Higher-order proton structure corrections to the Lamb shift in muonic hydrogen

The recent conundrum with the proton charge radius inspires reconsideration of the corrections that enter into determinations of the proton size. We study the two-photon proton-structure corrections, with special consideration of the nonpole subtraction term in the dispersion relation and using fits to modern data to evaluate the energy contributions. We find that individual contributions change more than the total and present results with error estimates.

Figure 1

The box diagram for the $O\left({\alpha }^5\right)$ corrections.

Figure 2

Elastic contributions to the box diagram.

Figure 3

Diagrams used for estimating the $Q^2$ dependence of the nonpole part of the subtraction term.