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

Abstract

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 $K^{\ast }(892)$ and $K_0^{\ast }(1430)$. We observe an overall compatibility and discuss possible improvements of our model to obtain a better description of the $B\to K\pi$ form factors over a large kinematic range.

51 pages, many figures

References in corpus (8)

• Form Factors from Light-Cone Sum Rules with B-Meson Distribution Amplitudes
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Analyticity constraints on the strangeness changing vector current and applications to $\tau \to K\pi {\nu }_{\tau }$, $\tau \to K\pi \pi {\nu }_{\tau }$
• Flavor Anomalies in Heavy Quark Decays
• CP Violation in Multibody $B$ Decays from QCD Factorization
• Strange resonance poles from $K\pi$ scattering below 1.8 GeV
• Combined analysis of the decays ${\tau }^{-}\to K_S{\pi }^{-}{\nu }_{\tau }$ and ${\tau }^{-}\to K^{-}\eta {\nu }_{\tau }$
• Timelike-helicity $B\to \pi \pi$ form factor from light-cone sum rules with dipion distribution amplitudes

Cited by in corpus (5)

• Dispersive Analysis of $B\to K^{(\ast )}$ and $B_s\to \varphi$ Form Factors
• Amplitude analysis of the $B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$ decay
• Determination of short- and long-distance contributions in $B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$ decays
• $S$-wave contribution to rare $D^0\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ decays in the Standard Model and sensitivity to New Physics
• A model-independent parameterization of $B\to \pi \pi \ell \nu$ decays