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Higgs Mechanism

  1. Mar 2, 2008 #1
    Hi there

    Lately, I have been irritated by some general articles about the Higgs Mechanism in newspapers. Those articles suggest that it gives mass to all particles (vector bosons + all fermions).
    However, if I read a textbook I can only extract from the context that it gives mass only to the three vector bosons (for which I have seen calculations which are pretty accurate).
    Last year I also attended a general lecture for the public about HEP where the lecturer said it gives mass to all particles. When asking if I can see some calculations, she said she would send me those by e-mail which I have never received.

    Can someone please clarify this for me?
  2. jcsd
  3. Mar 2, 2008 #2
    The Higgs Mechanism gives mass to the vector bosons. I never heard anything about the other fermions though.

    Hey, i once wrote an intro text on the way the Higgs system works. This text was reviewed by our dear SelfAdjoint. If you wanna check it out, here it is : https://www.physicsforums.com/blogs/marlon-13790/what-the-hell-is-a-higgs-particle-134/

    This text also explains WHEN a particle would acquire mass through interaction with the Higgs field. So, about the other fermions, you could verify YOURSELF if they acquire mass through the Higgs Mechanism.


    Last edited: Mar 2, 2008
  4. Mar 2, 2008 #3


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    Cool explanation.
    Maybe you could give an explanation to my question in, "How were quarks or hydrogen made in the early universe?"
    Can the radiation, which produced the CMB, be produced at this early phase?
    Would the production of the radiation coincide with the acquisition of mass or later?
  5. Mar 2, 2008 #4


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    In the standard model, *all* the particles (inclduing the fermions) acquire their mass through their interaction with the Higgs field. Basically, the Standard model does not contain any explicit mass term for any of the particles. The fermions interact with the Higgs field through so-called Yukawa coupling terms which are interaction terms with the fermion fields multiplied by the Higgs field. When the Higgs field acquire a vacuum expectation value (vev) which is not zero through spontaneous symmetry breaking (SSB), these interaction terms turn into constants multiplying the fermion fields (bilinear in the fermion fields to be more precise) and these terms are mass terms for the fermions.
    Last edited: Mar 2, 2008
  6. Mar 2, 2008 #5
    Some people have been saying on this forum sometimes, and I share this opinion, that indeed the vector bosons aquire mass elegantly in this mechanism, but fermions masses are trivially added by those Yukawa couplings, and there is really nothing interesting happening in this sector. But maybe I miss a point somewhere, for instance I know that I am not aware of all the anomalies cancellation conditions. I would be pretty happy to learn that the Higgs has something interesting to say about fermion masses. Is there anywhere something non-trivial about fermion masses ?
  7. Mar 3, 2008 #6
    Wow, you guys seem to know what you're talking about.
    Can one of you rough-up some explanation regarding the speed of light and the higgs particle ?
    I mean, does gravitation continue to work beyond an event horizon ? Then why black holes, etc... That doesn't seem to make sense to me.
  8. Mar 3, 2008 #7


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    why would you call the gauge-boson mass "elegant" and the fermion mass "trivial"?? In all cases, you write down all the operators allowed by the symmetries, and then you let the Higgs boson condense. That will generate masses for the W,Z bosons and all the fermions except the neutrinos. I don't see where the "elegance" vs "triviality" comes in!
  9. Mar 3, 2008 #8
    There are so many things to say about that, that I don't know where to begin... The subject deserves more attention than the few lines I am going to type right now, and I may not render a service to it, but otherwise I will not be able to answer you at all for now.

    From the start, it is the local gauge invariance which both gives birth to the vector bosons and allows us to bypass the Goldstone theorem. So in the very beginning, the vector bosons appear in the covariant derivative, as connection, of the scalar Higgs field, already coupled together from symmetry principles. Then we proceed to fixing the vacuum, and the Weinberg angle which gives you the ratio of the masses of the bosons appears also in the universal coupling constants, and we gain a genuine experimental test. Considering the situation we were in before introducing this mechanism, it seems there is tremendous improvement. In fact, without this all construction, the mere term "electroweak sector" does not fully make sens. I am unaware of anybody claiming there is no beauty in the procedure.

    But what about fermions ? We merely form a scalar term with them, multiply by the Yukawa coupling and the vacuum expectation value of the Higgs, and that's it. So what ? The Yukawa coupling term is as good in arbitrariness as a mass term. We only saved the good old gauge principle because we can start from massless particle, but to say the least, the beauty of the procedure in the fermoin sector is not so obvious to me.

    Then, as I mentionned before, I think there are anomaly cancellations on top of that, which I am not familiar with, and they may well provide at least one non-trivial relation between the Yukawa couplings, which I may very well have forgotten since kindergarden :smile:
  10. Mar 3, 2008 #9
    In some theories the gauge bosons acquire mass when the symmetry is spontaneously broken (Higgs mechanism) whereas the fermions acquire mass at a higher energy scale as a result of some explicit symmetry breaking.
  11. Mar 4, 2008 #10


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    But the beauty of the Yukawa terms comes from the fact that they are allowed. As blechamn said:
    Instead of saying: why should the Yukawa terms be there?, I think one should turn the question around and ask: why should they not be there?
    They are allowed by renormalization and gauge invariance, and since all other allowed terms are part of the Standard Model Lagrangian, wouldn't it be strange to just remove the Yukawa terms?

    Also note that explicit massterms for fermions would be allowed by gauge invariance and renormalization if it wasn't for the fact that left and right handed fermions transformed in different ways under SU(2).
  12. Mar 4, 2008 #11


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    To humanino: I'm sorry, but I'm not really impressed by this argument. As I said, and EL reiterated, these operators are allowed by the symmetries, so they really should be there! it is true that they will not be generated by quantum corrections since there is a chiral symmetry that forbids that. However, why can't I turn your argument around and say: hey, WHY should there be a Higgs at all? You say: well, the gauge bosons have to be heavy, as we know from experiment. And I say: you're right, and SO DO THE FERMIONS! You say that the gauge symmetry protects the W/Z bosons from getting mass without a higgs, and I say: you're right, SAME WITH THE FERMIONS!!

    I just don't see why you are so impressed with the gauge sector and not the Yukawas. The Yukawa sector is not arbitrary - it's everything that we can write down. Then you perform all your field redefinitions and Lo! you discover 6 quark masses, three lepton masses, 3 CKM angles and a CP-violating phase, all neat and in line with experiment. Everything comes out for free! And you aren't impressed by this?!
  13. Mar 4, 2008 #12


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    I'm not sure what you're referring to here. Anomaly cancellation occurs because of the structure of the fermion generations and their gauge quantum numbers. It has nothing to do with the Higgs boson. Anomaly cancellation would occur even if all the Yukawas were set to zero.

    You might be thinking of SUSY models, where there is a HIGGSINO that contributes to the anomalies and requires the presence of TWO Higgs doublets to cancel. But that's a totally different issue.
  14. Mar 4, 2008 #13
    It is not as if I tried, or even cared, to impress you. Also, not that I am impressed by the way gauge bosons acquire mass in the SM. I am just stating that there is a difference in the way it occurs for them and for fermions. Note that I am nobody to state that, I am not here on PF to participate to agressive discussions, and I also do not intend to lecture you, supposedely theoretician, by using authority arguments, and quoting excerpt from textbooks and/or major articles. The issue might be just that we don't have the same mathematical sensivity. I feel, and I am not the only one, that there is a substential esthetical gap between the two sectors. Maybe we just don't have the same esthetical tastes, and discussing about that here is pointless.

    All right, so you agree with me at least on one point. We won't get anything non-trivial from anomaly cancellation.
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