Charm-loop effect in B → K(*)l+l- and B → K*γ

We calculate the long-distance effect generated by the four-quark operators with c-quarks in the B -> K-(*()) l(+)l(-) decays. At the lepton-pair invariant masses far below the (c) over barc-threshold, q(2) << 4m(c)(2), we use OPE near the light-cone. The nonfactorizable softgluon emission from c-quarks is cast in the form of a nonlocal effective operator. The B -> K-(*()) matrix elements of this operator are calculated from the QCD light-cone sum rules with the B-meson distribution amplitudes. As a byproduct, we also predict the charm-loop contribution to B -> K*gamma beyond the local-operator approximation. To describe the charmloop effect at large q(2), we employ the hadronic dispersion relation with psi = J/psi, psi( 2S), ... contributions, where the measured B -> K-(*())psi. amplitudes are used as inputs. Matching this relation to the result of QCD calculation reveals a destructive interference between the J/psi and psi(2S) contributions. The resulting charm-loop effect is represented as a q(2)-dependent correction Delta C-9(q(2)) to the Wilson coefficient C-9. Within uncertainties of our calculation, at q(2) below the charmonium region the predicted ratio Delta C-9(q(2))/C-9 is <= 5% for B -> K l(+)l(-), but can reach as much as 20% for B -> K l(+)l(-), the difference being mainly caused by the soft-gluon contribution.