Two-loop current–current operator contribution to the non-leptonic QCD penguin amplitude

The computation of direct CP asymmetries in charmless B   decays at next-to-next-to-leading order (NNLO) in QCD is of interest to ascertain the short-distance contribution. Here we compute the two-loop penguin contractions of the current–current operators Q1,2Q1,2 and provide a first estimate of NNLO CP asymmetries in penguin-dominated b→sb→s transitions.