QCD Factorization for $B\to \pi \pi \ell \nu$ Decays at Large Dipion Masses

Abstract

We introduce a factorization formula for semi-leptonic $b\to u$ transitions in the exclusive decay mode $B^{-}\to {\pi }^{+}{\pi }^{-}{\ell }^{-}{\bar{\nu }}_{\ell }$ in the limit of large pion energies and large dipion invariant mass. One contribution can be described in terms of a universal $B\to \pi$ form factor and the convolution of a short-distance kernel $T^{\mathrm{I}}$ with the respective light-cone distribution amplitudes (LCDAs) of the positively charged pion. The second contribution, at leading power, completely factorizes, with a short-distance kernel $T^{\mathrm{II}}$ convoluted with the leading-twist LCDAs for both pions and the $B$-meson. We calculate the leading contributions to the short-distance kernels $T^{\mathrm{I}}$ and $T^{\mathrm{II}}$ in fixed-order perturbation theory, and discuss the approximate relations among the resulting $B\to \pi \pi$ partial-wave form factors. Our results provide useful theoretical constraints for phenomenological models that aim to analyze the complete $B\to \pi \pi \ell \nu$ phase space.

arXiv comment38 pages, 5 figures; v2: as published, conclusions unchanged

References in corpus (43)

• An effective field theory for collinear and soft gluons: heavy to light decays
• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• QCD factorization for B->PP and B->PV decays
• QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil
• Symmetries and Asymmetries of B -> K* mu+ mu- Decays in the Standard Model and Beyond
• Final State Interactions in Hadronic B Decays
• The Physics of the B Factories
• Implications of LHCb measurements and future prospects
• Branching fractions, polarisation and asymmetries of B -> VV decays
• Flavor Physics in the Quark Sector
• Probing New Physics Via the Transverse Amplitudes of B0-> K*0(-> K- pi+) l+l- at Large Recoil
• Factorization of heavy-to-light form factors in soft-collinear effective theory
• Resolution to the B -> pi K puzzle
• The Benefits of B ---> K* l+ l- Decays at Low Recoil
• B_l4 decays and the extraction of |V_ub|
• Towards the Identification of New Physics through Quark Flavour Violating Processes
• Form Factors for Lambda_b -> Lambda Transitions in SCET
• Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays
• NNLO vertex corrections to non-leptonic B decays: Tree amplitudes
• Spectator scattering at NLO in non-leptonic B decays: Tree amplitudes
• Three-Body Non-Leptonic B Decays and QCD Factorization
• $B\to D^{(\ast )}$ Form Factors from QCD Light-Cone Sum Rules
• NNLO Vertex Corrections in charmless hadronic B decays: Imaginary part
• Two-loop current-current operator contribution to the non-leptonic QCD penguin amplitude
• Generalized Heavy-to-Light Form Factors in Light-Cone Sum Rules
• Angular Analysis of the Decay ${\Lambda }_b\to \Lambda (\to N\pi ){\ell }^{+}{\ell }^{-}$
• Spectator scattering at NLO in non-leptonic B decays: Leading penguin amplitudes
• NNLO vertex corrections in charmless hadronic B decays: Real part
• Disentangling the Decay Observables in $B^{-}\to {\pi }^{+}{\pi }^{-}{\ell }^{-}{\bar{\nu }}_{\ell }$
• Extrapolation and unitarity bounds for the $B\to \pi$ form factor
• Hard spectator interactions in B to pi pi at order alpha_s^2
• (A)symmetries of weak decays at and near the kinematic endpoint
• ${\mathbf{B}}_{\mathbf{s}}\to {\mathbf{K}}^{(\ast )}\mathbf{\ell }\bar{\nu }$, Angular Analysis, S-wave Contributions and $|{\mathbf{V}}_{\mathbf{ub}}|$
• SCET Analysis of B -> K pi, B -> K Kbar, and B -> pi pi Decays
• Form factors in $B\to \pi \pi \ell {\bar{\nu }}_{\ell }$ from QCD light-cone sum rules
• Radiative corrections to hard spectator scattering in $B\to \pi \pi$ decays
• Extracting $B\to K^{\ast }$ Form Factors from Data
• New Physics Effects and Hadronic Form Factor Uncertainties in B -> K^* l^+ l^-
• Is there a non-Standard-Model contribution in non-leptonic b -> s decays?
• Spectator interactions and factorization in B -> pi ell nu decay
• Non-Leptonic Heavy Meson Decays - Theory Status

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