uncertainty.

The largest contribution and the source of the largest uncertainty is the quasielastic piece, in particular the $Q^2$-dependence of the inelastic structure function $F_2(\nu,Q^2)$ in the range $\nu\leq10$ MeV, $Q^2\leq0.01$ GeV$^2$ from which the dominant contribution to the Lamb shift stems. A dedicated measurement at Mainz with the existing A1 apparatus at $E_0=180$ MeV and angles $\theta_{lab}\geq15^\circ$ is planned [@A1], and it would help somewhat to constrain the uncertainty with $Q^2\gtrsim2.2\times10^{-3}$ GeV$^2$. Going to lower energies will be possible with the new linear accelerator machine MESA at Mainz, and we include a few plots demonstrating the sensitivity to the parameter $a_1$ in several representative kinematics in Fig. \[sensitivity\].

![(Color online) Sensitivity to the variation of the parameter $a_1$ entering $f_T^{PWBA}$ in the range \[0.99, 1\] and $a_2$ entering $f_T^{FSI}$ in the range \[180, 250\] is shown by the dashed and solid lines, respectively, in the kinematics relevant for the MAMI A1 apparatus [@A1] (three upper panels), and for MESA at 80 MeV (lower panel).[]{data-label="sensitivity"}](sigma180mev_30deg.pdf "fig:"){width="7.5cm"} ![(Color online) Sensitivity to the variation of the parameter $a_1$ entering $f_T^{PWBA}$ in the range \[0.99, 1\] and $a_2$ entering $f_T^{FSI}$ in the range \[180, 250\] is shown by the dashed and solid lines, 