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Register a new userCharm-loop effect in $B to K^{(*)} ell^{+} ell^{-}$ and $Bto K^*gamma$
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We calculate the long-distance effect generated by the four-quark operators with $c$-quarks in the $Bto K^{(*)} ell^+ell^-$ decays. At the lepton-pair invariant masses far below the $bar{c}c$-threshold, $q^2ll 4m_c^2$, 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 $Bto K^{(*)}$ 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 $Bto K^*gamma$ 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 $ Bto 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 $leq 5% $ for $Bto K ell^+ell^-$, but can reach as much as 20% for $Bto K^*ell^+ell^-$, the difference being mainly caused by the soft-gluon contribution.
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We predict the amplitude of the $Bto K ell^+ell^-$ decay in the region of the dilepton invariant mass squared $0<q^2leq m_{J/psi}^2$, that is, at large hadronic recoil. The $Bto K$ form factors entering the factorizable part of the decay amplitude are obtained from QCD light-cone sum rules. The nonlocal effects, generated by the four-quark and penguin operators combined with the electromagnetic interaction, are calculated at $q^2<0$, far below the hadronic thresholds. For hard-gluon contributions we employ the QCD factorization approach. The soft-gluon nonfactorizable contributions are estimated from QCD light-cone sum rules. The result of the calculation is matched to the hadronic dispersion relation in the variable $q^2$, which is then continued to the kinematical region of the decay. The overall effect of nonlocal contributions in $Bto Kell^+ell^-$ at large hadronic recoil is moderate. The main uncertainty of the predicted $Bto K ell^+ell^-$ partial width is caused by the $Bto K$ form factors. Furthermore, the isospin asymmetry in this decay is expected to be very small. We investigate the deviation of the observables from the Standard Model predictions by introducing a generic new physics contribution to the effective Hamiltonian.
We propose measurements of weighted differences of the angular observables in the rare decays $B to K^*ell^+ell^-$. The proposed observables are very sensitive to the difference between the Wilson coefficients $mathcal{C}_9^{(e)}$ and $mathcal{C}_9^{(mu)}$ for decays into electrons and muons, respectively. At the same time, the charm-induced hadronic contributions are kinematically suppressed to $lesssim 7% (4%)$ in the region $1,$GeV$^2 leq q^2 leq 6,$GeV$^2$, as long as LFU breaking occurs only in $mathcal{C}^{(ell)}_{9}$. This suppression becomes stronger for the region of low hadronic recoil, $q^2 geq 15,$GeV$^2$.
We study the rare decay $Bto K_2^ast(1430)(to Kpi)ell^+ell^-$ in the Standard Model and beyond. Working in the transversity basis, we exploit the relations between the heavy-to-light form factors in the limit of heavy quark ($m_bto infty$) and large energy ($E_{K_2^ast}to infty$) of the $K^ast_2$ meson. This allows us to construct observables where at leading order in $Lambda_{rm QCD}/m_b$ and $alpha_s$ the form factor dependence involving the $Bto K^ast_2$ transitions cancels. Higher order corrections are systematically incorporated in the numerical analysis. In the Standard Model the decay has a sizable branching ratio and therefore a large number of events can be expected at LHCb. Going beyond the Standard Model, we explore the implications of the global fit to presently available $bto sell^+ell^-$ data on the $Bto K_2^ast ell^+ell^-$ observables.
The present status of the LHC anomalies found in exclusive semileptonic $bto sell^+ell^-$ decays is discussed with special emphasis on the exclusive 4-body angular distribution $B to K^*(to Kpi)ell^+ell^-$. The treatment of hadronic uncertainties in this mode is briefly reviewed, and some of the analyses in the literature are critically reassessed. The global picture provided by the global fit points to a coherent pattern of deviations with a significance substantially above 4$sigma$ for different New Physics scenarios. Finally, we propose as the next step in the field to focus on the study of optimized observables that compare electron and muon modes, sensitive to lepton-flavour universality violations and free from hadronic uncertainties (including charm) in the SM, the so called $Q_i$ observables.
We present a measurement of angular observables and a test of lepton flavor universality in the $Bto K^ast ell^+ell^-$ decay, where $ell$ is either $e$ or $mu$. The analysis is performed on a data sample corresponding to an integrated luminosity of $711~mathrm{fb}^{-1}$ containing $772times 10^{6}$ $Bbar B$ pairs, collected at the $Upsilon(4S)$ resonance with the Belle detector at the asymmetric-energy $e^+e^-$ collider KEKB. The result is consistent with Standard Model (SM) expectations, where the largest discrepancy from a SM prediction is observed in the muon modes with a local significance of $2.6sigma$.
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