The Pionic Proof Of The Precise Down-Up Quark Mass Differential

Summary: For a number of years now the Particle Data Group (http://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 subt...

For a number of years now the Particle Data Group (http://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 it follows that 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 calculated d-u mass differential m(d) - m(u) = 4.593453 MeV = (pi)