In the old theory of the strong nuclear force, this force is transmitted by massive pions. Just as the weak nuclear force is transmitted by massive W- and Z- particles. Is it possible to develop a Higgs mechanism for the old view on the strong force, and does this (if so) imply that the weak nuclear force is maybe a residual force, as the old nuclear force is?
In the light of the Higgs mechanism the following relation (prediction of parameters) exists (I can't remember the source, but I wrote it down in a big notebook):
$ W^2 (1-\frac{W^2} {Z^2} )=\frac{\pi\sqrt2\alpha} { G_f} $
in which W and Z are the masses of the W- and Z-particles (see here), $\alpha$ is the fine structure constant ($\frac {1} {137}$), and $G_f$ is the relative coupling strength of the weak force if we set the coupling strength of the strong force equal to 1.
Now there is a somewhat similar relation for the masses of the pions, which I found after playing with these masses, in the light of the formula above:
$(1-\frac {\pi^0} {\pi^{+/-}})=\frac{\pi\sqrt2\alpha} {G_s}=\pi\sqrt2\alpha=0.032$, where the ${\pi}^0$ and the ${{\pi}^{+/-}}$ represent the masses of the pions (see here), $\alpha$ again the fine structure constant and $G_s$ the strength of the strong nuclear force , which is equal to 1. tea Is it a coincidence that this second expression, involving the masses of the $\pi$'s, instead of the masses of the $W$ and $Z$, is equal to $\pi\sqrt2\alpha=0.032$? If not, does this imply that the weak force is a residue force, just as the old strong force was one a long time ago?
