Reduction of charm quark mass scheme dependence in B¯→Xsγ at the NNLL level

The uncertainty of the theoretical prediction of the B¯→Xsγ branching ratio at NLL level is dominated by the charm mass renormalization scheme ambiguity. In this Letter we calculate those NNLL terms which are related to the renormalization of mc, in order to get an estimate of the corresponding uncertainty at the NNLL level. We find that these terms significantly reduce (by typically a factor of two) the error on BR(B¯→Xsγ) induced by the definition of mc. Taking into account the experimental accuracy of around 10% and the future prospects of the B factories, we conclude that a NNLL calculation would increase the sensitivity of the observable B¯→Xsγ to possible new degrees of freedom beyond the SM significantly.