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Comment on form factor shape and extraction of |V_ub| from B --> pi l nu
High Energy Physics - Phenomenology · Submitted 9 Sep 2005
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Together with current and future lattice determinations of the form factor normalization this result gives an accurate, model independent determination of |V_ub|.
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The abstract, sentence by sentence
We point out that current experimental data for partial B --> pi l nu branching fractions reduce the theoretical input required for a precise extraction of |V_ub| to the form factor normalization at a single value of the pion energy. We show that the heavy-quark expansion provides a bound on the form factor shape that is orders of magnitude more stringent than conventional unitarity bounds. We find |V_ub| = (3.7 +/- 0.2 +/- 0.1) x [0.8/F_+(16 GeV^2)]. The first error is from the experimental branching fractions, and the second is a conservative bound on the residual form factor shape uncertainty, both of which will improve with additional data. Together with current and future lattice determinations of the form factor normalization this result gives an accurate, model independent determination of |V_ub|. We further extract semileptonic shape observables such as |V_ub F_+(0)| = 0.92 +/- 0.11 +/- 0.03 and show how these observables can be used to test factorization and to determine low-energy parameters in hadronic B decays.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We point out that current experimental data for partial B --> pi l nu branching fractions reduce the theoretical input required for a precise extraction of |V_ub| to the form factor normalization at a single value of the pion energy. | contribution 0.51 | 0.47 | 0.34 | asserted 0.99 |
| s1 | We show that the heavy-quark expansion provides a bound on the form factor shape that is orders of magnitude more stringent than conventional unitarity bounds. | contribution 0.48 | 0.88 | 0.10 | asserted 1.00 |
| s2 | We find |V_ub| = (3.7 +/- 0.2 +/- 0.1) x [0.8/F_+(16 GeV^2)]. | result 1.00 | 0.96 | 0.60 | asserted 1.00 |
| s3 | The first error is from the experimental branching fractions, and the second is a conservative bound on the residual form factor shape uncertainty, both of which will improve with additional data. | interpretation 0.83 | 0.64 | 0.07 | asserted 0.87 |
| s4 | Together with current and future lattice determinations of the form factor normalization this result gives an accurate, model independent determination of |V_ub|. | interpretation 0.99 | 0.59 | 0.50 | asserted 0.96 |
| s5 | We further extract semileptonic shape observables such as |V_ub F_+(0)| = 0.92 +/- 0.11 +/- 0.03 and show how these observables can be used to test factorization and to determine low-energy parameters in hadronic B decays. | result 0.77 | 0.95 | 0.08 | asserted 0.99 |
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The paper
Original abstract
We point out that current experimental data for partial B --> pi l nu branching fractions reduce the theoretical input required for a precise extraction of |V_ub| to the form factor normalization at a single value of the pion energy. We show that the heavy-quark expansion provides a bound on the form factor shape that is orders of magnitude more stringent than conventional unitarity bounds. We find |V_ub| = (3.7 +/- 0.2 +/- 0.1) x [0.8/F_+(16 GeV^2)]. The first error is from the experimental branching fractions, and the second is a conservative bound on the residual form factor shape uncertainty, both of which will improve with additional data. Together with current and future lattice determinations of the form factor normalization this result gives an accurate, model independent determination of |V_ub|. We further extract semileptonic shape observables such as |V_ub F_+(0)| = 0.92 +/- 0.11 +/- 0.03 and show how these observables can be used to test factorization and to determine low-energy parameters in hadronic B decays.
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References
How the literature uses it
41 arXiv papers cite this in 70 sentences
Papers citing it · 43 sentences without a confident label
Uses its method or tool 11 papers
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We obtain our preferred results for the form factors $f_+(q^2)$ and $f_0(q^2)$ using the BCL form of the $z$-expansion [ref] and imposing the kinematic constraint $f_+(0) = f_0(0)$ and a constraint on the sum of the coefficients for $f_+(q^2)$ based on heavy-quark power counting [ref] .
$B \to \pi \ell \nu$ and $B_s \to K \ell \nu$ form factors and $|V_{ub}|$ from 2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks · Results and conclusions · 1.00
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The analyticity-based parameterization described in Ref. [ref] captures the energy-dependence of the form factors throughout the kinematic domains, so using it to fit the data and extract CKM matrix elements does not introduce model-dependent systematic errors.
Progress on charm semileptonic form factors from 2+1 flavor lattice QCD · Renormalization and chiral-continuum-energy extrapolation-interpolation · 0.80
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For an arbitrary function $g$, [equation] The contribution to the integrand from a form factor $F$ is then written as $|ϕ_F|^2 |F|^2$, where the outer function $ϕ_F$ is constructed such that the product $ϕ_F F$ is free of kinematic singularities on the unit disk $|z|<1$ [ref] .
Dispersive bounds for local form factors in $\Lambda_b \to \Lambda$ transitions · Parametrization · 0.88
Compares with it 1 paper
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This is similar to the recommendations of Becher and Hill [ref] , $t_0 = t_+ - ( t_+^2 - t_+t_-)^1/2 ≈14.65 GeV^2$, and Bourrely, Caprini, and Lellouch (BCL) [ref] , $t_0=(M_B + M_K)(√(M_B) - √(M_K))^2 ≈14.69 GeV^2$.
Rare decay B -> K ll form factors from lattice QCD · Kinematic Extrapolation · 0.99
Cites it as support 2 papers
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It has only recently become clear with the advent of rigorous power-counting arguments that we can “take seriously” the expansion provided by analyticity [ref] .
Update on semileptonic charm decays · Introduction · 0.97
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A shortcoming of these parametrizations is that comparisons of lattice-QCD and experimental slope parameters can be misleading [ref] , because lattice-QCD slopes are determined near $q^2=q^2_max$, whereas experimental slopes are determined near $q^2=0$.
Visualization of semileptonic form factors from lattice QCD · Introduction · 0.96
Cites it as background 11 papers
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The analyses of the experimental data from BELLE [ref] , BABAR [ref] , CLEO [ref] and BESIII [ref] on $D →π(K) e(μ) ν$ decays are based on a variety of parameterizations for the shape of the vector form factor $f_+^D π(K)(q^2)$, like effective pole models, inspired by either dispersion relations [ref] or heavy-quark expansion arguments [ref] , the $z$-expansion method [ref] or even relativistic quark model predictions [ref] .
Extraction of $|V_{cd}|$ and $|V_{cs}|$ from experimental decay rates using lattice QCD $D \to \pi(K) \ell \nu$ form factors · Introduction · 0.86
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These include the two-parameter Bećirević-Kaidalov (BK) ansatz [ref] , the three-parameter Ball-Zwicky (BZ) ansatz [ref] , the so-called Series Expansion (SE) ansatz [ref] , as well as the representation from the Omnes solution to the dispersive bounds [ref] .
Determination of the strong coupling $g_{B^* B\pi}$ from semi-leptonic $B\to \pi \ell \nu$ decay · Introduction · 0.90
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In order to interpolate between the results for small and large momentum transfers, various form factor parameterizations have been suggested in the literature: the two-parameter Bećirević-Kaidalov (BK) ansatz [ref] , the three-parameter Ball-Zwicky (BZ) ansatz [ref] , the so-called Series Expansion (SE) representation [ref] , as well as the representation from the Omnes solution to the dispersive bounds [ref] .
Constraints on B--->pi,K transition form factors from exclusive semileptonic D-meson decays · Introduction · 0.93
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