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:

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

 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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