Is the Higgs Field Merely a Dressing Field?

[ensabah6]

http://arxiv.org/abs/1012.5529
Asymptotically safe weak interactions
Xavier Calmet
(Submitted on 26 Dec 2010)
"We emphasize that the electroweak interactions without a Higgs boson are very similar to quantum general relativity. The Higgs field could just be a dressing field and might not exist as a propagating particle. In that interpretation, the electroweak interactions without a Higgs boson could be renormalizable at the non-perturbative level because of a non-trivial fixed point. Tree-level unitarity in electroweak bosons scattering is restored by the running of the weak scale."

What is a dressing field?

 

[suprised]

A dressing field is usually a field that multiplies ("dresses") another field, often in exponentiated form. It is normally used to restore some symmetry like scale transformations, as such they are also called compensator fields. Goldstone fields can be thought of as such compensators too, as they restore the broken symmetry by dressing other matter fields. They are however propagating degrees of freedom, I am thus not sure how to understand non-propagating Higgs fields.

 

[Finbar]

There's an explanation of the Higgsless Higgs mechanism in this paper

http://arxiv.org/pdf/0910.5167

Read part II THE HIGGS PHENOMENON

There is a variant of this that we may call the Higgsless Higgs mechanism...
imagine freezing the Higgs field to its VEV, so that one remains only with the Goldstone
bosons. This can be achieved formally by taking the limit λ → ∞, keeping υ constant. However,
it is not necessary to think of the theory in this way. One can just think of constructing a scalar
theory where the the field has values in SN−1; it is called a NonLinear Sigma Model (NLSM)...a gauged NLSM is just a gauge invariant way of writing a massive gauge theory... we see that strictly speaking only the Goldstone bosons are necessary for the Higgs mechanism; the Higgs field ρ, which is gauge invariant, is a mere spectator. The geometrical reason why one prefers to have ρ is that the full multiplet φa transforms linearly, and the physical reason for preferring a linearly transforming multiplet of N scalars, over the nonlinearly transforming multiplet of N − 1 Goldstone bosons, is that perturbatively a linear scalar theory with a quartic potential is renormalizable, whereas the NLSM is not.

 

[suprised]

Oh I see, the author proposes to give up the good UV properties of perturbative, spontaneusly broken gauge theory by introducing a non-renormalizable NLSM, and hopes for a non-perturbative fixed point that would unitarize the theory in the UV instead. That's part of the classicalization programme.. ... I'd call it fixed-point mania ;-)

 

[ensabah6]

Oh I see, the author proposes to give up the good UV properties of perturbative, spontaneusly broken gauge theory by introducing a non-renormalizable NLSM, and hopes for a non-perturbative fixed point that would unitarize the theory in the UV instead. That's part of the classicalization programme.. ... I'd call it fixed-point mania ;-)

thanks. Is it physically plausible? What would LHC see under this program?

 

[MTd2]

I'd call it fixed-point mania ;-)

Great name for a blog! :D

 

[MTd2]

Done! :D

http://fixedpointmania.blogspot.com/2011/01/fixed-point-mania.html

 

[Finbar]

Oh I see, the author proposes to give up the good UV properties of perturbative, spontaneusly broken gauge theory by introducing a non-renormalizable NLSM,

What good UV properties of perturbative, spontaneusly broken gauge theory? The standard higgs mechanism suffers from triviality so it is inconsistent in the UV.

 

[suprised]

What good UV properties of perturbative, spontaneusly broken gauge theory? The standard higgs mechanism suffers from triviality so it is inconsistent in the UV.

Well wasn't the whole point of 't Hooft et al to prove unitarity and renormalizability of spontaneously broken YM theory? That is the main feature of why gauge theories are considered to be relevant for the weak interactions. Abandoning this in favor of a speculative non-perturbative mechanism without good motivation doesn't sound compelling to me.

I guess ppl just want to bet on the possibility that the Higgs is not found; fortunately this issue will be settled in a few years of time so let's wait and see!

 

[ensabah6]

Well wasn't the whole point of 't Hooft et al to prove unitarity and renormalizability of spontaneously broken YM theory? That is the main feature of why gauge theories are considered to be relevant for the weak interactions. Abandoning this in favor of a speculative non-perturbative mechanism without good motivation doesn't sound compelling to me.

I guess ppl just want to bet on the possibility that the Higgs is not found; fortunately this issue will be settled in a few years of time so let's wait and see!

Thus far the Higgs has not been found.

By what year should the LHC collect enough data to settle this over Higgs expected range? If the Higgs isn't found, what's the best alternative explanation?

 

[suprised]

Thus far the Higgs has not been found.

By what year should the LHC collect enough data to settle this over Higgs expected range? If the Higgs isn't found, what's the best alternative explanation?

Well the search just started and it may take a couple of years to find it, even under moderately favorable circumstances. If not, it may be an "interesting disaster" ;-) Here a good recent review of the subject: http://arxiv.org/pdf/0910.4976

 

[Finbar]

Well wasn't the whole point of 't Hooft et al to prove unitarity and renormalizability of spontaneously broken YM theory? That is the main feature of why gauge theories are considered to be relevant for the weak interactions. Abandoning this in favor of a speculative non-perturbative mechanism without good motivation doesn't sound compelling to me.

I guess ppl just want to bet on the possibility that the Higgs is not found; fortunately this issue will be settled in a few years of time so let's wait and see!

Both QED and the higgs have a landau pole at finite energy. So the standard model is not consistent in the UV. Only the YM part of the SM is asymptotically free and hence valid to arbitrarily high energies.

But your right that at least up to the energies of the LHC the theory needs the higgs to be unitary with in perturbation theory. The point here is only that there is another way to restore unitarity without the higgs.

 

[ensabah6]

Both QED and the higgs have a landau pole at finite energy. So the standard model is not consistent in the UV. Only the YM part of the SM is asymptotically free and hence valid to arbitrarily high energies.

But your right that at least up to the energies of the LHC the theory needs the higgs to be unitary with in perturbation theory. The point here is only that there is another way to restore unitarity without the higgs.

If true, what would it mean for the LHC, hierarchy problem, fine-tuning, higgs quadratic radiative corrections, SUSY, strings, and future physics research and QG?