Abstract
We evaluate the complete four-loop anomalous dimension matrix that is necessary for determining the effective flavour-changing neutral current couplings qbar-q'-gamma and qbar-q'-g at the next-to-next-to-leading order in QCD. The resulting O(alpha_s^2(mu_b)) correction to the B -> X_s gamma branching ratio amounts to around -2.9% for mu_b = 5 GeV, and -4.4% for mu_b = 2.5 GeV
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