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I Is mass of top quark based solely on the Higgs field?

  1. Nov 20, 2016 #1
    the top quark is the heaviest quark. the current theory is its invariant mass is based solely on its interactions with the higgs field. in absence of the higgs field, fermions, quarks and leptons are massless, and in the presence of the higgs field, they acquire mass.

    the reason the top quark is the heaviest quark is that it couples to the higgs field more strongly than an electron or up or down quark.

    is there any theory that explains why a top quark interacts with the higgs more strongly than up or down quark, or electron?

    is there any research into the possibility that fundamental particles can gain additional mass, through say the color force or electromagnetic force?

    i.e the reason the top quark quark is so massive is it couples to both the higgs and color force and electromagnetic force where as electrons do not couple to the color force.
     
  2. jcsd
  3. Nov 21, 2016 #2

    arivero

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    "more strongly" is misleading. It interacts with coupling 1.00, and such (I answer you, not existent) theory should explain that.
     
  4. Nov 21, 2016 #3

    ohwilleke

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    Short Answer In The Standard Model

    The Standard Model does not explain why the top quark has the mass that it does other than to state that it is a function of the Higgs boson Yukawa coupling to the top quark. It does suggest some relationships between top quark mass, Higgs boson mass and W boson mass that are sometimes used in making global fits of those three values.

    Conjectures About First Generation Fermion Masses

    There have been speculations along these lines (some in published paper and unpublished preprints by professional physicists), but there is no consensus explanation. The gist of these is that (1) the electron mass roughly corresponds to the self-interact of its electric field with itself, (2) the neutrinos which interact via the weak force but lack electric charge have a mass roughly equal in order of magnitude to the ratio of the strength of the electromagnetic coupling constant to the weak force coupling constant, and (3) the first generation quarks have masses of the same order of magnitude as the electron, suggesting that the color force doesn't impact their rest mass.

    Now, the trouble is that strong force, weak force and electric force interactions of each of the first generation fermions is exactly identical to that of their respective second and third generation fermions, so self-interactions can't explain why these higher generation particles are heavier.

    These theories were very popular until the second and third generation of particles were discovered, but lost their gleam at that point, until the discovery of the order of magnitude of the neutrino masses was discovered, when they gained some renewed interest.

    Koide's Rule and Its Extensions

    Koide discovered an empirical relationship between the electron, muon and tau charged lepton masses that continues to hold to high precision decades after it was proposed despite the fact that much more accurate measurements have now been made of those masses than were available to him at the time, in a published and widely known result which he had made several attempts to explain.

    There are near "Koide triples" extending the Koide relationship for charged leptons that can fit some sets of three quark masses reasonable well (also documented in published work). It is possible to get an even better fit by considering all three opposite type quarks that can couple to a quark in question via the W boson. But, while there have been a variety of theories advanced to explain why these relationships hold in published papers, none of them has secured much support among physicists. To the extent that there is any merit to this, the top mass has the mass that it does because if you follow the chain of Koide triples from lighter quarks to it, this is the result that you get (there is even a 3-1 relationship between the charged lepton triple and one of the corresponding quark triples). Follow this line of reasoning to the end and you get a mass matrix that is a decent approximation of the one we see in real life (including the top quark mass) that can be derived from the electron and muons masses, and a handful of other rules for determining extended Koide triples.

    There is also an extension of Koide's rule, modifying it a bit, that seeks to explain the relative neutrino masses.

    Fundamental Particle Masses And The Higgs Vev

    It is also the case that the sum of the square of the fundamental fermion masses is very close to the sum of the square of the fundamental boson masses and that those two sums together are almost exactly equal to the square of the Higgs vacuum expectation value (there are also papers about this fact).

    There is no real solid theoretical explanation for the reason that this is the case either.

    But, if that relationship does have some valid theoretical basis, then the top quark has the mass it does, because that is the mass necessary to balance out the masses of the other fundamental fermions (to the extent that the sum of the square of fermion masses and the sum of the boson masses), or (to the extent that only the total relationship to the Higgs vev is true) to the masses of all of the other fundamental particles.

    Other Theories

    This list isn't an exclusive roundup of theories that have been plausibly advanced to explain the values of these constants (e.g. SUSY theories take a completely different approach).

    The mix of masses within the fermion mass matrix is sometimes called its "texture" and a search for "texture zeros" will reveal many theoretical efforts on this front.

    There are other approaches as well. For example, the Higgs boson mass itself has been theorized to be determinable by assuming that it is zero at some high energy GUT scale necessary to assure that the universe is stable or at least metastable and running the mass with renormalization beta functions to a pole mass (this was one of the ways that it was predicted) and if the Higgs boson sets the mass scale for the rest of the fundamental particles, that could play a part as well.

    Definitional Issues

    It also isn't theoretically clear which definition of mass is fundamental and ties into the scheme that sets these masses in some "within the Standard Model" deeper theory. In lots of circumstances, "pole masses" for rest mass seem fundamental, but this definition can become problematic when applied to the light quarks where perturbative QCD methods used in connection with determining the heavy quark masses don't apply and different schemes must be used.

    Also, any consideration of source of the fermion masses is equivalent to a consideration of the reason behind the Higgs bosons couplings in the Standard Model.

    References

    There are references for these points, many at prior posts at PF, that I'll try to update and include later.
     
    Last edited: Nov 21, 2016
  5. Nov 21, 2016 #4

    ohwilleke

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    Quite possibly and indeed probably, "almost 1" rather than exactly 1. There are theoretically important reasons to think it might be on the order of 0.99996 (which is the value it would have if the coupling for all of the fundamental fermions summed to exactly 1).
     
  6. Nov 21, 2016 #5

    arivero

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    Another way to look at it is to ask: what symmetry does protect the other quarks and leptons, so that they get a mass almost zero relative to the Higgs scale?

    It is the most straightforward way of looking at the top, along the lines formulated by 't Hooft: if some adimensional couplings of a theory (the yukawas in this case) have a value near zero, it is to be expected that in the limit where they are zero some slightly broken theory is restored.

    Regretablely, in this case the symmetry crosses the generation pattern, as it only saves one of the quarks of the third generation. So nobody, as far as I can tell, has provided arguments about what it could be. Note that there is not such problem for other mass protection, the one forbidding particles to get a Majorana mass. In such case the three unprotected neutrinos are distributed evenly across generations.

    For the speculative part: One could consider that the symmetry protects 84 degres of freedom, the ones of the almost massless quarks and leptons, and then look for symmetry groups having some 84, 42 or 21 irreducible representation. Interestingly the count of unprotected degrees of freedom is the same for the case of Majorana mass.

    For the even more speculative part: there is a 11D object having 84 degrees of freedom, but bosonic ones: the antisymmetric tensor of three components, pretty common in sugra and supermembrane theories. Interestingly in these theories there is not one but two 84-objects, one dual of the other, acting as sources for the 2-brane and the 5-brane. Regrettably the naturality of the yukawas seems a question to be answered at electroweak scale, not at GUT nor Planck scale.
     
    Last edited: Nov 21, 2016
  7. Nov 22, 2016 #6
    if misleading what is the reason that the mass of the top quark is higher than up or down quarks or electrons?
     
  8. Nov 22, 2016 #7

    ChrisVer

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  9. Nov 24, 2016 #8
    At the end of the day, this is all speculation.

    In the standard model, the Higgs mechanism is responsible for the top quark mass, and a yukawa coupling close to one is actually natural.

    The fact that the other yukawa couplings are so small, and have a hierarchical structure is strange.

    Of course we know there should be physics beyond the sm. but why should it have something to do with the top mass?
     
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