W-, and Z bosons seen in weak interactions. In other words, at low enough energies, three of the original massless vector fields propagate in a vacuum that makes them massive.

[editor]

For all its mathematical elegance the Higgs field is remarkably like the Aether of old. I don\'t believe that Higgs bosons exist and I\'m in good company here, Hawking says that the CERN group will not find them.

What then gives mass, or inertia to particles ? I believe that the acceleration of a particle is resisted by the zero-point vacuum energy and this is the basis for inertia. After all, mass is only evident in a particle when you try to accelerate it.

[Xerxes314]

Umm, how do you get spontaneous breaking of the electroweak symmetry without a Higgs mechanism?

Xerxes

[editor]

Ask Hawking.
I\'m paddling a bit out of my depth here. But I see that Sheldon Glashow called Higgs particles the toilet of physics because they deal with things better not brought into the open.
It\'s always a worry to invent a new particle that has never been seen, especially a particle with unknown properties. And what happens to the Higgs at high energy levels - is the mass of the Higgs scalar not affected ? or does supersymmetry have something magic up its sleeve ? Will we see SUSY partners of ordinary matter when the CERN collider is up and running ? This is a really exciting prospect. I will be equally happy to be right or wrong.

[Edited on 7-24-2004 by editor]

[Xerxes314]

SuSy cleans up some of the mess involved in the Higgs sector, but it doesn\'t really answer the question. You have a specific problem: spontaneous electroweak symmetry breaking. You have a specific solution: a single complex isodoublet scalar field. What\'s not to like?

Xerxes

[editor]

The whole SUSY thing leaves me feeling a bit itchy. I haven\'t followed this recently but the last time I looked the following had not been seen.
Bosons: selectron, sneutrino, squark, Higgs, graviton.
Fermions: photino, wino, zino, Higgsino, gravitino

Out of 16 susy partners there are 10 that are theoretical. That\'s not good. notice that for the Higgs and the graviton neither partner has been seen !
I don\'t have answers, just doubts that these two will ever be seen.
Physics is an experimental science and until experiment shows a better weight on the \'seen\' side, the SUSY hypothesis must be questioned.

My objection to Higgs includes the \'miraculous\' contribution to the effective mass of the Higgs from bosons and fermions having opposite signs,thus the effect of all virtual particles cancels and the mass of the Higgs scalar is not affected by higher energy scales. Or: if susy is spontaneously broken etc, etc

Sounds suspiciously like a fudge factor.

[jefferywinkler]

If you want to learn about the Higgs mechanism, read my paper on the Standard Model on my homepage.

http://www.geocities.com/jefferywinkler

Jeffery Winkler

[marlon]

The Higgsfield really is a field on the background. Elementary particles (which are massless) appear to have mass (due to the interaction with the Higgsfield) when we look through this background.

What happens, in fact, is that the Higgs particle is a very heavy one, but - like all particles - corresponds in fact to a quantum field.

The problem people had when they were building a quantum theory of elementary particles is that the usual way of giving a mass to a fermion, namely by introducing a term m^2 psi-dagger psi in the lagrangian, didn\'t work because these terms do not respect the required symmetries of the theory (this is a bit a complicated issue).


However, it turned out that the introduction of a scalar particle (field), that was subject to a funny potential such that in the ground state (lowest energy) the field values would NOT be 0, could solve several problems.

Indeed, the non-zero value of that field, coupled with an interaction term between that field and, say, the electron field, gave a term in the lagrangian which DID respect the symmetries required, but mimicked, at low energies, as a term that was essentially the same as a mass term.


It also solved another problem: there were 2 theorems in quantum field theory that made life hard. The first one was by \'t Hooft, and said that if you want to have a renormalizable (calculable) theory, your interactions need to be described by fields such that the lagrangian obeys, what is called, a gauge symmetry. The problem with a gauge symmetry was that gauge particles have to be massless. People tried to find tricks around it, but Goldstone proved an annoying theorem (Goldstone\'s theorem), that said that you always have to have massless particles associated with the degrees of freedom of a gauge symmetry, the socalled \"goldstone bosons\". As these were not observed, that was annoying.
And then the Higgs mechanism was invented. It gave terms that mimicked mass to the gauge particles, it eliminated the goldstone bosons and gave, by its interactions, a mimicked mass term to the fermions.

Go see the Higgs mechanism being performed live :
http://www.shef.ac.uk/physics/teaching/phy604/ew4.pdf
http://www.shef.ac.uk/physics/teaching/phy604/ew5.pdf

marlon

[Xerxes314]

Originally posted by marlon
Goldstone proved an annoying theorem (Goldstone\'s theorem), that said that you always have to have massless particles associated with the degrees of freedom of a gauge symmetry, the socalled \"goldstone bosons\". As these were not observed, that was annoying.

I think you mean: you always have to have massless particles associated with the breaking of a continuous symmetry. And there are some observed (quasi-)Goldstone bosons: the pions, for example, get their (near-)masslessness from the spontaneous breaking of chiral symmetry in the QCD vacuum. (They gain their tiny masses from the fact that chiral symmetry is slightly broken by the quark masses to start out with.)

Xerxes

[marlon]

Originally posted by Xerxes314
Originally posted by marlon
Goldstone proved an annoying theorem (Goldstone\'s theorem), that said that you always have to have massless particles associated with the degrees of freedom of a gauge symmetry, the socalled \"goldstone bosons\". As these were not observed, that was annoying.

I think you mean: you always have to have massless particles associated with the breaking of a continuous symmetry. And there are some observed (quasi-)Goldstone bosons: the pions, for example, get their (near-)masslessness from the spontaneous breaking of chiral symmetry in the QCD vacuum. (They gain their tiny masses from the fact that chiral symmetry is slightly broken by the quark masses to start out with.)

Xerxes

This is all very true, however that was NOT the key point of my argument. If someone asks me how the Higgs system works, then this is my answer. Let us not start nitpicking and let us stick to bringing over the general system.

Your remark is correct, but it was NOT what i intended to say

marlon

[marlon]

Originally posted by Xerxes314
Originally posted by marlon
Goldstone proved an annoying theorem (Goldstone\'s theorem), that said that you always have to have massless particles associated with the degrees of freedom of a gauge symmetry, the socalled \"goldstone bosons\". As these were not observed, that was annoying.

I think you mean: you always have to have massless particles associated with the breaking of a continuous symmetry. And there are some observed (quasi-)Goldstone bosons: the pions, for example, get their (near-)masslessness from the spontaneous breaking of chiral symmetry in the QCD vacuum. (They gain their tiny masses from the fact that chiral symmetry is slightly broken by the quark masses to start out with.)

Xerxes

This is all very true, however that was NOT the key point of my argument. If someone asks me how the Higgs system works, then this is my answer. Let us not start nitpicking and let us stick to bringing over the general system.

Your remark is correct, but it was NOT what i intended to say

marlon

[editor]

Still not convinced. I await the CERN search for the Higgs. In the meantime I note that it has not been seen, and is only a proposed mechanism for mass. As I have said a few times, nice maths doesn\'t prove that anything exists in the real world, experimental proof is required..

[marlon]

Originally posted by editor
Still not convinced. I await the CERN search for the Higgs. In the meantime I note that it has not been seen, and is only a proposed mechanism for mass. As I have said a few times, nice maths doesn\'t prove that anything exists in the real world, experimental proof is required..

All very true and what you say applies for every physicist out there. However, theory doesn\'t present a better way up till now...at least not as widely accepted as the Higgs mechanism...but in the end, we are all waiting...

marlon

[amwreck]

Scientists in Switzerland may have seen the Higgs Boson. Read this article:

http://news.bbc.co.uk/1/hi/sci/tech/3546973.stm

[Edited on 5-14-2005 by amwreck]