Reduction of Charm Quark Mass Scheme Dependence in Bˉ→Xsγ\bar B \to X_s \gamma at the NNLL Level

The uncertainty of the theoretical prediction of the $\bar B \to X_s \gamma$ branching ratio at NLL level is dominated by the charm mass renormalization scheme ambiguity. In this paper we calculate those NNLL terms which are related to the renormalization of $m_c$, 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 ${BR}(\bar B \to X_s \gamma)$ induced by the definition of $m_c$. 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 $\bar B \to X_s \gamma$ to possible new degrees of freedom beyond the SM significantly.Comment: 13 pages including 3 figure

The First Estimate of BR(\bar B to X_s\gamma) at O(\alpha_s^2)

Combining our results for various {Omicron}({alpha}{sub s}{sup 2}) corrections to the weak radiative B-meson decay, we are able to present the first estimate of the branching ratio at the next-to-next-to-leading order in QCD. We find {Beta}({bar B} {yields} X{sub s}{gamma}) = (3.15 {+-} 0.23) x 10{sup -4} for E{sub {gamma}} > 1.6 GeV in the {bar B}-meson rest frame. The four types of uncertainties: non-perturbative (5%), parametric (3%), higher-order (3%) and m{sub c}-interpolation ambiguity (3%) have been added in quadrature to obtain the total error