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We present a high-accuracy calculation of the deuteron structure radius inchiral effective field theory. Our analysis employs the state-of-the-artsemilocal two-nucleon potentials and takes into account two-body contributionsto the charge density operators up to fifth order in the chiral expansion. Thestrength of the fifth-order short-range two-body contribution to the chargedensity operator is adjusted to the experimental data on the deuteron chargeform factor. A detailed error analysis is performed by propagating thestatistical uncertainties of the low-energy constants entering the two-nucleonpotentials and by estimating errors from the truncation of the chiral expansionas well as from uncertainties in the nucleon form factors. Using the predictedvalue for the deuteron structure radius together with the very accurate atomicdata for the difference of the deuteron and proton charge radii we, for thefirst time, extract the charge radius of the neutron from light nuclei. Theextracted value reads $r_n^2 = - 0.106 \substack{ +0.007\\ -0.005\\} \,\text{fm}^2$ and its magnitude is about $1.7\sigma$ smaller than the currentvalue given by the Particle Data Group. In addition, given the high accuracy ofthe calculated deuteron charge form factor and its careful and systematic erroranalysis, our results open the way for an accurate determination of the nucleonform factors from elastic electron-deuteron scattering data measured at theMainz Microtron and other experimental facilities.

Extraction of the neutron charge radius from a precision calculation of the deuteron structure radius