Dmitry67 said:
How it is different of 'dressed' particles where their 'dress' consists of all sorts of virtual particles, including themselves, all other particles, ...
Your confusion probably arises from an imprecise notion of mass and "dressing". I will assume that, by "dressing", you are referring to the higher order Feynman diagrams as compared to a given "tree-level". In particular, a tree-level propagator is "dressed" with loops, but there remains only one input line and one output line. If this is what you are talking about, then the relevant notion of mass is the pole mass of the Fourier transform of the 2-point correlation function when the input time is taken to -∞ and the output time is taken to +∞; i.e. the pole of the propagator. This is actually one of the three ways of
defining the mass of the particle.
I will use the photon as a clean example. You can speak of the tree-level photon propagator, and it has a naive pole at E
2-p
2=0. This means that the "undressed", or "bare", photon is massless. However, quantum theory tells us that we must add every possible contribution to a given process, and for the photon propagator that means we have to add the loop diagrams (the vacuum polarization etc.). In general, loop diagrams can "shift" mass poles away from their tree-level locations. However, the Standard Model imposes electromagnetic gauge invariance and Lorentz invariance. These two requirements restrict the form of the full propagator such that the pole is not allowed to shift. (See, for example, Peskin & Schroeder, Chapter 7, Section 5, regarding "Renormalization of the Electric Charge".) We say that the masslessness of the photon is "protected by (electromagnetic gauge) symmetry". (I don't know if anyone even bothers to mention the Lorentz symmetry, even though it is essential for the protection of the zero mass pole. I think that particle physicist either actively try to test for violations of Lorentz symmetry, or they just take it for granted.)
Of course, you could argue the restrictions of invariance under the various groups themselves (and physics isn't science unless we always do so). Asking these kinds of questions is rather contextual. One unavoidable fact remains: the photon
is massless (or at least very very very ... very light). So, if you argue away the symmetry that elegantly protects this fact, then you have quite an undertaking. The photon is special. It enjoys the above-mentioned protection and also remains free of (direct) self-interactions or interactions with the Higgs field (well, sort of.). This nature of the photon is the big clue that leads to the notion of gauge symmetry in the first place, not the other way around.
The other gauge bosons do not provide such a clean demonstration of how the symmetry protects their mass. Furthermore, most other particles, including some of the gauge bosons, are given some coupling to the Higgs field in the Standard Model, and this is so because they have experimentally nonzero masses. (Neutrinos are another can of worms. Gluons are supposedly massless, but I don't know how seriously I should take gluons.)
However, if you take the symmetry principle seriously, then you can make the same basic argument regarding the other particles that acquire their mass from the Higgs mechanism: their masslessness is protected by symmetry, and they acquire their mass through the Higgs mechanism that breaks one of the symmetries. In fact, the Higgs mechanism breaks the SU(2)
W symmetry directly, and this is why it "gives" mass to the weak bosons. Then, there is a clever interplay between the two chiralities of fermions in the Yukawa interactions, so that the Higgs mechanism breaks the chiral symmetry of the fermions in a sort of indirect way.
It should be noted that the Higgs boson is not included in this list of protected particles. First of all, the Higgs field is set up to be strange from the beginning, having a |φ|
2 term in the Lagrangian with a
positive coefficient! You may be tempted to interpret that as an indication of
imaginary mass! I don't know a good way to interpret it "at tree-level". At any rate, I wouldn't say that the bare Higgs boson is massless, so it is hard to say whether or not the Higgs mechanism is responsible for the Higgs mass. The two concepts are inextricable. I suppose that you could talk about a dynamical Higgs potential such that the coefficient of the |φ|
2 can become negative (or could have been negative a long time ago). Then, you could naively think of that as the mass term. However, the "quantum corrections" will destroy this notion regardless of what the Higgs mechanism does, because the mass is not protected by a symmetry.
Dmitry67 said:
... including the ones we don't know yet?
If you want to consider such things, then all bets are off.
