$B \to K \ell^{+}\ell^{-}$ decay at large hadronic recoil

Abstract

We predict the amplitude of the $B\to K \ell^+\ell^-$ decay in the region of the dilepton invariant mass squared $0<q^2\leq m_{J/ψ}^2$, that is, at large hadronic recoil. The $B\to K$ 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 $B\to K\ell^+\ell^-$ at large hadronic recoil is moderate. The main uncertainty of the predicted $B\to K \ell^+\ell^-$ partial width is caused by the $B\to K$ 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.