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MadMax
MadMax
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Yes you are right that for electrons or muons, their Yukawa coupling is certainly NOT $O(1)$. You can have two interpretations of Mark Thomson's remark:

  1. The ratio of electron mass vs top quark mass is around $10^{-5}$. It is certainly NOT $O(1)$, but it is not as bad as $10^{-20}$ when comparing fermion mass with Planck mass. So Mark Thomson means that the Yukawa couplings isare roughly $O(1)$.
  2. Mark Thomson actually means that the top Yukawa coupling is naturally $O(1)$, while the other Yukawa coupling are NOT natural, but he does not want to get into much speculations in his book. As the other answer pointed out, in the hypothetical top-condensation model, the top quark-antiquark pair condensates and plays the role of Higgs field. In this case, top quark mass is of order of the electroweak scale. So the top Yukawa coupling is naturally $O(1)$. That said, the original top-condensation model does not address the problem of why other fermion mass is much smaller than top mass. Note that there are some extensions of top-condensation model which attempted to address this issue.

Yes you are right that for electrons or muons, their Yukawa coupling is certainly NOT $O(1)$. You can have two interpretations of Mark Thomson's remark:

  1. The ratio of electron mass vs top quark mass is around $10^{-5}$. It is certainly NOT $O(1)$, but it is not as bad as $10^{-20}$ when comparing fermion mass with Planck mass. So Mark Thomson means that the Yukawa couplings is roughly $O(1)$.
  2. Mark Thomson actually means that the top Yukawa coupling is naturally $O(1)$, while the other Yukawa coupling are NOT natural, but he does not want to get into much speculations in his book. As the other answer pointed out, in the hypothetical top-condensation model, the top quark-antiquark pair condensates and plays the role of Higgs field. In this case, top quark mass is of order of the electroweak scale. So the top Yukawa coupling is naturally $O(1)$. That said, the original top-condensation model does not address the problem of why other fermion mass is much smaller than top mass. Note that there are some extensions of top-condensation model which attempted to address this issue.

Yes you are right that for electrons or muons, their Yukawa coupling is certainly NOT $O(1)$. You can have two interpretations of Mark Thomson's remark:

  1. The ratio of electron mass vs top quark mass is around $10^{-5}$. It is certainly NOT $O(1)$, but it is not as bad as $10^{-20}$ when comparing fermion mass with Planck mass. So Mark Thomson means that the Yukawa couplings are roughly $O(1)$.
  2. Mark Thomson actually means that the top Yukawa coupling is naturally $O(1)$, while the other Yukawa coupling are NOT natural, but he does not want to get into much speculations in his book. As the other answer pointed out, in the hypothetical top-condensation model, the top quark-antiquark pair condensates and plays the role of Higgs field. In this case, top quark mass is of order of the electroweak scale. So the top Yukawa coupling is naturally $O(1)$. That said, the original top-condensation model does not address the problem of why other fermion mass is much smaller than top mass. Note that there are some extensions of top-condensation model which attempted to address this issue.
Source Link
MadMax
MadMax
  • 4.5k
  • 11
  • 34

Yes you are right that for electrons or muons, their Yukawa coupling is certainly NOT $O(1)$. You can have two interpretations of Mark Thomson's remark:

  1. The ratio of electron mass vs top quark mass is around $10^{-5}$. It is certainly NOT $O(1)$, but it is not as bad as $10^{-20}$ when comparing fermion mass with Planck mass. So Mark Thomson means that the Yukawa couplings is roughly $O(1)$.
  2. Mark Thomson actually means that the top Yukawa coupling is naturally $O(1)$, while the other Yukawa coupling are NOT natural, but he does not want to get into much speculations in his book. As the other answer pointed out, in the hypothetical top-condensation model, the top quark-antiquark pair condensates and plays the role of Higgs field. In this case, top quark mass is of order of the electroweak scale. So the top Yukawa coupling is naturally $O(1)$. That said, the original top-condensation model does not address the problem of why other fermion mass is much smaller than top mass. Note that there are some extensions of top-condensation model which attempted to address this issue.