Charm-loop effect in $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ and $B\to K^{\ast }\gamma$

Abstract

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 $\le 5$ 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.

A few comments added, version to appear in JHEP

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• Searching for New Physics with $B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$
• Flavour Physics at LHCb -- 50 years of the KM paradigm
• Associated Production of Different Flavor Heavy Quarks Through $W^{\prime }$ Bosons at the LHC
• Recent developments in HQET
• Investigating non-local contributions in $B_s\to \varphi \bar{\ell }\ell$ including higher-twist effects
• Radiative B to tensor meson decays at NLO in SCET
• Non-parametric and continuous extraction of amplitudes in electroweak penguin decays
• Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints
• Summary of the CKM 2014 working group on rare decays
• First search for $B\to X_s\nu \bar{\nu }$ decays
• Model-independent unbinned analysis of $B\to K^{\ast }(\to K^{+}{\pi }^{-}){\mu }^{+}{\mu }^{-}$: zeroes, bounds, Wilson coefficients and symmetries
• Theoretical implications of recent heavy flavour measurements at the LHC
• Analysis of $B\to K{M}_X$ and $B\to K^{\ast }{M}_X$ decays in scalar- and vector-mediator dark-matter scenarios