# Deuteron charge radius from the Lamb-shift measurement in muonic deuterium

## TL;DR

This paper determines the deuteron charge radius from muonic deuterium Lamb shift measurements, revealing a large electron vacuum polarization correction that aligns deuteron and proton radii, suggesting previous discrepancies stem from underestimated uncertainties.

## Contribution

It introduces a refined calculation of the deuteron charge radius from muonic deuterium, accounting for significant vacuum polarization effects, resolving previous inconsistencies with electronic measurements.

## Key findings

- Deuteron charge radius from muonic deuterium matches isotope shift data.
- Large electron vacuum polarization correction impacts nuclear-structure effects.
- Discrepancy in proton radius likely due to underestimated uncertainties in hydrogen spectroscopy.

## Abstract

The deuteron charge radius is calculated from the measurement of the Lamb shift in muonic deuterium, taking into account the electron vacuum polarization correction to the nuclear-structure effects. This correction is unexpectedly large and gives a mean-square charge-radii difference $ r_d^2-r_p^2 = 3.81747(346)\, {\rm fm}^2 $, which is now consistent with that obtained from the ordinary H-D isotope shift in the 1$S$-2$S$ transition. This suggests that the long-standing discrepancy in the proton charge radius obtained from electronic and muonic systems is due to an underestimated uncertainty in ordinary hydrogen spectroscopy.