Before I head out on holiday, I also wanted to post one more item:
In equation (11.8) of my earlier post at:
I showed the matrix inverse for mesons based on the values of S=2 and mu=0 using the parameters of the theory developed in that work (which is based on the post I made a few hours ago).
I finished a detailed calculation of the predicted meson masses as a fraction of “.5vg” and put them in ascending order, in the following one-page listing:
This is the type of theoretical result that we need to try to fit to experimental meson masses. That is, this is where the “rubber meets the road.”
In this regard, I point that there are good reasons from the underlying theory to compare and take the ratios of numbers in the above with the 1+/-i factors, and to consider the SU(3) vector to be (uds) from the old quark flavor models (as opposed to the (RGB) of color).
One of these ratios is that of what is the 4,5 mass matrix element to the 1,2 element:
and this should be related to the ratio of the meson K^0=d s-bar to pi^0=d d-bar. That experimental ratio is, in fact:
K^0/pi^0 = 497.614 MeV / 134.9766 MeV = 3.6867
This is *very* close (they differ by 1.5 parts per thousand!), and could be an experimental validation of the whole theory, since the only thing not accounted for theoretically are QED corrections!
Another ratio of interest is:
This is because the experimental pi^+/- to pi^0 ratio is:
pi^+/- / pi^0 = 139.5701 MeV / 134.9766 MeV = 1.0340
This also is rather tantalizing, and is off by just under 2 parts per thousand!
Still trying to figure out the whole fit, but I’ll leave you all with that for now.
Happy new year!