should the Z0 decay at the same rate that the neutral pion?

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.

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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You can download the table for this plot from pdg, here pdg.lbl.gov/2014/html/computer_read.html – arivero Aug 27 at 19:15
– arivero Aug 30 at 2:27