Next-to-Leading-Order Weak-Annihilation Correction to Rare B→{K,π}ℓ+ℓ− Decays

We accomplish for the first time the next-to-leading-order computation of the weak annihilation contribution to the electroweak penguin decays B→{K,π}ℓ+ℓ−, which is an essential missing piece of the complete QCD correction to the matrix elements of hadronic operators in the weak effective Hamiltonian. Both the hard functions and the jet functions in the perturbative factorization formulas from the short-distance fluctuations at the two distinct scales mb and mbΛ are determined at O(αs). We then demonstrate that the one-loop weak annihilation correction can bring about the noticeable impacts on theory predictions for the CP asymmetries and the isospin asymmetry in the B→πℓ+ℓ− decays.