  In this work we use the low-energy EFT called potential non-relativistic QCD
(pNRQCD) to calculate the partial decay width of different $b\bar{b}$-states
undergoing an electric dipole transition at next-to-next-to leading order
(NNLO). Explicitly, the $\chi_{b J}$, for $J=0,1,2$, and the $h_b$ are
investigated by computing the processes $\chi_{b J} \to \Upsilon + \gamma$ and
$h_b \to \eta_b + \gamma$. Relativistic corrections of relative order $v^2$ to
the leading electric dipole operator are included. The analysis separates those
contributions that account for the electromagnetic interaction terms in the
pNRQCD Lagrangian, which are $v^2$ suppressed, and those that account for
quarkonium state corrections of relative order $v$ and $v^2$. Within the last
ones, corrections come from higher order potentials ($\frac{1}{m}$ and
$\frac{1}{m^2}$ terms), and from higher order Fock states which account for the
coupling of the quark-antiquark state to other low-energy degrees of freedom
and thus demand non-perturbative input. Finally, the experimentally known
branching fractions are used to predict the total decay with of the respective
initial states.
