Abstract
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 \( \bar{c}c \)-threshold, q 2 ≪ 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 → 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 * γ beyond the local-operator approximation. To describe the charm-loop effect at large q 2, we employ the hadronic dispersion relation with ψ = J/ψ, ψ(2S),... contributions, where the measured B → K (∗) ψ amplitudes are used as inputs. Matching this relation to the result of QCD calculation reveals a destructive interference between the J/ψ and ψ(2S) contributions. The resulting charm-loop effect is represented as a q 2-dependent correction ΔC 9(q 2) to the Wilson coefficient C 9. Within uncertainties of our calculation, at q 2 below the charmonium region the predicted ratio ΔC 9(q 2)/C 9 is ≤5% for B → Kℓ + ℓ −, but can reach as much as 20% for B → K * ℓ + ℓ −, the difference being mainly caused by the soft-gluon contribution.
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ArXiv ePrint: 1006.4945
On leave from Institute for Nuclear Research, 117312 Moscow, Russia. (A.A. Pivovarov)
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Khodjamirian, A., Mannel, T., Pivovarov, A. et al. Charm-loop effect in B → K (*) ℓ + ℓ − and B → K * γ . J. High Energ. Phys. 2010, 89 (2010). https://doi.org/10.1007/JHEP09(2010)089
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DOI: https://doi.org/10.1007/JHEP09(2010)089