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Charm-loop effect in \(B \to K^{(\ast)}\ell^{+}\ell^{-}\) and \(B \to K^{\ast}\gamma\). (English) Zbl 1291.81390
Summary: We calculate the long-distance effect generated by the four-quark operators with \(c\)-quarks in the \(B \to K^{(\ast)}\ell^{+}\ell^{-}\) decays. At the lepton-pair invariant masses far below the \(\bar{c}c\)-threshold, \(q^{2} \ll 4m_{c}^{2}\), we use OPE near the light-cone. The nonfactorizable soft gluon emission from \(c\)-quarks is cast in the form of a nonlocal effective operator. The \(B \to K^{(\ast)}\) 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 \(B \to K^{\ast}\gamma\) beyond the local-operator approximation. To describe the charm-loop effect at large \(q^{2}\), we employ the hadronic dispersion relation with \(\psi = J/\psi, \psi(2S),...\) contributions, where the measured \(B \to K^{(\ast)}\psi\) 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 \(\leq 5\)% for \(B \to K\ell^{+}\ell^{-}\), but can reach as much as 20% for \(B \to K^{\ast}\ell^{+}\ell^{-}\), the difference being mainly caused by the soft-gluon contribution.

81V05 Strong interaction, including quantum chromodynamics
81V35 Nuclear physics
81U99 Quantum scattering theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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