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Two-loop Corrections to the B to pi Form Factor from QCD Sum Rules on the Light-Cone and |V(ub)|
High Energy Physics - Phenomenology · Submitted 7 Mar 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This suggests the insensitivity of the form factors calculated in the light-cone sum rules approach to this source of radiative corrections.
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The abstract, sentence by sentence
We calculate the leading-twist O(alphas^2 beta0) corrections to the B to pi transition form factor f+(0) in light-cone sum rules. We find that, as expected, there is a cancellation between the O(alphas^2 beta0) corrections to fB f+(0) and the large corresponding corrections to fB, calculated in QCD sum rules. This suggests the insensitivity of the form factors calculated in the light-cone sum rules approach to this source of radiative corrections. We further obtain an improved determination of the CKM matrix element |V(ub)|, using latest results from BaBar and Belle for f+(0)|V(ub)|.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We calculate the leading-twist O(alphas^2 beta0) corrections to the B to pi transition form factor f+(0) in light-cone sum rules. | contribution 1.00 | 0.96 | 0.07 | asserted 1.00 |
| s1 | We find that, as expected, there is a cancellation between the O(alphas^2 beta0) corrections to fB f+(0) and the large corresponding corrections to fB, calculated in QCD sum rules. | result 1.00 | 0.95 | 0.37 | asserted 1.00 |
| s2 | This suggests the insensitivity of the form factors calculated in the light-cone sum rules approach to this source of radiative corrections. | interpretation 1.00 | 0.52 | 0.35 | hedged possibility 1.00 |
| s3 | We further obtain an improved determination of the CKM matrix element |V(ub)|, using latest results from BaBar and Belle for f+(0)|V(ub)|. | result 0.93 | 0.93 | 0.25 | asserted 1.00 |
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The paper
Original abstract
We calculate the leading-twist O(alphas^2 beta0) corrections to the B to pi transition form factor f+(0) in light-cone sum rules. We find that, as expected, there is a cancellation between the O(alphas^2 beta0) corrections to fB f+(0) and the large corresponding corrections to fB, calculated in QCD sum rules. This suggests the insensitivity of the form factors calculated in the light-cone sum rules approach to this source of radiative corrections. We further obtain an improved determination of the CKM matrix element |V(ub)|, using latest results from BaBar and Belle for f+(0)|V(ub)|.
Human review
References
How the literature uses it
39 arXiv papers cite this in 53 sentences
Papers citing it · 28 sentences without a confident label
Uses its data or values 9 papers
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The LCSR contribution to the total $χ^2$ is: [equation] where $f_+^LCSR(0) = 0.261^+0.020_-0.023$ from [ref] .
Study of Exclusive B->X_u l nu Decays and Extraction of |V_{ub}| using Full Reconstruction Tagging at the Belle Experiment · Extraction of $|V_ub|$ · 1.00
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In this work, we use $f_+(0)=0.261^+0.020_-0.023$ determined in a light-cone sum rules calculation [ref] [Actually, for this quantity we use $f_+(0)=0.2595±0.0215$, where we have symmetrised the errors.].
Study of $B\to\pi\ell\nu_{\ell}$ and $B^{+}\to\eta^{(\prime)}\ell^{+}\nu_{\ell}$ decays and determination of $|V_{ub}|$ · Fits to the $B→πℓν_ℓ$ BaBar and Belle data · 1.00
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Afterwards, the LECs could be either determined by fitting to the results obtained in the LQCD analyses of the $D→π(K̅)$ decays carried out in Refs. [ref] or to the LQCD and LCSR combined $B̅→π$ and $B̅_s→K$ scalar form factors reported in Refs. [ref] and [ref] , respectively.
Heavy-to-light scalar form factors from Muskhelishvili-Omn\`es dispersion relations · Introduction · 0.83
Compares with it 6 papers
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Concerning the form factor values at $q^2=0$, we obtain: [equation] which can be compared with the output values: $f_+,0^Bπ(0)=0.253(11)$ [ref] and $f_+,0^B_sK(0)=0.135(50)$ [ref] from the FNAL/MILC Lattice Collaborations; $f_+,0^Bπ(0)=0.26^+0.04_-0.03$ [ref] and $f_+,0^B_sK(0)=0.30^+0.04_-0.03$ [ref] , $f_+,0^Bπ(0)=0.301(23)$ and $f_+,0^B_sK(0)=0.336(23)$ [ref] , and $f_+^Bπ(0)=0.252^+0.019_-0.028$ [ref] from light-cone sum rules; $f_+,0^Bπ(0)=f_+,0^B_sK(0)=0.26^+0.04_-0.03±0.02$ from perturbative QCD [ref] ; and $f_+,0^B_sK(0)=0.284(14)$ from relativistic quark model [ref] .
Pad\'{e} approximants to $B\to\pi\ell\nu_{\ell}$ and $B_{s}\to K\ell\nu_{\ell}$ and determination of $|V_{ub}|$ · Combined fits to the decays $B→πℓν_ℓ$ and $B_s→Kℓν_ℓ$ · 0.99
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On the other hand, our result and the one in [ref] exhibit a tension with the calculation [ref] (and the partial NNLO update [ref] ).
Extrapolation and unitarity bounds for the $B \to \pi$ form factor · Calculation of the form factor from LCSR and uncertainty analysis · 0.85
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Also notice that the fits to BaBar11 experimental data lead the worst $χ^2/dof$, in agreement with Ref. [ref] , and the largest values for $|V_ub|$, in line with Ref. [ref] but in contradiction with Refs. [ref] .
Study of $B\to\pi\ell\nu_{\ell}$ and $B^{+}\to\eta^{(\prime)}\ell^{+}\nu_{\ell}$ decays and determination of $|V_{ub}|$ · Fits to the $B→πℓν_ℓ$ BaBar and Belle data · 0.84
Cites it as background 7 papers
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Because of the appearance of the endpoint singularity in the factorization of the heavy-to-light form factors, the form factors are regarded, in many approaches, as dominated by long-distance QCD dynamics and can be calculated only with non-perturbative methods, such as Lattice QCD, (Light-Cone) QCD Sum Rules, et al. In [ref] , the light-cone sum rules (LCSR) with pion light-cone distribution amplitudes (LCDAs) has been employed to study the $B →π$ form factors, and next-to-leading-order (NLO) corrections to the twist-2 and the twist-3 terms as well as renormalization-group (RG) evolution effects [ref] have been considered.
Renormalization group equation improved analysis of $B \to \pi$ form factors from Light-Cone Sum Rules · INTRODUCTION · 0.85
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The precise determination of the CKM matrix element $V_ub$ remains an important goal in flavour physics, instrumental in performing stringent tests of the CKM matrix unitarity, see [ref] for a review. $|V_ub|$ can be extracted from $b→u ℓν$ decays, and in in particular from $B→πℓν$, using lattice QCD [ref] or light-cone sum rules [ref] calculations of the relevant form factors.
NNVub: a Neural Network Approach to $B\to X_u \ell \nu$ · Introduction · 0.90
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Meanwhile, there are also several theoretical non-perturbative methods which allows one to determine this form factor but usually in a limited $q^2$-range, for example the LCSRs [ref] and the $k_T$-factorization approach [ref] , which are often invoked in estimating the vector $B →π$ transition form factor.
Precise Calculation of the Dilepton Invariant-Mass Spectrum and the Decay Rate in $B^\pm \to \pi^\pm \mu^+ \mu^-$ in the SM · Introduction · 0.81
What it cites · 50 sentences without a confident label
Uses the method or tool of 3 papers
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These should be chosen such that the following conditions are met: * the sum rule exhibits little dependence on, but a clear extremum as a function of these parameters; * the corresponding sum rule for $m_B$, which can be obtained by differentiating the sum rule for $f_B$ or $f_+(0)f_B$ by $1/M^2$, is fulfilled to $0.1%$, as in Ref. [ref] ; * the continuum contribution is under control, i.e. we impose that the integral of the spectral density between $s_0$ and $∞$ should be approximately 25-30% of the $B$ contribution, between $m_b^2$ and $s_0$, for $f_+(0)f_B$, and 50% for $f_B$; * as far as possible, the contributions of higher orders in perturbation theory and twists should be suppressed.
New Results on B->pi, K, eta Decay Formfactors from Light-Cone Sum Rules · Numerical analysis · 0.91
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We can express $ρ^(2)_pert(s)$ in terms of the quantity $R^(2),s_FL(s)$, kindly provided by the authors of Ref. [ref] in publically available code, via [equation] To obtain the $𝒪(α_s^2 β_0)$ result, $N_f$ in $ρ_pert(s)$ should be replaced by $-3/2 β_0$.
Heavy-light current correlators at order $\alpha_s^2$ in QCD and HQET · Decay constant $f_B$ · 0.85
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We perform the traces using the package [ref] , and expand the hypergeometric functions using the Mathematica package [ref] .
HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters · Calculation of the fermion bubble diagrams · 1.00
Uses data or values from 8 papers
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However, as this is a LCSR calculation, we accordingly adopt $a_2,4(1 GeV)$ from Ref. [ref] where the LCSR result for the pion electro-magnetic form factor [ref] is fitted to experimental data [ref] .
$B \to \pi \ell \nu_l$ Width and $|V_{ub}|$ from QCD Light-Cone Sum Rules · Numerical analysis · 0.93
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However, as this is a LCSR calculation, we accordingly adopt $a_2,4(1 GeV)$ from Ref. [ref] where the LCSR result for the pion electro-magnetic form factor [ref] is fitted to experimental data [ref] .
Charged pion form factor between Q^2=0.60 and 2.45 GeV^2. II. Determination of, and results for, the pion form factor · Numerical analysis · 0.93
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However, as this is a LCSR calculation, we accordingly adopt $a_2,4(1 GeV)$ from Ref. [ref] where the LCSR result for the pion electro-magnetic form factor [ref] is fitted to experimental data [ref] .
Exploring Light-Cone Sum Rules for Pion and Kaon Form Factors · Numerical analysis · 0.93
Compares with 4 papers
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They are also in good agreement with the most recent value obtained from LCSR in Ref. [ref] , $|V_ub|=(3.50^+0.38_-0.33|_th.±0.11|_exp.)10^-3$.
$B \to \pi \ell \nu_l$ Width and $|V_{ub}|$ from QCD Light-Cone Sum Rules · Determination of $|V_ub|$ · 0.91
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We find that although there is a slight tension between Refs [ref] and [ref] , these predictions are on the whole in keeping with the CKMFitter result [ref] , $|V_ub|=(3.501^+0.196_-0.087)10^-3$ and the UTFit result [ref] , $|V_ub|=(3.64±0.11)10^-3$.
Predictions of selected flavour observables within the Standard Model · Determination of $|V_ub|$ · 0.91
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We find that although there is a slight tension between Refs [ref] and [ref] , these predictions are on the whole in keeping with the CKMFitter result [ref] , $|V_ub|=(3.501^+0.196_-0.087)10^-3$ and the UTFit result [ref] , $|V_ub|=(3.64±0.11)10^-3$.
Study of B --> pi l nu and B --> rho l nu Decays and Determination of |V_ub| · Determination of $|V_ub|$ · 0.91
Cites as background 9 papers
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The next-to-leading order (NLO) twist-2 corrections to $f_+(q^2)$ were first calculated in LCSR in Ref. [ref] and the leading order (LO) corrections up to twist-4 were calculated in Ref. [ref] .
Perturbative QCD Correction to the $B\to\pi$ Transition Form Factor · Introduction · 0.93
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The next-to-leading order (NLO) twist-2 corrections to $f_+(q^2)$ were first calculated in LCSR in Ref. [ref] and the leading order (LO) corrections up to twist-4 were calculated in Ref. [ref] .
Predictions on $B \to \pi \bar{l} \nu_l$, $D \to \pi \bar{l} \nu_l$ and $D\to K \bar{l} \nu_l$ from QCD Light-Cone Sum Rules · Introduction · 0.93
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A more recent update where the $MS$ mass is used in place of the pole mass for $m_b$ can be found in Ref. [ref] .
$B \to \pi \ell \nu_l$ Width and $|V_{ub}|$ from QCD Light-Cone Sum Rules · Introduction · 0.82
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