Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of Muonic Hydrogen

Abstract

The sixth-order electron-loop vacuum-polarization contribution to the ${2P}_{1/2}-{2S}_{1/2}$ Lamb shift of the muonic hydrogen ( ${\mu }^{-}{p}^{+}$ bound state) is evaluated numerically. Our result is 0.007 608(1) meV. This eliminates the largest theoretical uncertainty. Combined with the proposed precision measurement of the Lamb shift it will lead to a precise determination of the proton charge radius.