Muonic hydrogen and the third Zemach moment

Abstract

We determine the third Zemach moment of hydrogen $\left({⟨r^3⟩}_{\left(2\right)}\right)$ using only the world data on elastic electron-proton scattering. This moment dominates the $\mathcal{O}{\left(Z\alpha \right)}^5$ hadronic correction to the Lamb shift in muonic atoms. The resulting moment, ${⟨r^3⟩}_{\left(2\right)}=2.71\left(13\right){\mathrm{fm}}^3$, is larger than some previously inferred values based on simple models. The contribution of that moment to the muonic hydrogen 2S level is $-0.0247\left(12\right)\mathrm{meV}$.