vs data from Ref. [@dytman].[]{data-label="fig2"}](dytman293.pdf){width="8.5cm"}

![(Color online) Same as in Fig. \[fig2\] vs data from Ref. [@parker].[]{data-label="fig3"}](parker220.pdf){width="8.5cm"}

![(Color online) Same as in Fig. \[fig2\] vs data from Ref. [@friedman].[]{data-label="fig4"}](Friedman_175mev_75deg_plot.pdf){width="8.5cm"}

![(Color online) Same as in Fig. \[fig2\] vs data from Ref. [@patterson].[]{data-label="fig5"}](Patterson_Barber_41p5MeV_180deg.pdf){width="8.5cm"}

![(Color online) Same as in Fig. \[fig2\] vs data from Ref. [@ricco].[]{data-label="fig6"}](ricco_q0p35invfm_155deg.pdf){width="8.5cm"}

![(Color online) Same as in Fig. \[fig2\] vs data from Ref. [@yearian] as function of excitation energy $E^x$.[]{data-label="fig7"}](yearian143mev.pdf){width="8.5cm"}

![(Color online) Same as in Fig. \[fig2\] vs. deuteron total photoabsorption data from Refs. [@Bernabei:1986ai; @Birenbaum:1985zz]. Older data compilation can be found in Ref. [@Govaerts:1981xu][]{data-label="fig8"}](sigma_gaD.pdf){width="8.5cm"}

The parameter $C_\perp$ is obtained from a fit to real photon data and the value of Baldin sum rule for real photons, \_E\^d+\_M\^d&=&\_[\_[th]{}]{}\^[\_]{} F\^d\_1(,0), where $\alpha_E^d$ and $\beta_M^d$ are the deuteron electric and magnetic polarizabilities, respectively. There exist calculations in chiral EFT by Chen et al. [@chen] and in non-relativistic potential models, [*e.g.*]{} by Friar [@friar], that give close results that can be cast in the following form: $\alpha_E^d=0.633(1)$ fm$^3$, and $\beta_M^d=0.072(5)$ fm$^3$. The uncertainty in the value of the polarizabilities was obtained by averaging over the two calculations. Evaluating Baldin integral with $F_1^\perp$ (the only piece that does not vanish at the real 