A model-independent parameterization of $B\to \pi \pi \ell \nu$ decays

Abstract

We introduce a novel parameterization of $B\to \pi \pi \ell \nu$ form factors relying on partial-wave decompositions and series expansions in suitable variables. We bound the expansion coefficients through unitarity and include left-hand cut contributions using established dispersive methods. The two-hadron lineshapes are treated in a model-independent manner using Omnès functions, thus allowing for a data-driven determination of the expansion parameters. We study the underlying composition of the di-pion system in $B\to \pi \pi \ell \nu$ decays through fits to differential spectra of $B^{+}\to {\pi }^{+}{\pi }^{-}{\ell }^{+}\nu$ measured by the Belle experiment. In contrast to previous works, we are able to study the full phase-space and are not limited to certain kinematic regions. As a consequence, we extract branching fractions for the different partial waves of the di-pion system. We find: \begin{align*} \mathcal{B}(B^+\rightarrow (π^+ π^-)_S \ell^+ ν) &= 2.2^{+1.4}_{-1.0}\times 10^{-5}\,,\\ \mathcal{B}(B^+\rightarrow (π^+ π^-)_P \ell^+ν) &= 19.6^{+2.8}_{-2.7}\times 10^{-5}\,,\\ \mathcal{B}(B^+\rightarrow (π^+ π^-)_D \ell^+ ν) &= 3.5^{+1.3}_{-1.1}\times 10^{-5}\,.\\ \end{align*} In addition, we derive predictions for the thus far unobserved $B^{+}\to {\pi }^0{\pi }^0{\ell }^{+}\nu$ decay and obtain a sizeable branching fraction of $\mathcal{B}(B^{+}\to {\pi }^0{\pi }^0{\ell }^{+}\nu )=2.9_{-0.7}^{+0.9}\times 10^{-5}$.

arXiv comment22 pages, 11 amazing figures; v2: typos corrected, version as published in PRD

References in corpus (71)

• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• Two-pion contribution to hadronic vacuum polarization
• $B\to V{\ell }^{+}{\ell }^{-}$ in the Standard Model from Light-Cone Sum Rules
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Roy equation analysis of pi pi scattering
• 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
• Precision Corrections to Dispersive Bounds on Form Factors
• Reanalysis of Hadronic Cross Section Measurements at CMD-2
• Precise Measurement of the e+ e- --> pi+ pi- (gamma) Cross Section with the Initial-State Radiation Method at BABAR
• High-statistics measurement of the pion form factor in the rho-meson energy range with the CMD-2 detector
• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• Update of the e^+e^-\toπ^+π^- cross section measured by SND detector in the energy region 400<\sqrt{s}<1000 MeV
• Measurement of sigma(e+ e- -> pi+ pi-) from threshold to 0.85 GeV^2 using Initial State Radiation with the KLOE detector
• Measurement of e+e- -> pi+pi- cross section with CMD-2 around rho-meson
• Measurement of $\sigma (e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma (\gamma ))$ and the dipion contribution to the muon anomaly with the KLOE detector
• Precision measurement of $\sigma (e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma )/\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma )$ and determination of the ${\pi }^{+}{\pi }^{-}$ contribution to the muon anomaly with the KLOE detector
• Pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• B_l4 decays and the extraction of |V_ub|
• Regge analysis of the pi pi scattering amplitude
• Study of B --> pi l nu and B --> rho l nu Decays and Determination 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
• Measurement of the e+e- -> pi+pi- cross section with the CMD-2 detector in the 370-520 MeV c.m. energy range
• Model-Independent Extraction of |V_{cb}| Using Dispersion Relations
• omega --> pi0 gamma* and phi --> pi0 gamma* Transition form factors in dispersion theory
• Non-local matrix elements in $B_{(s)}\to \{K^{(\ast )},\varphi \}{\ell }^{+}{\ell }^{-}$
• Measurement of resonant and $CP$ components in ${\overline{B}}_s^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays
• Theory determination of $\bar{B}\to D^{(\ast )}{\ell }^{-}\bar{\nu }$ form factors at $\mathcal{O}(1/m_c^2)$
• Study of the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ in the energy region 400<\sqrt[]{s}<1000 MeV
• Measurement of the resonant and CP components in ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays
• A model-independent analysis of final-state interactions in \bar B_{d/s}^0 --> J/psi pi pi
• A new parametrization for the scalar pion form factors
• Rho-Omega Mixing and the Pion Form Factor in the Time-like Region
• EOS -- A Software for Flavor Physics Phenomenology
• Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
• Dispersive Analysis of $B\to K^{(\ast )}$ and $B_s\to \varphi$ Form Factors
• Disentangling the Decay Observables in $B^{-}\to {\pi }^{+}{\pi }^{-}{\ell }^{-}{\bar{\nu }}_{\ell }$
• $B\to \pi \pi$ Form Factors from Light-Cone Sum Rules with $B$-meson Distribution Amplitudes
• Light-Cone Sum Rules for $B\to K\pi$ Form Factors and Applications to Rare Decays
• Study of $D^{+}\to K^{-}{\pi }^{+}{e}^{+}{\nu }_e$
• Form factors in $B\to \pi \pi \ell {\bar{\nu }}_{\ell }$ from QCD light-cone sum rules
• Search for $B^{+}\to {\mu }^{+}{\nu }_{\mu }$ and $B^{+}\to {\mu }^{+}N$ with inclusive tagging
• Measurement Of |V_ub| From Inclusive Charmless Semileptonic B Decays
• A Dispersive Treatment of $K_{\ell 4}$ Decays
• First observation of the decay $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ and a measurement of $|V_{ub}|/|V_{cb}|$
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• Search for the rare decay of $B^{+}\to {\ell }^{+}{\nu }_{\ell }\gamma$ with improved hadronic tagging
• Measurements of Partial Branching Fractions of Inclusive $B\to X_u{\ell }^{+}{\nu }_{\ell }$ Decays with Hadronic Tagging
• 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
• Study of the decay $D^0\to {\bar{K}}^0{\pi }^{-}{e}^{+}{\nu }_e$
• Study of the rare $B_s^0$ and $B^0$ decays into the ${\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ final state
• A dispersive analysis of ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\ell }^{+}{\ell }^{-}\gamma$
• Branching fraction measurement of B -> omega l nu decays
• $B\to \rho l\bar{\nu }$ and $\omega l\bar{\nu }$ in and beyond the Standard Model: Improved predictions and $|V_{ub}|$
• How to employ ${\bar{B}}_d^0\to J/\psi (\pi \eta ,\bar{K}K)$ decays to extract information on $\pi \eta$ scattering
• Dispersive bounds for local form factors in ${\Lambda }_b\to \Lambda$ transitions
• Toward a complete description of $b\to u{\ell }^{-}\bar{\nu }$ decays within the Weak Effective Theory
• Measurement of the Branching Fraction of the Decay ${\mathbf{B}}^{+}\to {\mathbf{\pi }}^{+}{\mathbf{\pi }}^{-}{\mathbf{\ell }}^{+}{\mathbf{\nu }}_{\mathbf{\ell }}$ in Fully Reconstructed Events at Belle
• Revisiting $B\to \pi \pi \ell \nu$ at Large Dipion Masses
• Global parametrizations of $\pi \pi$ scattering with dispersive constraints: Beyond the S0 wave
• Unitarity bounds with subthreshold and anomalous cuts for $b$-hadron decays
• Light-Cone Sum Rules for $S$-wave $B\to K\pi$ Form Factors
• $B\to \rho \ell \bar{\nu }$ resonance form factors from $B\to \pi \pi \ell \bar{\nu }$ in lattice QCD
• Measurement of the B+ --> omega l+ nu branching fraction with semileptonically tagged B mesons
• Moments of heavy-light current correlators up to three loops
• A Simple Parametrisation of the Pion Form Factor
• Study of the semileptonic decay $D^0\to {\bar{K}}^0{\pi }^{-}{e}^{+}{\nu }_e$
• Role of $\rho -\omega$ interference in semileptonic $B\to {\pi }^{+}{\pi }^{-}\ell {\bar{\nu }}_{\ell }$ decays
• Inclusive semileptonic $B_s^0$ meson decays at the LHC via a sum-of-exclusive modes technique: possibilities and prospects

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