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

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.

Comments: journal version, references added; 14 pages, 3 figures, 1 table; some intermediate results in ancillary files