Towards $B\to V\gamma$ Decays at NNLO in SCET

Abstract

We compute NNLO ($\mathcal{O}({\alpha }_s^2)$) corrections to the hard-scattering kernels entering the QCD factorization formula for $B\to V\gamma$ decays, where $V$ is a light vector meson. We give complete NNLO results for the dipole operators $Q_7$ and $Q_8$, and partial results for $Q_1$ valid in the large-${\beta }_0$ limit and neglecting the NNLO correction from hard spectator scattering. Large perturbative logarithms in the hard-scattering kernels are identified and resummed using soft-collinear effective theory. We use our results to estimate the branching fractions for $B\to K^{\ast }\gamma$ and $B_s\to \varphi \gamma$ decays at NNLO and compare them with the current experimental data.

Comments: 33 pages, 2 figures; text modified in sections 3 and 4, added 3 equations [(23),(40),(46)] and corrected Eq. (39); added 4 references; title slightly modified; to appear in the European Physical Journal C