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In these proceedings, we briefly review the individual interferencecontribution of the electromagnetic dipole operator $\mathcal{O}_{7}$ to thedouble differential decay width $d\Gamma_{77}/(ds_1\, ds_2)$ for the process$\bar{B} \to X_s \gamma \gamma$ at $O(\alpha_s)$ in QCD, which is based on ourprevious work. We define two kinematical variables $s_1$ and $s_2$ as $s_i=(p_b- q_i)^2/m_b^2$, where $p_b$, $q_1$, $q_2$ are the momenta of b-quark and twophotons. While the (renormalized) virtual corrections are worked out exactlyfor a certain range of $s_1$ and $s_2$, we retained in the gluon bremsstrahlungprocess only the leading power w.r.t. the (normalized) hadronic mass$s_3=(p_b-q_1-q_2)^2/m_b^2$ in the underlying triple differential decay width$d\Gamma_{77}/(ds_1 ds_2 ds_3)$. We found that the double differential decaywidth, based on this approximation, is free of infrared- and collinearsingularities when summing up the virtual- and real-radiation corrections,while this was not the case when keeping all powers in $s_3$ in the gluonbremsstrahlung process due to the configurations allowing collinear photonemission from the (massless) $s$-quark. Lastly, we compare our analyticalresults with those obtained in a recently extended work, where a non-zerostrange quark mass was introduced to regulate the collinear photonconfigurations.

The double radiative $\bar{B}\to X_s\gamma \gamma$ decay at $O(\alpha_{s})$ in QCD