Scale uncertainties in the B-->Xsγ decay

We analyze the theoretical uncertainties in Br(B-->X_sγ) due to the choice of the high energy matching scale μ_W=≀(M_W) and the scale μ_t at which the running top quark mass is defined: <OVL STYLE = "S">moverline_t(μ_t). To this end we have repeated the calculation of the initial conditions confirming the final results of Adel and Yao and Greub and Hurth and generalizing them to include the dependences on μ_t and μ_W with μ_t≠μ_W. In the leading order the μ_W and μ_t uncertainties in Br(B-->X_sγ) turn out to be +/-13% and +/-3% respectively. We show analytically how these uncertainties are reduced after including next-to-leading QCD corrections. They amount to +/-0.4% and +/-0.3% respectively. Reanalyzing the uncertainties due to the scale μ_b=≀(m_b) we find that after the inclusion of NLO effects they amount to +/-3.2% which is smaller by a factor of two than claimed in the literature. Including the uncertainties due to input parameters as well as the non-perturbative 1/m_b² and 1/m_c² corrections we find Br(B-->X_sγ)=(3.48+/-0.31)x10^-4 where the error is dominated by uncertainties in the input parameters. This should be compared with (3.28+/-0.33)x10^-4 found by Chetyrkin et al. where the error is shared evenly between the scale and parametric uncertainties.