– 0.417(2)
  ---------------------- --------------
    $\Delta E^{PWBA}$     – 1.616(739)
     $\Delta E^{FSI}$     – 0.391(44)
    $\Delta E^{\perp}$     – 0.322(3)
    $\Delta E^{hadr}$      – 0.028(2)
    $\Delta E^{\beta}$     0.740(40)
     $\Delta E^{Th}$        0.023(1)
    $\Delta E_{total}$    – 2.011(740)

  : TPE corrections to the $2S_{1/2}$ energy level in muonic deuterium in units of meV.[]{data-label="tab2"}

Discussion of Results and Impact of Further Scattering Experiments
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The total result for the $2P-2S$ Lamb shift obtained from the sum of all terms ${\cal O}(\alpha^5)$ due to two-photon exchange amounts to E \_[2P-2S]{}&=&2.01(74). The uncertainty of our result comes from three sources: elastic deuteron form factors, inelastic hadronic excitations and nuclear (quasi-elastic) contributions. The deuteron elastic form factors have been measured over a wide $Q^2$-range with good precision, and the error associated with different parametrizations of these data amounts to $2\mu$eV or relative 2% uncertainty. The hadronic part contribution is constrained to a relative 7%, however fortunately the contribution itself is rather small, so this somewhat large relative uncertainty translates in $2\mu$eV absolute uncertainty.

At the moment, for the calculation of the subtraction contribution we rely on the $Q^2$-dependence for the magnetic polarizability obtained from a model. A direct calculation of $\bar T_1(0,Q^2)$, for instance in chiral EFT would help reducing the corresponding 