# Higgs Field

Why doesn't the Higgs field give photons mass?

It has to do with the spontaneous symmetry breaking of $$SU(2) x U(1)$$, the photon essentially doesn't couple to the Higgs Field.

"The simplest implementation of the mechanism adds an extra Higgs field to the gauge theory. The spontaneous symmetry breaking of a local symmetry causes this Higgs field to interact with (at least some of) the other fields in the theory, in a manner producing mass terms for (at least some of) the gauge bosons. The symmetry breaking can also produce elementary scalar (spin-0) particles, known as Higgs bosons." - Wikipedia

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tom.stoer
b/c it is constructed such that it couples to the SU(2) triplet, not to the U(1) gauge field

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Is this same answer used for gluons and gravitons.

Yea, I'm not sure about gravitons though.

tom.stoer
The Higgs is constructed explicitly to generate a mass for the W and the Z and to leave to photon massless. b/c one does not believe that gluons have mass, one does not introduce a Higgs in the SU(3) sector.

b/c it is constructed such that it couples to the SU(2) triplet, not to the U(1) gauge field

This is not correct. The U(1) force in the standard model's SU(3)xSU(2)xU(1) couples to hypercharge, not to electric charge. The Higgs couples to both SU(2) and to U(1). However, it necessarily leaves one superposition of the U(1) and SU(2) gauge bosons massless, indicating a residual, unbroken U(1) symmetry, which is the U(1) of EM.

tom.stoer
it simply depends if you talk about U(1) and SU(2) before symmetry breaking and rotation or after; there is no coupling of the Higgs vev to the photon which is the physical U(1) EM gauge boson; that's why the photon remains massless.

So my sentence should read ... b/c it is constructed such that it couples to the physical SU(2) triplet (W, Z), not to the physical U(1) EM gauge field

is the Higgs field necessarily associated with the Higgs boson and does it give mass to EVERY fermion?

tom.stoer
The Higgs boson is the oscillation of the Higgs field around its vacuum. Its like any other quantum field and the corresponding relation between field and particle in QFR - excpet for the fact that its vev is nonzero.

The fermion masses are subtle. Usually one is allowed to introduce standard mass terms. But due to the chiral structure of the electro-weak interaction this would violate a local gauge symmetry and one must therefore find a new mechanism to introduce these masses.

Again this is ad-hoc: instead of introducing a mass mf for each fermion f one introduces a coupling constant gf which couples the fermion to the Higgs. The mass is related to gf and to the vev of teh Higgs. So the arbitrary masses are replaced by arbitrary coupling constants (ugly!). If there are massless fermions on is allowed to set this coupling to zero.

but what about the energy instead of the mass? for example neutrinos have a very small mass but move at relativistic speeds, so more energy than mass. is the higgs boson responsible for all that energy then? where does the energy of fermions come from?

tom.stoer
The fermion energy is

E² = (mc²)² + (cp)²

where m is generated via the Higgs vev and p is the usual kinematical momentum and has nothing to do with the Higgs.

So once the rest mass m is created via the Higgs vev, everything remains unchainged.

ok, thank you. but how likely can the Higgs be found? and what happens if there is no higgs, where does the mass come from?

tom.stoer
ok, thank you. but how likely can the Higgs be found? and what happens if there is no higgs, where does the mass come from?

There are Higgs-less models for mass creation, but most people today do believe in the Higgs.

See e.g.
http://arxiv.org/abs/0905.3187
Unanswered Questions in the Electroweak Theory
Authors: Chris Quigg
(Submitted on 19 May 2009 (v1), last revised 7 Jul 2009 (this version, v2))
Abstract: This article is devoted to the status of the electroweak theory on the eve of experimentation at CERN's Large Hadron Collider. A compact summary of the logic and structure of the electroweak theory precedes an examination of what experimental tests have established so far. The outstanding unconfirmed prediction of the electroweak theory is the existence of the Higgs boson, a weakly interacting spin-zero particle that is the agent of electroweak symmetry breaking, the giver of mass to the weak gauge bosons, the quarks, and the leptons. General arguments imply that the Higgs boson or other new physics is required on the TeV energy scale. Indirect constraints from global analyses of electroweak measurements suggest that the mass of the standard-model Higgs boson is less than 200 GeV. Once its mass is assumed, the properties of the Higgs boson follow from the electroweak theory, and these inform the search for the Higgs boson. Alternative mechanisms for electroweak symmetry breaking are reviewed, and the importance of electroweak symmetry breaking is illuminated by considering a world without a specific mechanism to hide the electroweak symmetry.
For all its triumphs, the electroweak theory has many shortcomings. . . .

The Higgs boson is the oscillation of the Higgs field around its vacuum. Its like any other quantum field and the corresponding relation between field and particle in QFR - excpet for the fact that its vev is nonzero.

The fermion masses are subtle. Usually one is allowed to introduce standard mass terms. But due to the chiral structure of the electro-weak interaction this would violate a local gauge symmetry and one must therefore find a new mechanism to introduce these masses.

Again this is ad-hoc: instead of introducing a mass mf for each fermion f one introduces a coupling constant gf which couples the fermion to the Higgs. The mass is related to gf and to the vev of teh Higgs. So the arbitrary masses are replaced by arbitrary coupling constants (ugly!). If there are massless fermions on is allowed to set this coupling to zero.

I would add to this that there are possible mechanisms for the generation of neutrino mass (such as the type 2 see-saw) that don't at all involve the standard model Higgs. In fact, any model that doesn't add new standard model-singlet fermions in the process of generating neutrino mass will necessarily not involve the SM Higgs.

tom.stoer
Yes, this is one example of a Higgs-less model, but afaik it does not account for all masses but only for special particles.

It has to do with the spontaneous symmetry breaking of $$SU(2) x U(1)$$, the photon essentially doesn't couple to the Higgs Field.

"The simplest implementation of the mechanism adds an extra Higgs field to the gauge theory. The spontaneous symmetry breaking of a local symmetry causes this Higgs field to interact with (at least some of) the other fields in the theory, in a manner producing mass terms for (at least some of) the gauge bosons. The symmetry breaking can also produce elementary scalar (spin-0) particles, known as Higgs bosons." - Wikipedia

Just a comment to the wikipedia quote. I think that it is a common misconception (because of sloppy treatment/terminology in most books ) that the gauge symmetry is spontaneously broken in the Higgs mechanism. The gauge symmetry is not a physical symmetry, but redundancy in our description and therefore it makes no physical sense to break this "symmetry". Even if we had some local symmetry, the famous http://prd.aps.org/abstract/PRD/v12/i12/p3978_1" [Broken] says that you cannot (spontaneously) break local symmetries!
One first need to explicitly (by hand) break the local gauge symmetry, and the residual physical global symmetry can then be spontaneously broken.

For a discussion of these issues in the case of Abelian gauge theory (superconductor oriented) see http://www.sciencedirect.com/scienc...2149863&md5=26858acdc59c7e515e3509f1c9e44a30").

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Yes, this is one example of a Higgs-less model, but afaik it does not account for all masses but only for special particles.

I never claimed the type-2 see-saw was a Higgsless model for EWSB. It's a Higgsless model of neutrino mass. I was specifically adding this as a caveat to you're post's implication that the Higgs field is responsible for all fermion masses. In the case of the neutrino (even presuming the existence of an ordinary standard model Higgs), it is simply unknown.

tom.stoer