Light-cone sum rules for B → K π form factors and applications to rare decays

We derive a set of light-cone sum rules relating the hadronic form factors relevant for B -> K pi l(+)l(-) decays to the B-meson light-cone distribution amplitudes (LCDAs). We obtain the sum rule relations for all B -> K pi form factors of (axial)vector and (pseudo)tensor b -> s currents with a P -wave K pi system. Our results reduce to the known light-cone sum rules for B -> K* form factors in the limit of a single narrow-width resonance. We update the operator-product expansion for the underlying correlation function by including a more complete set of B-meson LCDAs with higher twists, and produce numerical results for all B -> K* form factors in the narrow-width limit. We then use the new sum rules to estimate the effect of a non-vanishing K* width in B -> K* transitions, and find that this effect is universal and increases the factorizable part of the rate of B -> K*X decays by a factor of 20%. This effect, by itself, goes in the direction of increasing the current tension in the differential B -> K*mu mu branching fractions. We also discuss B -> K pi transitions outside the K* window, and explain how measurements of B -> K pi ll observables above the K* region can be used to further constrain the B -> K* form factors.