NLO analysis of the subleading-power $Q_1-Q_{7\gamma }$ interference in $\bar{B}\to X_s\gamma$ at large photon energies

We report on progress towards including next-to-leading order (NLO) radiative corrections to the subleading-power factorization formula for the $Q_1^q-Q_{7\gamma }$ interference contribution in $\bar{B}\to X_s\gamma$ at large photon energies, $m_b-2E_{\gamma }=\mathcal{O}({\mathrm{\Lambda }}_{\mathrm{Q}\mathrm{C}\mathrm{D}})$. The novel ingredients for a NLO analysis are the one-loop anomalous dimension of the subleading shape function $g_{17}(\omega ,{\omega }_1;\mu )$, which was recently computed by us, and the two-loop corrections to the jet function with an internal charm loop. Here we summarize the renormalization of $g_{17}(\omega ,{\omega }_1;\mu )$, and further discuss that our insights allow for a simplified renormalization of a specific generalization of a three-particle $B$-meson light-cone distribution amplitude, but with non-aligned light-like separations of the fields.