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?