Light-cone sum rules for S-wave B → Kπ form factors

Abstract

We derive a set of light-cone sum rules relating the S-wave B → Kπ 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 → Kπ form factors obtained earlier. We then use the new sum rules to estimate the S-wave contributions to B → Kπℓℓ decays as a function of the Kπ invariant mass. We pay particular attention to the fact that the S-wave Kπ 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^{ast }(1430) . We observe an overall compatibility and discuss possible improvements of our model to obtain a better description of the B → Kπ form factors over a large kinematic range.