REVIEW
B -> K^* Form Factors from Flavor Data to QCD and Back
High Energy Physics - Phenomenology · Submitted 20 Aug 2013 · 75 references
Pith's verdict: A careful, useful update to the data-extracted B→K* form factor program — but the abstract's A_FB/P'_5 'agreement' is a consistency check of the OPE, not an independent form factor test.
T0 · AI review
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Referee report
The paper
The paper claims
The hadronic form factors that blur predictions for the rare decay $B^0_s$ into a $K^*$ and a lepton pair can themselves be measured from that decay's angular data, and the resulting Standard Model predictions for two benchmark observables,
The reading
What carries the argument
The load-bearing mechanism is the low-recoil operator product expansion, which at leading order in $1/m_b$ writes each transversity amplitude as $A_i^{L,R}(q^2) = C^{L,R}(q^2) f_i(q^2)$ up to corrections of order $m_b^{-1}$, with $C^{L,R}$ independent of the $K^*$ polarization. Because the short-distance coefficients cancel in ratios, the angular observables reduce to functions of the form factor ratios alone: $F_L = f_0^2/(f_0^2+f_1^2+f_0^2)$, and similarly for $A_T^{(2)}$ and $P'_4$. The second piece is the double ratio $R=(V/A_1)/(T_1/T_2)$, shown to equal $1+O(1/m_b)$ both at maximum recoil (from large-energy symmetry relations) and at low recoil (from the Isgur-Wise relations), which stitches the two kinematic ends together. The form factors themselves are parametrized by a $z$-series expansion truncated at first or second order, with the endpoint relations $F_L=1/3$, $A_T^{(2)}=-1$, $P'_4=1/2$ imposed exactly.
Extended reading notes
Core claim
The central claim is that form factor ratios in $B^0_s$ to $K^*$ transitions can be extracted from $B^0_s$ to $K^*$ dilepton data with enough control to be useful, and that the extracted ratios agree with lattice and light-cone sum rule determinations. The authors improve their earlier extraction by adding heavy-quark symmetry constraints, by studying how the low-recoil fit talks to the large-recoil region, and by recomputing the sum-rule ratios with correlated uncertainties, obtaining $R(0)=V(0)/A_1(0)=1.31$ and $R'(0)=A_2(0)/A_1(0)=0.83$. They argue that the double ratio $R=(V/A_1)/(T_1/T_2)$ equals one up to corrections of order $1/m_b$ at both maximum and low recoil, which is what licenses the extrapolation across the whole dilepton mass range. The payoff is that predictions for $A_{FB}$ and $P'_5$ built from the fitted ratios match the world averages, which the authors read as evidence that any new physics in the semileptonic short-distance coefficients must be small — in particular, explanations of the large-recoil $P'_5$ anomaly through an order-one shift in the Wilson coefficient $C_9$ alone are strongly disfavored.
Load-bearing premise
Everything rests on the low-recoil operator product expansion: that the decay amplitudes factorize into a polarization-independent short-distance piece times a form factor, up to corrections of only a few percent, and that no sizable right-handed current breaks that factorization.
Editorial extensions
If this is right
- The data-extracted ratios give benchmarks that lattice QCD and light-cone sum rules must reproduce; the updated sum-rule values sit about 7% below earlier predictions, mainly because of revised hadronic inputs and correlated continuum thresholds.
- Standard Model predictions for $A_{FB}$ and $P'_5$ at low recoil tighten relative to earlier estimates, with the quoted uncertainties coming from form factors alone and the short-distance coefficient uncertainty subleading at about 2%.
- Explanations of the large-recoil $P'_5$ anomaly that rely on an order-one new-physics contribution to $C_9$ alone are strongly disfavored, since the low-recoil data are consistent with the Standard Model.
- A roughly $2\sigma$ discrepancy in $P'_4$ in the lower dilepton-mass bin cannot be accommodated within the operator product expansion and is flagged for further experimental investigation.
- The fit scenarios combining data with large-energy or sum-rule input (SE2 LEL and SE2 LCSR) are put forward as the best currently available for low-recoil phenomenology, while a combined fit with lattice input previews the precision reachable with future data.
Reading between the lines
- If the double ratio $R$ really equals one at both kinematic ends, it becomes a clean null test: a measured deviation at intermediate dilepton mass would signal either a breakdown of quark-hadron duality or a right-handed current, independently of the form factor normalization.
- The agreement on $A_{FB}$ and $P'_5$ is presently a check on the operator product expansion more than on new physics; once lattice input shrinks the error on $V/A_1$, the same comparison turns into a genuine search for shifts in the short-distance coefficients.
- The same helicity factorization should hold for other $b \to s$ transitions such as $B_s \to \phi \ell^+\ell^-$ and $B \to K \ell^+\ell^-$, so the method offers cross-checks in hadronic environments with different systematic uncertainties.
- Because the extraction is binned, the residual short-distance dependence that survives binning is a small but real systematic; finer bins would trade statistical power for a cleaner factorization test.
Original abstract
Sufficient control of transition form factors is a vital ingredient for the precision flavor programs including the nearer term searches at the Large Hadron Collider (LHC) and the forthcoming Belle II experiment. We improve on existing methods to extract B -> K^* form factor ratios at low hadronic recoil from B -> K^* l^+ l^- data on the angular observables F_L, A_T^(2) and P'_4 by adding heavy quark symmetry-based constraints and by investigating the cross talk between low and large recoil. The data-extracted form factor ratios i) provide benchmarks for the lattice and light cone sum rule predictions, the latter of which have been updated including improved uncertainty estimations and ii) allow to improve the predictions for benchmark observables. We find that present data on the forward-backward asymmetry A_FB and the angular observable P'_5 at low recoil are in good agreement with the Standard Model.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Sufficient control of transition form factors is a vital ingredient for the precision flavor programs including the nearer term searches at the Large Hadron Collider (LHC) and the forthcoming Belle II experiment. We improve on existing methods to extract B -> K^* form factor ratios at low hadronic recoil from B -> K^* l^+ l^- data on the angular observables F_L, A_T^(2) and P'_4 by adding heavy quark symmetry-based constraints and by investigating the cross talk between low and large recoil. The data-extracted form factor ratios i) provide benchmarks for the lattice and light cone sum rule predictions, the latter of which have been updated including improved uncertainty estimations and ii) allow to improve the predictions for benchmark observables. We find that present data on the forward-backward asymmetry A_FB and the angular observable P'_5 at low recoil are in good agreement with the Standard Model.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Sufficient control of transition form factors is a vital ingredient for the precision flavor programs including the nearer term searches at the Large Hadron Collider (LHC) and the forthcoming Belle II experiment. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s1 | We improve on existing methods to extract B -> K^* form factor ratios at low hadronic recoil from B -> K^* l^+ l^- data on the angular observables F_L, A_T^(2) and P'_4 by adding heavy quark symmetry-based constraints and by investigating the cross talk between low and large recoil. | method 0.52 | 0.96 | 0.18 | asserted 1.00 |
| s2 | The data-extracted form factor ratios i) provide benchmarks for the lattice and light cone sum rule predictions, the latter of which have been updated including improved uncertainty estimations and ii) allow to improve the predictions for benchmark observables. | interpretation 0.47 | 0.77 | 0.32 | asserted 0.99 |
| s3 | We find that present data on the forward-backward asymmetry A_FB and the angular observable P'_5 at low recoil are in good agreement with the Standard Model. | result 0.97 | 0.93 | 0.23 | asserted 0.97 |
What was examined, and what was not
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- figures and tables
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- relations to other papers
- P abstract
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Figures
Showing 9 of the paper's 13 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:1308.4379 by the authors.
References
How later papers used it
45 later papers cite it
1 later paper by other authors is listed below: 1 compared its own results with it. 2 more papers by the same authors are listed: 1 built on it, 1 used its data or values and 1 cited it as support. 1 of them appears under more than one label.
Builds on it 1 paper · 1 by the same authors
By the same authors
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Argued, extending this paper's work, that use of the equation of motion enforces the correlation of the non-parametric, sum rule specific, input parameters.
$B\to V\ell^+\ell^-$ in the Standard Model from Light-Cone Sum Rules (2015) (same authors) · 0.99 · paraphrased: the licence does not allow quoting
Uses its data or values 1 of 3 papers with this label · 1 by the same authors
By the same authors
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Employed an uncertainty estimate from this paper for the ratios V/A_1 of 8% and A_2/A_1 of 10%.
B->K\pi ll in and outside the K* window (2015) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Compares with it 1 paper
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Reported that its own results for the ratio A_2(0)/A_1(0) are consistently higher than this paper's, with a 2 sigma variance.
Comprehensive Bayesian Analysis of Rare (Semi)leptonic and Radiative B Decays (2013) · 1.00 · paraphrased: the licence does not allow quoting
Cites it as support 1 paper · 1 by the same authors
By the same authors
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Said that the good agreement in the observables usable to extract form factor ratios (F_L, S_3, S_4) that this paper suggests indicates the low q^2 OPE appears to work within present uncertainties.
B->K\pi ll in and outside the K* window (2015) (same authors) · 0.98 · paraphrased: the licence does not allow quoting
How the literature uses it
45 arXiv papers cite this in 77 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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We find that recent LHCb data on the B0->K*0mumu angular observables at low recoil are in good agreement with the standard model.
Papers citing it · 60 sentences without a confident label
Builds on it 1 paper
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[ref] , that the use of the equation of motion enforces the correlation of the non-parametric, sum rule specific, input parameters.
$B\to V\ell^+\ell^-$ in the Standard Model from Light-Cone Sum Rules · Introduction · 0.99
Uses its method or tool 1 paper
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A similar simplification procedure could be repeated by use of the equation of motion $i ∂^ν(s̅ i σ_μν b) = - (m_s+m_b) s̅ γ_μb +i ∂_μ(s̅ b) - 2 s̅ i ←D_μ b$ (as used in [ref] ) for $H^T_t_$ if all of the operators present in the equation were used in the effective Hamiltonian.
Generalised helicity formalism, higher moments and the $B \to K_{J_K}(\to K \pi) \bar{\ell}_1 \ell_2$ angular distributions · Explicit Helicity Amplitudes in terms of Form Factors · 0.90
Uses its data or values 3 papers
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We use the $B→K^∗$ form factors given in Ref. [ref] , which were obtained from a combined fit [ref] of lattice QCD [ref] and light-cone sum rules (LCSR) results [ref] .
Revisiting $B\to K^\ast( \to K\pi) \nu\bar{\nu}$ decays · $B→K^∗νν̅$ · 0.92
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Specifically, the form factors are taken from [ref] as compiled in [ref] , and we employ an uncertainty estimate for the ratios $V/A_1$ of $8%$ and $A_2/A_1$ of $10%$ from [ref] .
B->K\pi ll in and outside the K* window · The $B̅→K̅^*ℓℓ$ form factors · 1.00
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Employing the form factor ratios from light cone sum rules at $q^2=0$ given in [ref] we estimate roughly $O(5 %)$ uncertainty in $p$ from form factors.
Diagnosing lepton-nonuniversality in $b \to s \ell \ell$ · The $K^*$ polarization fraction · 0.98
Compares with it 1 paper
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Our results for the ratio $A_2(0)/A_1(0)$ are consistently higher than those of [ref] , with a $2σ$ variance, which can be attributed to our usage of the constraint on $A_0(0)$, see eq:FF-constr:A0:LCSR.
Comprehensive Bayesian Analysis of Rare (Semi)leptonic and Radiative B Decays · Fitting the Nuisance Parameters · 1.00
Cites it as support 1 paper
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The good agreement in the observables which can be used to extract form factor ratios ($F_L, S_3, S_4$) [ref] suggests that within present uncertainties the low $q^2$ OPE appears to work, specifically that the binning is sufficient and non-universal $c̅ c$-effects are sufficiently small.
B->K\pi ll in and outside the K* window · Comparison of $B̅ →K̅^* μμ$ data with SM predictions · 0.98
Cites it as background 8 papers
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Recently, a significant amount of work has been devoted to the study of $b→sℓℓ$ processes [ref] , where experimental progress has been outstanding (see e.g. Refs. [ref] ).
B -> K* mu+ mu- optimised observables in the MSSM · Introduction · 0.95
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Consistent SM and new physics interpretations of the measured deviation in the $B →K^* ℓ^+ℓ^-$ mode have been discussed in a large number of references [ref] .
Signs for new physics in the recent LHCb data? · New physics interpretations of the anomaly · 0.98
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It should be emphasized at this point that these analyses are subject to theoretical uncertainties, which have been discussed at length in [ref] and it remains to be seen whether the observed anomalies are only result of statistical fluctuations and/or underestimated error uncertainties.
331 models facing new b -> s mu^+ mu^- data · Introduction · 0.86
What it cites · 57 sentences without a confident label
Uses the method or tool of 9 papers
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Following Ref. [ref] , we parametrize the transversity form factors $f_i$, $i=⊥,0,∥$ in $B →K^* ℓ^+ ℓ^-$ decays through a Series Expansion (SE) [ref] [equation] in the variable $z$ defined as [equation] Here, $t$ denotes the analytic continuation of $q^2$ to the complex plane, $t_±=(m_B ±m_K^*)^2$ and $t_0$ is a free parameter in the range $0 ≤t_0<t_+$ for which a common choice is $t_0 = t_opt$ with $t_opt=t_+ (1 - √(1 - t_-/t_+))$ [ref] .
Analyticity, Shapes of Semileptonic Form Factors, and B to pi l nu · Form factor series expansion · 0.98
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Following Ref. [ref] , we parametrize the transversity form factors $f_i$, $i=⊥,0,∥$ in $B →K^* ℓ^+ ℓ^-$ decays through a Series Expansion (SE) [ref] [equation] in the variable $z$ defined as [equation] Here, $t$ denotes the analytic continuation of $q^2$ to the complex plane, $t_±=(m_B ±m_K^*)^2$ and $t_0$ is a free parameter in the range $0 ≤t_0<t_+$ for which a common choice is $t_0 = t_opt$ with $t_opt=t_+ (1 - √(1 - t_-/t_+))$ [ref] .
Dispersive Bounds on the Shape of B -> D^(*) l nu Form Factors · Form factor series expansion · 0.98
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Following Ref. [ref] , we parametrize the transversity form factors $f_i$, $i=⊥,0,∥$ in $B →K^* ℓ^+ ℓ^-$ decays through a Series Expansion (SE) [ref] [equation] in the variable $z$ defined as [equation] Here, $t$ denotes the analytic continuation of $q^2$ to the complex plane, $t_±=(m_B ±m_K^*)^2$ and $t_0$ is a free parameter in the range $0 ≤t_0<t_+$ for which a common choice is $t_0 = t_opt$ with $t_opt=t_+ (1 - √(1 - t_-/t_+))$ [ref] .
Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays · Form factor series expansion · 0.98
Uses data or values from 3 papers
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Shown are predictions for $V$, $A_1$, $A_2$ and $f_0$ in the SE2 full fit, including form factors from the lattice [ref] (blue data points) which fix the normalization.
Lattice QCD calculation of form factors describing the rare decays $B \to K^* \ell^+ \ell^-$ and $B_s \to \phi \ell^+ \ell^-$ · Results · 0.98
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Also shown in the figures (right-handed plots) are the resulting SM predictions taking the short-distance factors $ρ_1,2$ in the SM from [ref] with parameters as in [ref] .
General Analysis of B -> K^(*) l^+ l^- Decays at Low Recoil · Predictions in SM and beyond · 0.80
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Also shown in the figures (right-handed plots) are the resulting SM predictions taking the short-distance factors $ρ_1,2$ in the SM from [ref] with parameters as in [ref] .
The Benefits of B ---> K* l+ l- Decays at Low Recoil · Predictions in SM and beyond · 0.80
Compares with 5 papers
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The largest discrepancies exist in $V/A_1$ (2$σ$) and at $q^2=15.64$ GeV$^2$ in $f_0/f_∥$ (3$σ$) between the lattice [ref] and the SE2 LEL fit.
Lattice QCD calculation of form factors describing the rare decays $B \to K^* \ell^+ \ell^-$ and $B_s \to \phi \ell^+ \ell^-$ · Results · 0.93
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The resulting combined uncertainties for $A_FB$ and $P_5^'$ are smaller than the ones obtained previously [ref] and can be further reduced by experimental measurements.
General Analysis of B -> K^(*) l^+ l^- Decays at Low Recoil · Predictions in SM and beyond · 0.97
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The resulting combined uncertainties for $A_FB$ and $P_5^'$ are smaller than the ones obtained previously [ref] and can be further reduced by experimental measurements.
Optimizing the basis of B->K*ll observables in the full kinematic range · Predictions in SM and beyond · 0.97
Cites as support 1 paper
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In fact, inspecting the general expressions in Ref. [ref] the above endpoint relations hold model-independently.
General Analysis of B -> K^(*) l^+ l^- Decays at Low Recoil · Short-distance independence · 0.97
Cites as background 9 papers
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For further details on the full angular distribution, see, e.g., [ref] .
General Analysis of B -> K^(*) l^+ l^- Decays at Low Recoil · Observables from angular coefficients · 0.98
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For $B →K^*$ transitions form factor estimations exist from relativistic quark models [ref] , light cone sum rules (LCSR) [ref] or lattice QCD [ref] .
A lattice calculation of B -> K(*) form factors · Introduction · 0.98
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For $B →K^*$ transitions form factor estimations exist from relativistic quark models [ref] , light cone sum rules (LCSR) [ref] or lattice QCD [ref] .
Lattice QCD calculation of form factors describing the rare decays $B \to K^* \ell^+ \ell^-$ and $B_s \to \phi \ell^+ \ell^-$ · Introduction · 0.98
Discussion
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