Proof of the Exact Up and Down Quark Masses from the Pion Mass-Differential

By: Sean Sheeter
Submitted: 2008-06-16 10:50:31
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For a number of years now the Particle Data Group (pdg.lbl.gov) has listed the measured mass difference between the charged and neutral pions as being equal to 4.5936 (with an experimental uncertainty = .0005) MeV. While this mass-difference is attributed to the added electric component of the charged state, one theoretically can equivalently derive the mass of the neutral pion by adding an up quark mass m(u) to the charged pion mass (~139.57 MeV) and subsequently subtracting a down quark mass m(d). But just as a quark’s mass can’t be individually measured directly, one can’t in any way infer the down or up quark mass from this differential, though it again must exactly correspond to this measurable difference between the charged and neutral pion.

Which somewhat naively might seem to preclude knowing the mass of either an up or down quark per se. However, the mass differential basically remains an independent issue, as the up and down quark masses are respectively derived from two different fine-structured sets of equations. But we’re certainly free to give the reader a tangible value for, say, the down mass, where m(d) = 7.763258 MeV. While we could go on to just as directly give the up mass, we’ll instead let you compute the up from the calculatedd-u mass differential

m(d) - m(u) = 4.593453 MeV = (pi)± - (pi)o

= [m(u+2d)o - m(2d+u)+] = {m(d+d)0 - m(u+d)± = m(u+d)± - m(u+u)0}

These equations and value constitutes the first, and one of the strongest, empirical and theoretic proofs I encountered after initially deriving the whole spectrum of similarly precise quark masses within a couple of weeks of solving the central problem of a fully dimensionless mapping of physics. For comparing the measured PDG value of 4.5936 MeV with the derived d-u quark mass differential of 4.593453 MeV differs my a mere .000147 MeV: clearly well within the bounds of the .0005 MeV experimental uncertainty - an empirical proof of no small order. Likewise, inspection of the lower set of equivalences give further theoretical support to the uppermost equations - where the square-bracketed relation on the bottom left refers to the quark content of the neutron minus that of the proton, while the lowermost parenthetical bracket on the right represents the differences between the respective quark contents of the charged and neutral pi mesons per se – pions mediating quark transformations between nucleon matter being the, or at least amongst, the most important processes in physics.

Adding to this significance is the fact that though direct measurement of individual quarks is impossible, they clearly are hardly incalculable, but even more precisely so than even the mass differential between pions themselves! And although perhaps more spectacular “pudding proofs” employing much heavier particle states exist that are open to similar empirical and theoretic confirmation (see second link in resource box), I still consider this the "Best Proof in Theory or ‘Empiric Pudding." Yet the mass-values of the quarks themselves are incidental to empirical confirmation or theory in either proof; where here the d-u or pion mass-differential suffices. Likewise, the education forum of 241Mumbers would be ill-served by giving away more precise masses other than for the two most important quarks since such values alone again gives one little information concerning its calculation for any individual particle, or an appreciation of the entire unified dimensionless system which underlies all these formulations.

In any case, the above equations and values are proof positive of what can be called ‘Kaluza-Klein Mumbers’ aren’t constrained by such obvious elusiveness; and positive proof, both from and that, standard theory and experiment is incapable of giving an exacting prediction for either quark at the core of the basic baryon matter in a neutron and proton - lacking an explanation for baryogenesis as well.

Sean Sheeter is an independent theorist, logician and author of "241-Mumbers: The Definitive Data for Fundamental Physics and Cosmology." This essay concerns the most useful of the four examples of the Sample Data and Proofs at http://www.241mumbers.com/page2.html, which also contains the related proof for strange and bottom quarks as further discussed at http://www.isnare.com/?aid=184377&ma=members&ca=Education.

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