Two loop virtual corrections to [Formula omitted] and [Formula omitted] for arbitrary momentum transfer

Non-factorizable two loop corrections to heavy to light flavor changing neutral current transitions due to matrix elements of current-current operators are calculated analytically for arbitrary momentum transfer. This extends previous work on [Formula omitted] transitions. New results for [Formula omitted] transitions are presented. Recent work on polylogarithms is used for the master integrals. For [Formula omitted] transitions, the corrections are most significant for the imaginary parts of the effective Wilson coefficients in the large hadronic recoil range. Analytical results and ready-to-use fitted results for a specific set of parameters are provided.