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.

arXiv comment51 pages, many figures

References in corpus (46)

• FLAG Review 2019
• RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
• FLAG Review 2021
• Symmetries and Asymmetries of B -> K* mu+ mu- Decays in the Standard Model and Beyond
• QCD at Low Energies
• Charm-loop effect in $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ and $B\to K^{\ast }\gamma$
• Understanding the B->K*mu+mu- Anomaly
• Asymptotics of Heavy-Meson Form Factors
• Global analysis of $b\to s\ell \ell$ anomalies
• Optimizing the basis of B->K*ll observables in the full kinematic range
• Implications from clean observables for the binned analysis of B -> K*ll at large recoil
• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• The B-Meson Distribution Amplitude in QCD
• Electromagnetic Logarithms in B -> X_s l+ l-
• Review of Lepton Universality tests in B decays
• $B\to P$ and $B\to V$ Form Factors from $B$-Meson Light-Cone Sum Rules beyond Leading Twist
• Form Factors from Light-Cone Sum Rules with B-Meson Distribution Amplitudes
• Strangeness-changing scalar form factors
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Decay constants of heavy-light vector mesons from QCD sum rules
• Improved Theory Predictions and Global Analysis of Exclusive $\mathbf{b}\to \mathbf{s}{\mathbf{\mu }}^{+}{\mathbf{\mu }}^{-}$ Processes
• QCD corrections to $B\to \pi$ form factors from light-cone sum rules
• Non-local matrix elements in $B_{(s)}\to \{K^{(\ast )},\varphi \}{\ell }^{+}{\ell }^{-}$
• The Strange Quark Mass from QCD Sum Rules
• Three-Body Non-Leptonic B Decays and QCD Factorization
• $B$-Meson Distribution Amplitude from the $B\to \pi$ Form Factor
• Higher-twist B-meson Distribution Amplitudes in HQET
• Impact of $B\to K_0^{\ast }{\ell }^{+}{\ell }^{-}$ on the New Physics search in $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ decay
• Analyticity constraints on the strangeness changing vector current and applications to $\tau \to K\pi {\nu }_{\tau }$, $\tau \to K\pi \pi {\nu }_{\tau }$
• Order-${\alpha }_s^3$ determination of the strange quark mass
• $B\to \pi \pi$ Form Factors from Light-Cone Sum Rules with $B$-meson Distribution Amplitudes
• The pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV
• Light-Cone Sum Rules for $B\to K\pi$ Form Factors and Applications to Rare Decays
• Strange Quark Mass from Pseudoscalar Sum Rule with O(alpha_s^4) Accuracy
• 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
• Inverse moment of the $B_s$-meson distribution amplitude from QCD sum rule
• 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
• CP Violation in Three-body $B$ Decays: A Model Ansatz
• Exact NLO Matching and Analyticity in $b\to s\ell \ell$
• First determination of $f_{+}(0)|V_{us}|$ from a combined analysis of $\tau \to K\pi {\nu }_{\tau }$ decay and $\pi K$ scattering with constraints from $K_{\ell 3}$ decays
• Three-Body Non-Leptonic Heavy-to-heavy $B$ Decays at NNLO in QCD
• On the scalar $\pi K$ form factor beyond the elastic region
• A complete description of P- and S-wave contributions to the $B^0\to K^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ decay

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