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Higgs particles and rest mass

  1. Jul 20, 2004 #1
    Are Higgs particles all the same mass?
    Does a proton have more Higgs particles associated with its rest mass
    than an electron has associated with its rest mass?
    And does the mass of all Higgs particles equal the total rest mass of
    the universe? Do Higgs particles have short lifetimes like other
    particles in the vacuum?
  2. jcsd
  3. Jul 21, 2004 #2


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    You seem to think that Higgs particles are a kind of marbles that you put in a proton bag to make up its mass. It is absolutely not the case.

    What happens, in fact, is that the Higgs particle is a very heavy one, but - like all particles - corresponds in fact to a quantum field.
    The problem people had when they were building a quantum theory of elementary particles is that the usual way of giving a mass to a fermion, namely by introducing a term m^2 psi-dagger psi in the lagrangian, didn't work because these terms do not respect the required symmetries of the theory (this is a bit a complicated issue). However, it turned out that the introduction of a scalar particle (field), that was subject to a funny potential such that in the ground state (lowest energy) the field values would NOT be 0, could solve several problems. Indeed, the non-zero value of that field, coupled with an interaction term between that field and, say, the electron field, gave a term in the lagrangian which DID respect the symmetries required, but mimicked, at low energies, as a term that was essentially the same as a mass term.
    It also solved another problem: there were 2 theorems in quantum field theory that made life hard. The first one was by 't Hooft, and said that if you want to have a renormalizable (calculable) theory, your interactions need to be described by fields such that the lagrangian obeys, what is called, a gauge symmetry. The problem with a gauge symmetry was that gauge particles have to be massless. People tried to find tricks around it, but Goldstone proved an annoying theorem (Goldstone's theorem), that said that you always have to have massless particles associated with the degrees of freedom of a gauge symmetry, the socalled "goldstone bosons". As these were not observed, that was annoying.
    And then the Higgs mechanism was invented. It gave terms that mimicked mass to the gauge particles, it eliminated the goldstone bosons and gave, by its interactions, a mimicked mass term to the fermions.

  4. Jul 21, 2004 #3
    Patrick gave a wonderful overview of the Higgs mechanism, but the answers to the questions posted don't immediately follow. Here they are:

    1) All Higgs particles DO have the same mass, as they are the quanta of the same Higgs field. Just like all electrons have the same mass.
    2) Neither electrons nor protons have Higgs particles "associated" with them. What happens is that the theory treats all fermions as massless, but the "vacuum" we know has in fact the peculiar Higgs background, which makes it appear that they have mass. All particles, except the photon and gluons, are assumed to interact with the Higgs field, and they develop masses proportional to the strength of this coupling, which for the fermions is arbitrary and independent of other constants (it is not so for the W and Z). The electron's coupling to the Higgs is smaller than the proton's, resulting in a smaller apparent mass for the electron.
    3) There are very few actual Higgs particles in the universe, as they are unstable. There is a difference between the Higgs background (which is non-zero even in the ABSENCE of Higgs particles), and the quanta of the Higgs field, which are excitations of the field above the background. The former does not contribute to mass of the universe (actually this is a tricky topic which deals with physics currently beyond me). It is the latter that are traditional "particles" and have mass, etc, but they are unstable.
    4) The Higgs particles have indeed a very short lifetime. They can decay directly into any pair of fermions, or a pair of W's or Z's. Since the decay constant is proportional to the coupling, the odds of it decaying into heavy particles are greater than for light particles. The lifetime of the Higgs should be pretty small like the t quark. The ATLAS experiment at Cern will try to produce real Higgs particles and observe them via their decays into pairs of Z (with subsequent decays of both Z)or t quarks.
  5. Jul 21, 2004 #4
    Thanks for those answers Zefram and Vanesch - it's not often you get answers as
    clear and detailed as that for such a technical topic.One more question - I've asked elsewhere on this forum: would black holes emit Higgs particles as part of the Hawking radiation?
  6. Dec 13, 2004 #5
    very late answer :smile:
    But yes : BH do emit Higgs bosons in their spectrum. Yet, at such a negligible rate, that if I say "No" you would probably never be able to prove it wrong. :tongue:

    I cannot tell it better than Baez :
  7. Dec 13, 2004 #6


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    "The former does not contribute to mass of the universe (actually this is a tricky topic which deals with physics currently beyond me)"

    This has always bugged me, b/c the whole thing confuses me tremendously.
    I think it confuses everyone incidentally, so im probably in good company, but perhaps someone might be a little less confused than me and help.


    "Mass of the universe" is very problematic even in vanilla GR, it is not well defined. In curved field theoretic spacetime, its even worse. There is no good interpretation of the particle paradigm globally. You cant simply count field modes (incidentally, the vast majority of the mass we see around us is not Higgs generated, but rather quark condensate in nature) and expect to get a good answer.


    Gravitons coupling to the Higgs field. I do not know or have not worked through this in any depth. Gravitons are often taken to be massless (protected by some symmetry), so they won't receive any Higgs corrections. But I am aware of models where this is not the case


    You would think the stress energy tensor of the Einstein-Hilbert action would sense any terms to the right of it (read matter and force fields). I see no reason why the Higgs field is different in that respect than any other field.

    Here's the jist of the problem: The theory of 1 loop truncated gravity is semiclassical in nature. That is treating fields classically and then proceeding to quantize. So here you would make the stress energy tensor a distribution valued operator and run some sort of heroic regularization scheme. What makes gravity so different, is the fact that it knows too much. It feels literally everything. Observable particles in the lab from other forces always sense energy differences. That is, we don't care if the vacuum energy is infinite, we can always subtract an equally large number to get a nice renormalized zero point answer. Backgrounds can be removed in the standard model, but not in quantum gravity, precisely b/c energy is a source of gravity and will bring about the fundamental geometry changes we are trying to study. So one wonders why the Higgs field perse must be excluded in the treatment a priori, and/or even if the entire semiclassical theory is sensible to begin with in this context! I won't even get into the surface term problem.
  8. Dec 16, 2004 #7
    Re: Higginsons boson

    I like what Plank said kind of sums up QM in a neat sound bite; 'anyone who is not shocked by QM hasn't really understood it'

    Let's not obscure conjecture with more conjecture, sinceas far as I'm aware noone has prooved or disproved the existence of a 'Higgs boson', it's kind of a moot point. I personally think there is no boson associated with gravity and have seen several theories that could substantiate this, but that is all they are theories, I will wait and see if the boson exists at all before I make judgements on it's nature, not very QM I know but I gues I'm just one of those people who like to see some proof; what are they called again erm scientists :wink:
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