Yukawa Couplings of Fermions to Higgs Field

Question

Context: The Yukawa couplings of fermions to the Higgs field are given by $$g_{f} = \sqrt{2}\frac{m_{f}}{v}.$$

Question: In his book "Modern Particle Physics", Mark Thomson writes on page 486:

Interestingly, for the top quark with $m_{t}\sim 173.5 \pm 1.0$ GeV, the Yukawa coupling is almost unity. Whilst this may be a coincidence, it is perhaps natural that the Yukawa couplings of the fermions are $\mathcal O(1)$.

I don't understand this last statement. Excluding neutrinos (whose small mass is really exceptional), if we just take electrons or muons, their Yukawa coupling is certainly NOT $\mathcal O(1)$..

Answer 1

There is a theory that links the Higgs to the top quark mass and suggests that the Higgs is a top quark condensate.

Answer 2

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.