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Is the list of particles complete and unique?

  1. Sep 25, 2012 #1
    I'm wondering if the list of particles in the SM is both complete and unique? Or could we find other particles and interactions that could also be included in the SM? Phyisicists sometimes invent fields and particles to account for Dark matter and inflation, etc. But that introduces particles not in the SM. And so my question as to whether the SM is complete and unique. Would any new particle imply a new symmetry besides the U(1)SU(2)SU(3)?Thanks.
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  3. Sep 25, 2012 #2


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    The gauge group specifies the interactions and its representations give the particle content of the theory. If you add particles to the SM, you must modify the symmetries. For example, dark matter might be a particle included in the supersymmetric extension of the SM.
  4. Sep 26, 2012 #3
    So what I'm understanding is that all the particles of the SM are specified by the U(1)SU(2)SU(3) symmetry, and those symmetries are completely represented by the particles of the SM. There could be no new particles without adding to that symmetry, and any new symmetry would add to the types of particles that should be discovered. Is that right?
  5. Sep 26, 2012 #4


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    I think (looking for confirmation from this group) that right-handed (aka "sterile") neutrinos can still be added to the SM without adding new symmetries. Several groups are suggesting sterile neutrinos as dark matter candidates.
  6. Sep 26, 2012 #5
    Are you talking about the difference between the types of particles determined by the symmetries and the coupling constants (such as the mass and charge) that determine the strength of the interactions? Does each type of particle (determined by the symmetries) have only one coupling constant? Or can there be two particles with the same symmetries but different coupling constants?
  7. Sep 26, 2012 #6
    The list of particles is probably not complete; there are likely new states associated with quantum gravity. The set of particles is certainly not unique. I can add a fourth generation without spoiling any symmetries; it's just that we haven't seen any such thing yet.
  8. Sep 27, 2012 #7
    For example, is the Higg boson a particle predicted by the U(1)SU(2)SU(3) symmetry?
  9. Oct 1, 2012 #8
    By itself, no, but if you tell me that the SU(2) x U(1) is broken to a U(1) subgroup (as it is in our universe), then that tells you that there must be something serving as a higgs field doing the breaking. However, it doesn't tell you that that Higgs field is elementary.

    Also, note that when we say the gauge group is SU(3)xSU(2)xU(1), realize that we don't mean that that's the absolute end all-be all gauge symmetry of the universe. It's the gauge symmetry of the effective field theory living below 1 TeV. It remains at higher energies, though perhaps as a subgroup of some bigger symmetry group, like SU(5) or SO(10). The jury is still out on that question.
  10. Oct 1, 2012 #9
    Thank you. That helps a lot. I guess what I'm trying to get at is whether given U(1)SU(2)SU(3), and the quantum mechanical formulism, is that enough information to identify all the fields and particles in the Standard Model and nothing else, well.. except maybe the Higgs boson?

    The reason I ask is because some people think that the underlying math that gives rise to the U(1)SU(2)SU(3) symmetry is the existence of the complex numbers, the quaternions, and the octonions. So I wonder if the complex, quaternions, and octonions were explained from a more fundamental basis, would the SM be derivable on that basis? Thanks.
    Last edited: Oct 1, 2012
  11. Oct 4, 2012 #10
    I'm not really sure what you mean; sure, you can associate SU(2) with unit quaternions and U(1) with unit complex numbers, but you can't associate any group structure to unit octonions because they're not even associative. They do have an automorphism group of G2, but that's about as close to SU(3) as you're gonna get. Regardless, no, once you have the group structure, you've fixed the gauge bosons of your theory, but you have yet to tell me the matter content.
  12. Oct 5, 2012 #11


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    There have been indeed ideas to relate the known particles to octonions in a rather indirect way, namely via the (largest finite-dimensional) exceptional Lie group E(8) which can be "understood" as a special symmetry structure on the "octo-octonionic projective plane" (I recommend John Baez homepage).

    To understand E(8) one would start with its algebra e(8) and the space E(8) acts on. But that doesn't help b/c the adjoint rep. of e(8) which could serve as a starting point is identical with its fundamental rep., therefore in a sense we are trying to describe E(8) in terms of E(8) which isn't a big step forward ;-)


    Afaik as I know all attempts to derive the SM from octonions failed.


    Some time ago Garrett was reading posts and private messages here the "beyond forum", so perhaps you are able to ask hom directly regarding the status of his research.
  13. Oct 5, 2012 #12
    Considering the multiverse interpretation of quantum mechanics, I wouldn't expect the SM to be holistically unique, but let's not delve there (for now). If there were more than one universe, there would undeniably be different sets laws governing reality- each of them independently tinkering along, but in coexistence with a bevy of differentiated others. Suggesting that they are all the same is impossibly implausible - they must be distinct.

    The current list of particles is theoretically adequate; we cannot know whether it is actually complete or not - the universe is a strange and mysterious place. After all, problem recognition is higher in the ladder of wisdom and innnovative ingenuity than correspondence in resolution. However, I highly doubt scientists have derived even the general knowledge concerning the entire family of various particles since more than 90% of the universe is presently unaccounted for, empirically speaking.

    On the other hand, the SM, although probably not unique/complete, is definitely our best shot at understanding the subatomic domain for now. There are no better alternatives now and, as it seems, for all eternity.
  14. Oct 5, 2012 #13
    Are you saying that the fermions are not accounted for in the U(1)SU(2)SU(3) symmetry? Or are you saying that just the strenght of the interactions between them is not accounted for by this symmetry?
  15. Oct 5, 2012 #14


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    Suppose the gauge bosons are defined (space-time vector fields in the adjoint representation of the gauge group G - well, not really b/c they don't transform as tensors but as connections). Then the construction of the matter content is not uniquely defined:
    1) the matter fields can be bosons or fermions (up to spin 3/2 in SUSY-gauge theories)
    2) they can live in various reprsentations of the gauge group (the SM matter fields live in the fundamental representation, but others are possible; adjoint fermions are studied in various models)
    3) they can come in several copies, the so-called generations of the standard model
  16. Oct 5, 2012 #15
    So I'm hearing that the SM symmetries U(1)SU(2)SU(3) do not uniquely or completely specify the particles of the SM. These symmetries don't specify the spin or mass generations. Is this right? Then what physical effects do these symmetries specify, I wonder?

  17. Oct 6, 2012 #16


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    you don't get these particles from symmetries but from experiment; you observe spin 1/2 leptons, so your model must contain spin 1/2 leptons; you observe spin 1/2 hadrons made of three quarks (three is fixed by SU(3) color), so you have spin 1/2 quarks; you observe three generations of fermions, so there must be three generations in your model(nothing, neither a known symmetry nor anything else, constrains the number of generations); you guess that the Higgs might be a nice way to generate masses (and you observe it) so you add the Higgs (you could add more complex Higgs multiplets as well)
  18. Oct 9, 2012 #17
    The Standard Model has some constraints on particle content, but nothing that fixes it outright.

    It's possible for there to be additional elementary-fermion generations or Higgs multiplets, for instance.

    Fermions with chirality in their gauge interactions, like the elementary fermions, have their gauge-interaction parameters constrained by anomaly cancellation, but I can't think of anything additional at the moment.
  19. Oct 9, 2012 #18


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    that's right, anomaly cancellation basically fixes the relation between different charges of different fermions within one multiplet; that was one reason why everybody believed in the existence of the top quark
  20. Oct 9, 2012 #19
    OK, then what physical properties does the U(1)SU(2)SU(3) symmetry determine in the SM? It's not the mass, nor the charge, nor the spin, not the speed, nor the position, nor the strength of interactions. Then what?

    I understand that with symmetries come conserved "charges". So I suppose that the U(1)SU(2)SU(3) symmetry specifies the existence if the electromagnetic charge and the color charge and the, what is it, the weak force charge. So it tells us what interacts with what. But am I right to say that the SM symmetry does not specify the strength of those charges?
    Last edited: Oct 9, 2012
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