Light-cone sum rules for $B\to K\pi$ form factors and applications to rare decays

International audienceWe derive a set of light-cone sum rules relating the hadronic form factors relevant for B → Kπℓ$^{+}$ℓ$^{−}$ decays to the B-meson light-cone distribution amplitudes (LCDAs). We obtain the sum rule relations for all B → K π form factors of (axial)vector and (pseudo)tensor b → s currents with a P -wave K π 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$^{∗}$μμ branching fractions. We also discuss B → K π transitions outside the K$^{∗}$ window, and explain how measurements of B → K πℓℓ observables above the K$^{∗}$ region can be used to further constrain the B → K$^{∗}$ form factors