The Pionic Proof Of The Precise Down-Up Quark Mass Differential
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The Pionic Proof of the Down-Up Quark Mass Differential
Summary
The Particle Data Group (http://pdg.lbl.gov) has long noted the mass difference between charged and neutral pions as 4.5936 MeV, with an uncertainty of 0.0005 MeV. Traditionally, this difference is linked to the electric component of the charged state. However, one can derive the neutral pions’ mass by adding the up quark mass to the charged pion's mass and then subtracting the down quark mass.
Article
For many years, the Particle Data Group has recorded the mass difference between charged and neutral pions as 4.5936 MeV with an experimental uncertainty of 0.0005 MeV. While this difference is attributed to the electric component of the charged state, theoretically, it is possible to derive the neutral pion's mass by adding the mass of an up quark \( m(u) \) to the charged pion mass (approximately 139.57 MeV) and subsequently subtracting a down quark mass \( m(d) \).
Since quark masses cannot be directly measured, one cannot infer individual down or up quark masses from this differential. However, it must exactly match the measured difference between charged and neutral pions.
The mass differential is handled independently as up and down quark masses are derived from different sets of equations. Nonetheless, for illustration, the down quark mass \( m(d) \) can be assigned a value of 7.763258 MeV. To find the up quark mass, one can calculate it from the d-u mass differential:
\[ m(d) - m(u) = 4.593453 \text{ MeV} \]
This remarkably close match between the measured PDG value of 4.5936 MeV and the derived differential of 4.593453 MeV offers significant empirical proof. Further, these equations provide theoretical support for the understanding of quark content in subatomic particles, highlighting the importance of pions in mediating quark transformations.
Despite the impossibility of direct quark measurement, these theoretical calculations are more precise than the pion mass differential itself. More significant proofs with heavier particles exist (see http://www.isnare.com/?aid=190170&ca=Education), yet this remains a compelling demonstration.
These findings suggest that Kaluza-Klein numbers provide clarity beyond what traditional theory has offered regarding quark masses in neutron and proton cores, essential for understanding baryogenesis.
In summary, the derived equations and values not only empirically support theoretical predictions but also bridge gaps in our understanding of fundamental baryon matter.
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