Abstract
The $$\bar{B}\rightarrow X_s\gamma $$ branching ratio is currently measured with around $$5\%$$ accuracy. Further improvement is expected from Belle II. To match such a precision on the theoretical side, evaluation of $${\mathcal O}(\alpha _{\mathrm s}^2)$$ corrections to the partonic decay $$b \rightarrow X_s^\textrm{part}\gamma $$ are necessary, which includes the $$b \rightarrow s \gamma $$, $$b \rightarrow s g\gamma $$, $$b \rightarrow s gg\gamma $$, $$b \rightarrow sq\bar{q}\gamma $$ decay channels. Here, we evaluate the unrenormalized contribution to $$b \rightarrow s \gamma $$ that stems from the interference of the photonic dipole operator $$Q_7$$ and the current–current operators $$Q_1$$ and $$Q_2$$. Our results, obtained in the cut propagator approach at the 4-loop level, agree with those found in parallel by Fael et al. who have applied the amplitude approach at the 3-loop level. Partial results for the same quantities recently determined by Greub et al. agree with our findings, too.
Czaja, M