A Defect That Died: The Proton Radius, Priced in Both Directions

For ten years the proton had two sizes, and the two sizes would not speak to each other. Measured with a muon in place of the electron, the proton's root-mean-square charge radius came out at 0.84087 femtometres, give or take 0.00039 (the combined muonic value, Antognini and collaborators, 2013, confirming the first muonic result of 2010). Measured the old way, with electrons — in hydrogen spectra and in electron scattering, gathered in the CODATA-2014 recommended value — it came out at 0.8751 femtometres, give or take 0.0061. The gap is 0.0342 femtometres, just under four percent of the radius, and five point six times the two error bars combined. A defect that size, in a number that basic, priced a decade of doors: forces that touch muons and not electrons, errors in the best theory we have, a Rydberg constant quietly wrong. Then the electron side rebuilt its own measurements, and the defect died. A windowless-target scattering experiment at Jefferson Lab (PRad, 2019) read 0.831 femtometres; a direct Lamb-shift measurement in ordinary hydrogen (Bezginov and collaborators, 2019) read 0.833; an earlier hydrogen measurement (Beyer and collaborators, 2017) read 0.8335; and CODATA itself moved, to 0.8414(19) femtometres in 2018 and 0.84075(64) in 2022 — each within a fraction of a standard deviation of the muonic value it had stood five point six away from. This paper prices the defect in both directions: what the decade of disagreement cost, in doors opened and effort spent, and what its death certifies — that the muonic measurement was right, that the missing lines were in the electron side's older budgets and averages, and that no new force was needed. It also prints the scatter that survives at its true size: the modern electron-side values still spread across about 0.017 femtometres, and one careful Paris measurement of 2018 still reads large. The defect is dead. The last word on the radius, at the muonic precision, has not been spoken by the electron side, and I do not pretend otherwise. Grade: DEFECT DIED — CONVERGENCE ON THE SMALL RADIUS; RESIDUAL SCATTER PRICED, NOT HIDDEN. This paper stands outside my work on the vacuum catastrophe; it draws nothing from that work and repairs nothing in it, and it touches no claim of that program.