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.

arXiv comment19 pages, 9 figures, references and the corresponding descriptions are added

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• ${\bar{B}}_s\to f_0(980)$ form factors and the width effect from light-cone sum rules
• Branching Fractions and CP Violation in $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ Decays
• S-wave contributions in ${\bar{B}}_s^0\to (D^0,{\bar{D}}^0){\pi }^{+}{\pi }^{-}$ within perturbative QCD approach
• Probing isovector scalar mesons in the charmless three-body $B$ decays
• Revealing chiral-odd two-meson generalized distribution amplitudes in $e^{-}{e}^{+}\to (\pi \pi )(\pi \pi )$ reactions
• Study $B_{(s)}^0$ decays into $\varphi$ and a scalar or vector meson