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The original title of the question was "In a composite Higgs..." and so the sub-questions were done around this theme: Should the decay rate of Z0 be related to the decay of the "higgs" composite field it is eating? And, should this composite field, being a pseudoscalar, decay at the same rate of the neutral pion?

But I hope that people will be able then to give at least partial answers and that other explanations could surface. For instance, some sum across all the decays of Z0 could simplify and leave only some QCD-dependent term.

Well, the observation is this: it is a fact, rarely mentioned, that the pseudoscalar neutrals have about the same electroweak decay rate, simply scaled by the cube of its mass. Just as the charged mesons scale by the quintic of its mass, a case which is more popular in textbook exercises. The particle data group provides the table of decay rates and masses for all the particles, and from it I drew this plot time ago. Surely some point has moved slightly by now, but you can see the blue line, cubic, where all the neutrals align to scale, and the green quintic power for the charged particles, whose decay is ruled by the Fermi mass, and then a lot slower than the neutrals.

decay widths against mass, for electroweak decays

You can see how the blue line touches the neutral pion in the left part of the plot and the Z0 in the right part. Yes, the muon and tau are also there, as they also decay via the electroweak interaction.

Current pdg numbers are off two sigma. More precisely we have for Z0: ${\Gamma\over m^3}=$ 2495.2/91187.6^3 = 3.291*10^-12 and for the neutral pion, using only indirect measurement: (6.58211928*10^-22/(8.30*10^-17))/134.9766^3 = 3.225*10^-12. The discrepancy goes up to almost 3 sigmas if we include the only direct measurement of the decay, ATHERTON 1985, but this measure is an outlier and usually discarded; it is also in stress with the theoretical value.

According arxiv:1112.4809v2 the theoretical value of the lifetime of pion, including effects from mixing and chiral symmetry breaking, is 8.1 eV, so that $\Gamma_\pi/m_\pi^3$= 8.1*10^-6/134.9766^3 = 3.29e-12. The theoretical value of $\Gamma_{Z^0}$ is 2495.5 ± 0.9 (pdg review, pg 23), and sp the theoretical reduced decay width does not differ from the experimental measurement. But it is encouraging that the theoretical values are even closer than the experimental ones.

Can this be interpreted as slight evidence of, or arguments for, technicolour or other composite models?

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Your blue line includes the pion, the J/psi, and the Z0. (See figure 2 here.)

In a theory in which the Higgs is actually a ttbar condensate, the spin-0 part of the Z0 is basically a toponium pseudoscalar.

And there is a theorem (Goldstone boson equivalence theorem) which says that under certain circumstances, a massive gauge boson can be approximated by that spin-0 mode. It has even been applied specifically to Z boson decay, see reference 11 here (I have not read those papers).

If the Z0 point on the plot could be identified with the scalar z Goldstone boson, and if that could be identified with a ttbar meson, then you would have a uniform interpretation of the blue line, from left to right.

Therefore I would now interpret this plot as a hint that the Higgs is some kind of top-antitop bound state, and that (following your suggestion) an anomaly-driven virtual decay of a neutral toponium goldstone somehow dominates Z0 decay.

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