The Proton Radius Puzzle Solved

The electron-proton scattering experiment by the PRad (proton radius) team at Jefferson Lab measured the root mean square (rms) charge radius of the proton as rp = 0.831 ± 0.007(stat) ± 0.012(syst) fm. Assuming all of the electric charge in the proton is packed into a single pointlike (elementary) charge and applying the ring current model to a proton, one gets a radius for the circular current that is equal to a = 2μ/qc = 0.58736 fm. Using CODATA values for all variables and constants in this equation, and applying a √2 form factor to, somehow, account for the envelope of the magnetic field around the ring current, yields an electric charge radius of 0.8065 fm. The difference between the PRad point estimate and this theoretical value is 0.00035 fm, which represents 5% of the standard error (0.007 fm) of PRad’s point estimate. It is, therefore, hard to argue this is a mere coincidence. We can also calculate a proton radius based on the idea of a strong charge. This radius corresponds to the range parameter in Yukawa’s equation and is equal to a = ħ/mpc = 0.2103, which is about 1/4 of the PRad point estimate. This 1/4 factor is, obviously, far more mysterious, and the difference between 0.831 and this strong charge radius multiplied by 4 is 0.01 fm, which is about 50% of the combined statistical and systematic error (0.007 + 0.012 = 0.019). We, therefore, think that, while being somewhat less precise, the 1/4 factor cannot be a coincidence. We, therefore, feel the new measurement of the proton radius by JLAB’s PRad team may lend credibility to attempts to extend the Zitterbewegung hypothesis from electrons to also include protons and other elementary particles. In contrast, the measurement is hard to fit into a model of oscillating quarks that have partial charge only.