Dipion light-cone distribution amplitudes and $B\to \pi \pi$ form factors

Abstract

We suggest to update the expansion coefficients of 2$\pi$DAs with the distribution amplitudes of light mesons evaluated from lattice QCD, with which we revisit ${\overline{B}}^0\to {\pi }^{+}{\pi }^0$ transition form factors from light-cone sum rules approach and extend the predictions from the threshold of dipion invariant mass to high energies with including the resonance intervals. We also derive $B^{-}\to {\pi }^0{\pi }^0$ transition form factors with the isoscalar dipion final state, serving as the supplement to the isovector ones to complete the set of light-cone sum rules prediction of $B\to \pi \pi$ form factors. Our numerics shows that the lowest resonance gives the dominant contribution to $P-$wave form factors, while the resonance contribution in $S-$wave is not so salient.

19 pages, 9 figures, references and the corresponding descriptions are added

References in corpus (10)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Light-cone sum rules for $B\to \pi$ form factors revisited
• Moments of pseudoscalar meson distribution amplitudes from the lattice
• $B\to \pi \ell {\nu }_l$ Width and $|V_{ub}|$ from QCD Light-Cone Sum Rules
• Light Cone Sum Rules for the pi0-gamma*-gamma Form Factor Revisited
• Lattice Results for Low Moments of Light Meson Distribution Amplitudes
• Comprehensive Amplitude Analysis of $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ and $\overline{K}K$ below 1.5 GeV
• Second moment of the pion distribution amplitude with the momentum smearing technique
• Timelike-helicity $B\to \pi \pi$ form factor from light-cone sum rules with dipion distribution amplitudes
• QCD Factorization for $B\to \pi \pi \ell \nu$ Decays at Large Dipion Masses

Cited by in corpus (2)

• Branching Fractions and CP Violation in $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ Decays
• Revealing chiral-odd two-meson generalized distribution amplitudes in $e^{-}{e}^{+}\to (\pi \pi )(\pi \pi )$ reactions