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The present NLL prediction for the decay rate of the rare inclusive process $\bar B \to X_s \gamma$ has a large uncertainty due to the charm mass renormalization scheme ambiguity. We estimate that this uncertainty will be reduced by a factor of 2 at the NNLL level. This is a strong motivation for the on-going NNLL calculation, which will thus significantly increase the sensitivity of the observable $\bar B \to X_s \gamma$ to possible new degrees of freedom beyond the SM. We also give a brief status report of the NNLL calculation.

Towards the NNLO precision in $B\rightarrow X_s \gamma$