$B\to \pi \pi$ Form Factors from Light-Cone Sum Rules with $B$-meson Distribution Amplitudes

Abstract

We study $B\to \pi \pi$ form factors using QCD light-cone sum rules with $B$-meson distribution amplitudes. These form factors describe the semileptonic decay $B\to \pi \pi \ell {\bar{\nu }}_{\ell }$, and constitute an essential input in $B\to \pi \pi {\ell }^{+}{\ell }^{-}$ and $B\to \pi \pi \pi$ decays. We employ the correlation functions where a dipion isospin-one state is interpolated by the vector light-quark current. We obtain sum rules where convolutions of the $P$-wave ${\bar{B}}^0\to {\pi }^{+}{\pi }^0$ form factors with the time-like pion vector form factor are related to universal $B$-meson distribution amplitudes. These sum rules are valid in the kinematic regime where the dipion state has a large energy and a low invariant mass, and reproduce analytically the known light-cone sum rules for $B\to \rho$ form factors in the limit of $\rho$-dominance with zero width, thus providing a systematics for so-far-unaccounted corrections to $B\to \rho$ transitions. Using data for the pion vector form factor, we estimate finite width-effects and the contribution of excited $\rho$-resonances to the $B\to \pi \pi$ form factors. We find that these contributions amount up to $\sim 20\%$ in the small dipion mass region where they can be effectively regarded as a nonresonant ($P$-wave) background to the $B\to \rho$ transition.

arXiv comment28 pages, 3 figures. A few comments added. Version published in JHEP

References in corpus (37)

• Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil
• B_{d,s}->rho, omega, K*, phi Decay Form Factors from Light-Cone Sum Rules Revisited
• $B\to V{\ell }^{+}{\ell }^{-}$ in the Standard Model from Light-Cone Sum Rules
• The ratios of the light quark masses
• Charm-loop effect in $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ and $B\to K^{\ast }\gamma$
• Asymptotics of Heavy-Meson Form Factors
• Model-independent description of $B\to \pi l\nu$ decays and a determination of $|V_{ub}|$
• Precise measurement of the e+ e- to pi+ pi- (gamma) cross section with the Initial State Radiation method at BABAR
• Probing partonic structure in gamma* gamma -> pi pi near threshold
• The B-Meson Distribution Amplitude in QCD
• Hard exclusive electroproduction of two pions and their resonances
• High-Statistics Study of the tau^- -> pi^- pi^0 nu_tau Decay
• Form Factors from Light-Cone Sum Rules with B-Meson Distribution Amplitudes
• B_l4 decays and the extraction of |V_ub|
• Study of Exclusive B->X_u l nu Decays and Extraction of |V_{ub}| using Full Reconstruction Tagging at the Belle Experiment
• Decay constants of heavy-light vector mesons from QCD sum rules
• B meson distribution amplitude from B --> γl ν
• QCD corrections to $B\to \pi$ form factors from light-cone sum rules
• Modeling the Pion and Kaon Form Factors in the Timelike Region
• NNLO vertex corrections to non-leptonic B decays: Tree amplitudes
• A new Parameterization for the Pion Vector Form Factor
• Three-Body Non-Leptonic B Decays and QCD Factorization
• $B$-Meson Distribution Amplitude from the $B\to \pi$ Form Factor
• $B\to D^{(\ast )}$ Form Factors from QCD Light-Cone Sum Rules
• Resonance chiral Lagrangian currents and tau decay Monte Carlo
• Soft contribution to $B\to \gamma \ell {\nu }_{\ell }$ and the $B$-meson distribution amplitude
• Light-cone sum rules in soft-collinear effective theory
• Disentangling the Decay Observables in $B^{-}\to {\pi }^{+}{\pi }^{-}{\ell }^{-}{\bar{\nu }}_{\ell }$
• Condensates in Quantum Chromodynamics
• Narrow resonances studies with the radiative return method
• Form factors in $B\to \pi \pi \ell {\bar{\nu }}_{\ell }$ from QCD light-cone sum rules
• Pion form factor in large $N_c$ QCD
• Pion Form Factor Phase, PIon Pion Elasticity and New Electron-Positron Data
• QCD Factorization for $B\to \pi \pi \ell \nu$ Decays at Large Dipion Masses
• Search for B+ -> l+ nu gamma decays with hadronic tagging using the full Belle data sample
• Electromagnetic form factor of pion in the field theory inspired approach
• Charmless Non-Leptonic Multi-Body B decays

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