Four-loop anomalous dimensions for radiative flavour-changing decays

We evaluate the complete four-loop anomalous dimension matrix that is nec- essary for determining the effective flavour-changing neutral current couplings ¯ qq 0 ° and ¯ qq 0 g at the next-to-next-to-leading order in QCD. The resulting O(® 2 (µb)) correction to the ¯ B ! Xs° branching ratio amounts to around i2.9% for µb = 5GeV, and i4.4% for µb = 2.5GeV.

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