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We compute three-loop vertex corrections to $b\to s\gamma$ induced bycurrent-current operators. The results are presented as expansions in $m_c/m_b$with numerical coefficients which allow to cover all relevant values for theheavy quark masses in different renormalization schemes. Moreover we providefor the first time analytic results for the next-to-leading order contribution.Our results present an important building block to the next-to-next-to-leadingorder interference contributions of the current-current operators $Q_1$ and$Q_2$ with the electric dipole operator $Q_7$.

Three-loop $b\to s\gamma$ vertex with current-current operators