Four-loop anomalous dimensions for radiative flavour-changing decays

We evaluate the complete four-loop anomalous dimension matrix that is necessary for determining the effective flavour-changing neutral current coupling (q) over barq'gamma and (q) over barq'g at the next-to-next-to-leading order in QCD. The resulting O(alpha(2)(s)(mu(b))) correction to the (B) over bar -> X-s gamma branching ration amounts to around -2.9% for mu(b) = 5 GeV, and -4.4% for mu(b) = 2.5 GeV.