Reduction of Charm Quark Mass Scheme Dependence in $\bar{B}\to X_s\gamma$ at the NNLL Level

Abstract

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.

13 pages including 3 figures

References in corpus (4)

• Physics at Super B Factory
• Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
• Three-Loop Mixing of Dipole Operators
• The Discovery Potential of a Super B Factory

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• Radiative and Electroweak Penguin Decays of B Mesons
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• NNLO QCD counterterm contributions to $B$ \to $X_s\gamma$ for the physical value of $m_c$
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