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

Abstract

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, $m_b - 2E_\gamma = \mathcal{O}(\Lambda_{\rm QCD})$. 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.