# Lab Notes for a Scientific Revolution (Physics)

## December 26, 2008

### S=2, mu=0 Meson Mass Spectrum, and some interesting possible ties to experimental meson data

Before I head out on holiday, I also wanted to post one more item:

In equation (11.8) of my earlier post at:

https://jayryablon.files.wordpress.com/2008/12/su-3-paper-20.pdf

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:

https://jayryablon.files.wordpress.com/2008/12/s2-mu0-mass-spectrum.pdf

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:

.625727090299/.169470755895=3.69220577135

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:

.169470755895/.163577444819=1.03602765089

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!

Jay.

### Finite Amplitudes Without +i\epsilon

To all,

I have now completed a paper at the link below, which summarizes the work I have been doing for the past two months (and in a deeper sense, for much of my adult life) to lay a foundation for understanding and calculating particle masses:

finite-amplitudes-without-i-epsilon

I have also taken the plunge and submitted this for peer review. ;-)?

The abstract is as follows:

By carefully reviewing how the invariant amplitude M is arrived at in the simplest Yang-Mills gauge group SU(2), we show how to arrive at a finite, pole-free amplitudes without having to resort to the “+i$\epsilon$ prescription.”  We first review how gauge boson mass is generated in the SU(2) action via spontaneous symmetry breaking in the standard model, and then carefully consider the formation of finite, on-shell amplitudes, without +i$\epsilon$.

Comments are welcome, and I wish everyone a happy holiday and New Year!

Jay.

## December 11, 2008

### Understanding the QCD Meson Mass Spectrum

Dear Friends:

It has been awhile since I last posted and it is good to be back.

Almost two years ago in the course of my work on Yang Mills, I came across what I believe is an approach by which mass spectrum of the massive mesons of QCD might be understood.  I had what I still believe is the right concept, and many of the pieces, but I could not figure out the right execution of the concept in complete detail.  Over the past year and a half I walked away from this to let the dust settle and to also arrive at a place where the basic principles of quantum field theory were no longer “new” to me but had become somewhat ingrained.  Now, I believe I have found the right way to execute this concept, and the results are intriguing.

In the file linked below, which I will update on a regular basis in the coming days:

I review how mass is known to be generated in SU(2), as a template for considering SU(3) QCD.  I have tried to explain as simply as possible, what I believe to be the origin of QCD meson masses, as well as to lay the foundation for theoretically predicting these.  Keep in mind, finding out how the vector mesons of QCD obtain their non-zero masses, which make the QCD interaction short range despite supposedly-massless gluons, is one aspect of the so-called “mass gap” problem, see point 1) on page 3 of
http://www.claymath.org/millennium/Yang-Mills_Theory/yangmills.pdf at
http://www.claymath.org/millennium/Yang-Mills_Theory/.

Then, I extend this development, in detail, to SU(3).

Several interesting results are already here:

1)  This approach neatly solves the problem of propagator poles (infinities) in a manner which I believe has not heretofore been discovered.  Goodbye to the +i\eta prescription, off mass-shell particles, and other inelegant dodges to achieve a finite propagator.

2) This approach may solve the confinement and the mass gap problems simultaneously.  It is important to understand that electroweak SU(2)xU(1) is a special case in which the gauge bosons are synonymous with the observed vector mesons, but that in SU(3) and higher order theories they are not.  The gauge bosons aka gluons, which show up in the Lagrangian, are not observed.  What is observed are the vector mesons which pass through to the denominator of the propagator in the invariant amplitude.

3) There emerges is a quantum number that is restricted to three discrete values, and depending on which value of chosen, all the meson masses are scaled up or down on a wholesale basis.  I believe that this may resolve the problem of generation replication.

I expect to be churning out mass calculations in the next day or two.  You may wish to check out the meson mass tables at http://pdg.lbl.gov/2008/tables/rpp2008-qtab-mesons.pdf, because that table contains the data which I am going to try to fit to equation (6.1), via (6.5).

Hope you enjoy!

Jay.

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