The $$Q_{1,2}$$–$$Q_7$$ interference contributions to $$b \rightarrow s \gamma $$ at $${\mathcal O}(\alpha _{\mathrm s}^2)$$ for the physical value of $$m_c$$

Abstract

AbstractThe $$\bar{B}\rightarrow X_s\gamma $$ B ¯ → X s γ branching ratio is currently measured with around $$5\%$$ 5 % accuracy. Further improvement is expected from Belle II. To match such a precision on the theoretical side, evaluation of $${\mathcal O}(\alpha _{\mathrm s}^2)$$ O ( α s 2 ) corrections to the partonic decay $$b \rightarrow X_s^\textrm{part}\gamma $$ b → X s part γ are necessary, which includes the $$b \rightarrow s \gamma $$ b → s γ , $$b \rightarrow s g\gamma $$ b → s g γ , $$b \rightarrow s gg\gamma $$ b → s g g γ , $$b \rightarrow sq\bar{q}\gamma $$ b → s q q ¯ γ decay channels. Here, we evaluate the unrenormalized contribution to $$b \rightarrow s \gamma $$ b → s γ that stems from the interference of the photonic dipole operator $$Q_7$$ Q 7 and the current–current operators $$Q_1$$ Q 1 and $$Q_2$$ 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.