# NNLO QCD counterterm contributions to $B$ \to $X_s \gamma$ for the physical value of $m_c$

## TL;DR

This paper calculates the ultraviolet counterterm contributions at the physical charm quark mass to improve the precision of the NNLO QCD corrections in the $B o X_s \gamma$ decay rate, reducing theoretical uncertainties.

## Contribution

It provides the first explicit calculation of all relevant ultraviolet counterterms for the physical charm mass, refining previous interpolation-based estimates.

## Key findings

- Enhanced accuracy in the NNLO QCD correction estimates.
- Reduced theoretical uncertainties in the $B o X_s \gamma$ branching ratio.
- Improved understanding of charm quark mass effects in rare B decays.

## Abstract

One of the most important O($\alpha_s^2$) corrections to the $B \to X_s \gamma$ branching ratio originates from interference of contributions from the current-current and photonic dipole operators. Its value has been estimated using an interpolation in the charm quark mass between the known results at $m_c=0$ and for $m_c \ll m_b/2$. An explicit calculation for the physical value of $m_c$ is necessary to remove the associated uncertainty. In the present work, we evaluate all the ultraviolet counterterm contributions that are relevant for this purpose.