Timelike-helicity $B\to \pi \pi$ form factor from light-cone sum rules with dipion distribution amplitudes

Abstract

We complete the set of QCD light-cone sum rules for $B\to \pi \pi$ transition form factors, deriving a new sum rule for the timelike-helicity form factor $F_t$ in terms of dipion distribution amplitudes. This sum rule, in the leading twist-2 approximation, is directly related to the pion vector form factor. Employing a relation between $F_t$ and other $B\to \pi \pi$ form factors we obtain also the longitudinal-helicity form factor $F_0$. In this way, all four (axial-)vector $B\to \pi \pi$ form factors are predicted from light-cone sum rules with dipion distribution amplitudes. These results are valid for small dipion masses with large momentum.

7 pages, 3 figures

References in corpus (1)

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