Light-Cone Sum Rules for $S$-wave $B\to K\pi$ Form Factors

We derive a set of light-cone sum rules relating the $S$-wave $B\to K \pi$ hadronic form factors to the $B$-meson light-cone distribution amplitudes (LCDAs), taking into account the complete set of LCDAs up to and including twist four. These results complement the sum rules for the $P$-wave $B\to K \pi$ form factors obtained earlier. We then use the new sum rules to estimate the $S$-wave contributions to $B\to K \pi\ell\ell$ decays as a function of the $K\pi$ invariant mass. We pay particular attention to the fact that the $S$-wave $K\pi$ spectrum cannot be modelled by a sum of Breit-Wigner resonances, and employ a more consistent dispersive coupled-channel approach. We compare our predictions for branching ratios and angular observables with LHCb measurements in two different kinematic regions, around $K^*(892)$ and $K^*_0(1430)$. We observe an overall compatibility and discuss possible improvements of our model to obtain a better description of the $B\to K\pi$ form factors over a large kinematic range.