Two loop virtual corrections to $$b\rightarrow (d,s)\ell ^+\ell ^-$$ b → ( d , s ) ℓ + ℓ - and $$c\rightarrow u\ell ^+\ell ^-$$ c → u ℓ + ℓ - for arbitrary momentum transfer

Abstract 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 $$b\rightarrow (d,s)\ell ^+\ell ^-$$ b → ( d , s ) ℓ + ℓ - transitions. New results for $$c\rightarrow u\ell ^+\ell ^-$$ c → u ℓ + ℓ - transitions are presented. Recent work on polylogarithms is used for the master integrals. For $$b\rightarrow s\ell ^+\ell ^-$$ b → s ℓ + ℓ - 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.