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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?

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    $\begingroup$ The sigma meson (not to be confused with Sigma baryon, a different particle) is sometimes regarded as the Higgs boson of the strong force. $\endgroup$ – Mitchell Porter Jan 23 '17 at 21:38
  • $\begingroup$ The usual nomenclature is "the strong nuclear force" or "the residual strong force". $\endgroup$ – dmckee Jan 23 '17 at 22:52
  • $\begingroup$ Can you reformulate the question? Why Develop a Higgs mechanism for the residual strong force? Through what formerly gauge boson? The answer is negative. And why are you unhappy with Fermi's effective force underlain by the well-understood Higgs mechanism of the weak interactions? Do you have any reference or evidence or understanding for the odd symmetry breaking formulas you adduce, if not introduce? $\endgroup$ – Cosmas Zachos Jan 23 '17 at 22:58
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    $\begingroup$ A note on your numerological caper. The first formula is a garbled version of the standard model formula: if you moved the W² of the lhside to the denominator of the rhside, you'd get the dimensionless version of the Fermi constant there, so the left hand side would be the square of the sine of the Weinberg angle, so ~ 0.23. That's very different from your astrological second formula, whose origins is electromagnetic, cf Donoghue & Perez. What are you up to? $\endgroup$ – Cosmas Zachos Jan 23 '17 at 23:57
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Similarities between strong and weak forces are interesting but usually the analogy is pushed in the other direction, i.e. the technicolor theory in which the Higgs is actually a "technipion" from a new strong force.

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