Light-Cone Sum Rules for $B\to K\pi$ Form Factors and Applications to Rare Decays

Understand

We derive a set of light-cone sum rules relating the hadronic form factors relevant for $B\to K\pi\ell^+\ell^-$ decays to the $B$-meson light-cone distribution amplitudes (LCDAs).

• We obtain the sum rule relations for all $B\to K\pi$ form factors of (axial)vector and (pseudo)tensor $b\to s$ currents with a $P$-wave $K\pi$ system.
• Our results reduce to the known light-cone sum rules for $B\to K^*$ 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 $B\to K^*$ form factors in the narrow-width limit.