Theory 002/Physics & Matter /Hadronic physics
The Proton Radius Is Two Numbers
Two measurements, one number, a decade of argument. They may not be measuring the same thing.
The proton charge radius and the proton stiffness radius are different quantities that experiments weight differently, so the discrepancy between electron and muon measurements reflects what each method probes rather than an error in either.
01The evidence
Electron scattering and muonic hydrogen spectroscopy give radii that differ by several standard deviations, and the difference has resisted every attempt to attribute it to a single systematic.
02The tension
The discrepancy is treated as an error to be found, and the search has narrowed to a few candidate systematics without resolution. An alternative is that the observable is not unique.
03The mechanism
A radius extracted from a form factor is a moment of the charge distribution, and different moments weight the periphery differently. Muonic hydrogen is sensitive to a different weighted moment than electron scattering because the muon orbit samples a different region.
If the two methods weight different moments, then the disagreement is a measurement of the difference between those moments, which is itself a probe of the proton's internal structure.
04What this is not
The standard analysis assumes one radius. This assumes several moments and treats the disagreement as signal.
05Predictions
- P1The discrepancy should scale with the moment difference between methods.
- P2A third method weighting a third moment should land between them predictably.
- P3The extracted moments should be mutually consistent once mapped.
06Refutation
A single moment fitting all methods once systematics are corrected would restore one radius.
07What it changes
It would turn a controversy into a structural measurement.