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

TL;DR

This paper advances the theoretical precision of $B o V \gamma$ decay predictions by calculating NNLO corrections within SCET, enabling more accurate comparisons with experimental results.

Contribution

It provides the first complete NNLO calculations for the hard-scattering kernels in $B o V\gamma$ decays, including dipole operators and partial results for others, with resummation of large logarithms.

Findings

NNLO corrections significantly affect branching fraction estimates.

Resummation of large logarithms improves theoretical predictions.

Results align better with experimental data for $B o K^*\gamma$ and $B_s o \phi\gamma$.

Abstract

We compute NNLO (${\cal O}(\alpha_s^2)$) 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 $B\to K^*\gamma$ and $B_s\to \phi\gamma$ decays at NNLO and compare them with the current experimental data.