behavior by adopting a Regge-behaved background. The Regge fit to world data on the deuteron total photoabsorption cross section was done in [@fesr]. We extend this description to virtual photoabsorption by supplementing a $Q^2$-dependence from generalized VDM, e.g. [@alwall], that provides good description of virtual photoabsorption data at $Q^2\lesssim3$ GeV$^2$. The result for $\Delta E^{hadr}$ is reported in Table \[tab2\].\

Quasielastic contribution
-------------------------

In the literature, there exist non-relativistic calculations of the Lamb shift in muonic deuterium with potential models or in zero-range approximations [@friar; @pachuckiD; @rosenfelder; @FriarPayne; @Friar:2013rha; @Ji:2013oba]. In this work we opt for a phenomenological, data-driven approach in the spirit of Ref. [@Carlson:2011zd] where real and virtual photoabsorption data on the proton were utilized to constrain the Lamb shift in the muonic hydrogen. For this purpose we need to fit the quasi-elastic data over the whole kinematical range with an appropriate function of $\nu,\,Q^2$.

We start with the plane wave Born approximation (PWBA) that allows to relate the deuteron structure functions in the quasi-elastic kinematics to the elastic nucleon structure functions. In doing this, we Fermi-smear the nucleon virtual Compton tensor, rather than just the structure functions, the result reads F\_1\^[PWBA]{}&=& G\_M\^2 S(,Q\^2)+S\_(,Q\^2)\
F\_2\^[PWBA]{}&=&\
&&. Above, we 