Photons are massless. Gluons also are thought to be massless, but they are not free particles, so their velocity or locus of interaction generally is assumed to be unobservable.

What is the nature of the Higgs field?

Well, because it determines rest mass, its effects must be Lorentz invariant. Therefore, it must be a differential field in which position is undefined. A similar "field" is that of the vacuum permittivity, which is everywhere and which, with the vacuum permeability, determines the

speed of light c, which of course is the same in all inertial frames.

Here's my question: If we don't need a "permittivity particle" to describe electrical properties of the vacuum, why should we need a "mass particle" to describe the mass-giving properties of the vacuum?

The "mass particle" in question is the Higgs boson -- a scalar to account for the differential nature of the Higgs field, and a boson to account for its assumed zero (or maybe unit) spin. By analogy, the electromagnetic forces are mediated by exchange of photon bosons, the weak

force by exchange of W or Z bosons, the strong force by gluons -- and, the mass force (as it were) by Higgs bosons.

The Higgs boson is calculated from Standard Model consistency not to be massless, but rather to have a mass probably between 100 and 200 GeV/c^2, as much as twice the mass of the weak force bosons. According to this model, the Higgs boson may possibly have a mass as great as 1000 GeV/c^2, but not more than this.

One of the goals of current work with the Large Hadron Collider at CERN is to observe the Higgs boson. But, if it represents a nonpositional field, why should energy concentrated at a certain position, the collision point, make any difference?

And, should the "mass particle" have mass? If so, it must react on itself in an illogical way. Also, if the Higgs boson is massive, and if it mediates mass by vacuum virtual exchanges, the exchange rate must be subject to Lorentz time dilation. Because other forces grow with boson exchange rate, time dilation would suggest that the rest mass of all particles should decrease with

increasing relativistic velocity, possibly cancelling the observed increase in particle momentum.

Thus, it appears that there may exist a Higgs vacuum field, but there may not exist a Higgs particle. And if there is a Higgs boson, it should be massless.

How can these objections be answered? The Standard Model apparently is wrong about the mass of neutrinos, so why should it be accepted uncritically in regard to the mass of the Higgs boson?

## Comments

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Photons are the only particle confirmed massless by measurement of their velocity. Gluons are observed only by inference, and gravitons, if they exist, have not yet been observed.

John,

I'll try to answer these points in the same order you asked.

Gluons are known to be massless. They mediate the color force, in the same way that the photon mediates the electromagnetic force. Color is an exact symmetry, and this requires gluons to be massless. Although they interact strongly with quarks and with each other, they do live long enough for their position and velocity to be meaningful. For example a high-energy gluon produced in a collision can be observed to decay into a "jet" of other particles.

The "permittivity of vacuum" is not a property of anything. It's just a defined constant that is used to convert between different sets of electromagnetic units.

The Higgs is not a "mass particle." The purpose of the Higgs field is to break electroweak symmetry. If electroweak symmetry were exact, the electromagnetic force and the weak force would have the same strength. And if it were not for the Higgs field, the photon, W-meson and Z-meson would all have the same properties. Indirectly, the existence of the Higgs field allows the fermions (quarks and leptons) to have a nonzero mass in a manner consistent with electroweak symmetry. But the Higgs particle does not couple to all particles through their mass -- the graviton plays that role.

(Note that the Higgs boson is not the same as the Higgs field. The Higgs boson is an excitation of the Higgs field. The Higgs field is uniform throughout space, while of course a Higgs boson is localized, the same as any other particle.)

Finally, it's not fair to say the Standard Model is "wrong" about neutrino masses. We now know these masses must be nonzero, and they may very easily be added to the model, but for most purposes they're ignored.

I disagree on permittivity: The vacuum permittivity is a property of the vacuum, just as is the Higgs field. The mass of the electron is assumed determined by the Higgs, and this is no different that saying that the speed of light is determined by the vacuum permittivity (and permeability). I would agree that it might be possible to use some other approach than Maxwell's to handle electromagnetic fields; nevertheless, the speed of light is determined by properties of the vacuum, and there is no essential reason why the speed of light (c) could not be some different value, were the vacuum itself different.

Maybe I was ambiguous on the objection to Higgs mass: I agree that the graviton, if it exists, is what couples massive particles by their mass. However, what determines the rest masses to be coupled is the Higgs field. If there is a Higgs boson, and it works by virtual exchange, and it is itself massive, then the REST masses of particles relativistically in motion should decrease because of time dilation. This in turn would alter graviton exchange, which was not intended to be my main point.

Yes, the Standard Model might be enhanced to accommodate massive neutrinos; however, at present, it has not been so (in a widely accepted way). Perhaps I should suggest that it be changed to eliminate the Higgs boson or at least define it to be massless?

I just don't think it is enough to BELIEVE in a graviton or a Higgs boson to make it exist; there has to be experimental evidence directly supporting such beliefs. At present, they may be reasonable hypotheses . . ..

"However, what determines the rest masses to be coupled is the Higgs field. If there is a Higgs boson, and it works by virtual exchange, and it is itself massive, then the REST masses of particles relativistically in motion should decrease because of time dilation."

All of these statements are incorrect. First of all, the Higgs field has a uniform value everywhere, and since it is a scalar field it is also the same in every rest frame. So all particles see the same value of the Higgs field regardless of their motion. This value is usually denoted v.

The Higgs field permits each fermion to have a mass, but does not "determine" it. The mass will be Gv (G times v) where G is a coupling constant different for each type of fermion. No one knows what determines the G values, but it is certainly not the Higgs or anything else within the standard model. There is no "virtual exchange of Higgs bosons" going on!

As far as the Higgs mass goes, if it were anything small it would have been seen long ago. Experiments at the previous CERN collider (the LEP) ruled out a Higgs mass below 115 GeV,

I disagree with the hair you are splitting with the rest: If other particles "couple" with the Higgs field, then standard application of field theory implies that this coupling is mediated by virtual particle exchange. It doesn't matter what determines each particle's coupling constant; that wasn't the point. If coupling to the Higgs field is required to determine the mass, then my point is as presented.

Look at a simpler analogy: The (nonrelativistic) momentum of a particle is given by m*v, m the rest mass and v the velocity. Therefore, one can assert that m determines the momentum, even though changing v (read, varying Higgs G across different particles) changes the momentum, too. If m is allowed to go to zero, the momentum goes to zero, regardless of v (of course, I am not trying to make an issue of how the singularity of EXACTLY zero mass could be reached). For a specific v, m determines the momentum of a particle.

If there were no Higgs field, then, accepting the theory, there could not be a mass for any of those particles, regardless of its particular G. Thus, coupling to the Higgs field determines the mass. Naturally, various particles have different masses; I did not intend to say that all particles had the same mass because the mass was determined by the one Higgs field.

OK. Let me ask you, what mediates the coupling of the Higgs field to a particle?

My answer is that it must be virtual exchange of Higgs bosons. Do you know this to be incorrect? Even if the Higgs bosons didn't couple to anything, but merely popped in and out of the vacuum, if they were massive, they would be associated with an inertial rest frame and thus would experience time dilation relative to other particles in relativistic motion. One can not have a scalar boson which fails to break symmetry (as would a scalar field) and is "massive" in any meaningful way. Mass is equivalent to failure of Lorentz invariance.

The illogic which I see here is the idea of a massive scalar particle. This contradicts special relativity, which has been confirmed in all other contexts.

As for your final point, you are begging the question that the Higgs exists, just because some thing can be calculated for it in the Standard Model. As I mentioned before, the Standard Model is known to be defective with regard to neutrino masses. It is just a model which provides a consistent analogical framework for much of particle physics. So, at least in my opinion, one can not assume that it is so correct as to be allowed to contradict special relativity.

There are couple of things about this article which I don't understand / misunderstand and I am going to express couple of my own opinion.

1) "Gluons also are thought to be massless, but they are not free particles, so their velocity or locus of interaction

generally is assumed to be unobservable."

According to wiki, experimental limit of the gluon is < 20 MeV/c^2

2) The part about vacuum permittivity

I don't understand how vacuum permittivity can be thought of as a field?

According to wiki, vacuum permittivity = permittivity of free space, which is a constant. Combine with vacuum permeability, it gives the speed of light in vacuum.

3) "mass force (as it were) by Higgs bosons"

I don't think mass is a force?

3) "why should energy concentrated at a certain position, the collision point, make any difference?"

Higgs couples to mass, I think the process they are mainly looking for in LHC is gluon-gluon fusion, which gives top quarks in the immediate stage and see if this will produce the Higgs. In order for this to happen often, it requires high energy.

4) "And, should the "mass particle" have mass? If so, it must react on itself in an illogical way. Also, if the Higgs boson is massive, and if it mediates mass by vacuum virtual exchanges, the exchange rate must be subject to Lorentz time dilation. Because other forces grow with boson exchange rate, time dilation would suggest that the rest mass of all particles should decrease with increasing relativistic velocity, possibly cancelling the observed increase in particle momentum."

I don't really understand this paragraph at all.

Higgs is not a "mass particle" (covered by Bill)

What is "vacuum virtual exchanges"? Why the exchange rate must be subject to Lorentz time dilation?

"Because other forces grow with boson exchange rate"

Are you saying, the strength of a force is proportional to the corresponding rate of boson exchange? If so, I think that is wrong, strength of a force is proportional to the coupling. It is the rate of a process that is proportional to the rate of boson exchange.

Rest mass by defination should not change, no matter what velocity it is travelling at.

Finally, you are correct about the neutrino having mass. Physicists know the Standard Model is not complete. There are actually quite a lot of different models beyond the Standard Model but we don't know which one is correct, that is one of the reason why we want to conduct experiments such as in the LHC and gives us hints which direction to head towards. If they can't find the Higgs in the LHC, then theorists might start to consider other mechanisms for the electroweak symmetry breaking.

One correction to my above comment, it should be intermediate stage rather than "immediate stage"

From wiki

"In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction."

I still don't quite understand your steps about Lorentz invariant.

From wiki again

"The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c^2, which is equal to the mass of the system as measured on a scale. If the system is one particle, the invariant mass may also be called the rest mass"

Which quantity are you saying is not Lorentz invariant? (Rest mass is Lorentz invariant)

Strictly speaking, everything moving with respect to (wrt) an observer will experience time dilation compare to the observer. This effect is barely noticable unless travelling at speed close to c.

So are you purposing the Higgs boson would be a free massless particle? If so, experiments would be able to detect it already. (as Bill said)

I personally think that, in order to talk about physics formally, it might be a good idea to study the actual physics, go through the mathematics. Then discuss possible mistakes in the physics (or maths). If you want to convince me with your theory, I think you will need to show me some maths.