Model-independent determination of the magnetic radius of the proton from spectroscopy of ordinary and muonic hydrogen

TL;DR

This paper derives a model-independent value for the magnetic radius of the proton by analyzing hyperfine intervals in ordinary and muonic hydrogen, providing a new constraint that complements existing scattering measurements.

Contribution

It introduces a self-consistent, model-independent method to determine the proton's magnetic radius using atomic spectroscopy data.

Findings

Proton magnetic radius constrained to R_M=0.78(8) fm.

Combined electric and magnetic radius squared sum: 1.35(12) fm^2 (ordinary) and 1.49(18) fm^2 (muonic).

Method reduces model dependence of proton radius measurements.

Abstract

To date the magnetic radius of the proton has been determined only by means of electron-proton scattering, which is not free of controversies. Any existing atomic determinations are irrelevant because they are strongly model-dependent. We consider a so-called Zemach contribution to the hyperfine interval in ordinary and muonic hydrogen and derive a self-consistent model-independent value of the magnetic radius of the proton. More accurately, we constrain not a value of the magnetic radius by itself, but its certain combination with the electric-charge radius of the proton, namely, R_E^2+R_M^2. The result from the ordinary hydrogen is found to be R_E^2+R_M^2=1.35(12) fm^2, while the derived muonic value is 1.49(18) fm^2. That allows us to constrain the value of the magnetic radius of proton R_M=0.78(8) fm at the 10% level.