Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil

M. Beneke; Th. Feldmann (Aachen)

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Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil

M. Beneke, Th. Feldmann (Aachen)

High Energy Physics - Phenomenology · Submitted 24 Aug 2000 · 33 references

Pith's verdict: A careful, honest NLO calculation that does what it claims; the limits are the ones the authors themselves flag, not hidden flaws.

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arXiv IDhep-ph/0008255 (version 2)

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CitationM. Beneke, Th. Feldmann (Aachen). "Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil." arXiv:hep-ph/0008255 (2000). https://pith.science/paper/VZ3LSM4Z

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Editor's note

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This is the paper that turns the Charles et al. large-recoil symmetry relations into something you can actually use at next-to-leading order. The genuinely new content is the order-αs computation of the symmetry-breaking corrections, split cleanly into the vertex piece (Eq. 28, a standard but complete one-loop calculation) and the hard-spectator piece (Section 3.2), plus the corrected form-factor ratios in Eqs. (62)-(67). The endpoint-divergence argument in Section 3.2 is the part I'd point a student to: they show explicitly that the divergent pieces have the symmetry-preserving Dirac structure and can be absorbed into the soft functions, so only the genuinely hard, computable terms break the relations. That is the real content, and it holds up on reading. The FB-asymmetry application in Section 5 is a nice payoff and correctly reduces to a clean C9 extraction, Eq. (78). The citation pattern is normal and appropriate; the symmetry relations are properly credited to Ref. [3]. I'd cite this without hesitation for the corrected ratios or the C9 relation. On the reader's circularity score of 3.0: I think that's too harsh. Eq. (29) is a scheme definition, stated as such, and defining the soft form factors to absorb the universal pieces is standard practice, not a circular argument. The 'Δf+ = 0 by construction' statements are scheme-dependent, and the authors say so. The soft spots are the ones the paper itself names: the default power counting at the end of Section 2.2 (if a Sudakov factor suppresses the soft term, the whole framework changes character), the 'tentative' factorization formula Eq. (27), and the numerical reliance on ⟨l_+^{-1}⟩_+ = (0.3 GeV)^{-1}, which drives the 60% uncertainty and makes the (6.5 ± 5)% FB correction consistent with zero. None of these are concealed, and none break the central claim; they limit its numerical reach. The stress-test concern lands, but it lands on ground the authors already staked out. This deserves a serious referee, mainly to check the hard-scattering convolution and the endpoint power-counting, not to relitigate the framing.

Referee report

Significance

If the central result holds, this paper puts heavy-to-light form factors at large recoil on the same conceptual footing as HQET at small recoil: the symmetry limit reduces ten form factors to three soft functions, and the breaking is organised into a computable short-distance part. The explicit one-loop vertex result Eq. (28) and the demonstration in Sec. 3.2.1 that hard-collinear and endpoint contributions preserve the symmetry structure are genuine technical achievements, and the identification of ⟨l+^{-1}⟩+ as a B-meson-universal parameter appearing in B→ππ, B→ℓνγ and here is a useful, falsifiable organising observation. The application to the FB-asymmetry zero is a concrete, testable prediction that connects an observable (s0) to a short-distance coefficient, and the paper is candid that the numerical correction is currently uncertainty-limited. The calculation is reproducible from the equations given.

Major objections (3)

[Sec. 3.3, Eqs. (64)-(65) and concluding sentence of Sec. 3.3] The statement that the A1/V and T1/T2 relations 'do not receive αs corrections to leading order in the 1/M expansion' is a consequence of the scheme definition Eq. (29), which sets V ≡ (M+mV)/M ξ⊥ and A1 ≡ 2E/(M+mV) ξ⊥ exactly at every order, so their ratio equals the symmetry value by construction. The authors disclose this ('The renormalisation convention (29) implies no correction to A0 and V'), and I do not read it as a circularity in the calculation of the other ratios, but the summary sentence of Sec. 3.3 and the corresponding sentence in the Conclusion read as dynamical statements about QCD rather than as artefacts of the scheme. Please reword so that the reader can distinguish the scheme-fixed ratios from the genuinely computed ones (Eqs. 62, 63, 65-67), and add one sentence on the residual scheme dependence: what would change if the soft functions were instead defined via f+, T1 and A1, for instance.
[Sec. 4, Eq. (70) and Fig. 2; Sec. 5, Eq. (78)] The hard-scattering correction is quoted with a 60% uncertainty dominated by ⟨l+^{-1}⟩+ = (0.3 GeV)^{-1} taken over (0.2-0.5) GeV^{-1}, together with αs(µ2) = 0.34 at µ2 = 1.47 GeV. The resulting FB-asymmetry correction, (6.5±5)%, is consistent with zero, and Eq. (78) is explicitly incomplete at order αs because of the four-quark and chromomagnetic operator contributions of Fig. 3e-g. The sentence in Sec. 5 that Eq. (78) 'provides an almost model-independent determination of C9' is therefore stronger than the numbers support; I would state the correction as 'of order 10%, currently uncertain at the ±5% level' and describe the C9 determination as conditional on (i) an independent determination of ⟨l+^{-1}⟩+ and (ii) the non-form-factor αs corrections. Relatedly, the discrepancy with the QCD sum rule curves in Fig. 2d,e is used as a point of comparison, but with a 60% band it is not statistically meaningful; the text should say so more plainly than 'this may explain the remaining numerical differences'.
[Sec. 3.2.1, Eqs. (47)-(50)] The argument that endpoint (soft) contributions preserve the large-recoil symmetry is the load-bearing step for the factorisation formula Eq. (27), and it is made at the level of the integrand: the leading-twist projectors annihilate n/−, and the twist-3 combinations in Eqs. (48)-(49) are asserted to vanish at ū = 0 with the ellipses denoting omitted three-particle and light-quark-mass terms. Because the scheme of Eq. (29) rests on being able to absorb these terms into ξ without specifying a regulator, a short quantitative statement on the neglected terms, or a demonstration that the argument survives one explicit regulator (for example dimensional regularisation of the ū→0 endpoint), would materially strengthen the paper. As written, the reader must take on faith that the omitted terms do not reintroduce a linear endpoint divergence of the kind the authors themselves identify as power-counting breaking.

Minor objections (8)

[Sec. 3.2.2, Eqs. (51)-(52)] The text refers to 'the second line of Eq. (52)' and to 'all four terms in Eq. (52)', but the f+ result is Eq. (51) and Eq. (52) is the identification of I1 and I2. Please correct these cross-references.
[Eq. (38)] Please verify the typeset form of L. The displayed expression should reduce to L = 1 at E = M/2 (q2 = 0), as stated in the text, and the printed form does not obviously do so.
[Fig. 2 caption] Seven panels (a)-(g) are said to correspond to 'Eqs. (62)-(67)', which is six equations; please map panels to equations explicitly. The caption should also state that the dashed QCD sum rule curves include 1/M and quadratic meson-mass effects (as the text notes), so that the comparison is not read as a like-for-like test of the same quantity.
[Eqs. (36)-(37)] The T3 expression is split across two equation numbers, with the ξ⊥ and ξ‖ terms on separate lines. Please combine into a single numbered equation or relabel so that the structure is unambiguous.
[Sec. 2.2, p. 7, and Secs. 4-5] The 'default power counting' sentence at the end of Sec. 2.2 is the single assumption on which the numerical sections rest. A forward reference from Sec. 4 and Sec. 5 back to it would help the reader keep the conditionality in view.
[Appendix B, Eq. (45) and Eq. (112)] The B-meson projector uses the equation-of-motion relation (112), which drops three-particle contributions. The text notes this, but an estimate of the numerical size of the neglected derivative term in the symmetry-breaking corrections would be useful, since it enters the same ∆F quantities that dominate the uncertainty.
[Sec. 5, p. 20] The remark that C9^eff(s0) 'is not a true short-distance quantity' would benefit from a reference to where its scheme and q2 dependence are defined, so that the reader can see what precisely is being extracted from s0.
[Editorial] There are several typographical and spacing errors, for example 'This is allows us' (p. 19) and 'the the functions' (p. 9), and the comparison is referred to inconsistently as 'Fig. 2d and e' and 'Fig. 2d vs Fig. 2e'. A careful proofread is warranted.

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The paper

The paper claims

At large recoil the ten heavy-to-light $B$ form factors collapse onto three functions; this paper computes how strong-interaction corrections break that collapse, and argues the breaking is calculable rather than incalculable.

The reading

When a $B$ meson decays into a light pion or vector meson carrying nearly half the $B$ mass, the strong-interaction form factors that parametrise the transition are believed to obey symmetry relations: ten independent functions reduce to three, one for pseudoscalar mesons and two (transverse and longitudinal) for vector mesons. Those relations are exact only in an idealised limit, and the question this paper takes up is whether the corrections that break them are computable or whether they are lost to soft, non-perturbative physics. The authors show that the breaking splits into two pieces: a vertex renormalisation of the heavy-to-light current, handled much as in heavy quark effective theory, and a genuinely new piece, hard rescattering with the spectator quark, which has no counterpart in heavy-to-heavy transitions and is described with light-cone distribution amplitudes. They then evaluate the corrected ratios numerically and find corrections of order ten percent over the accessible range, with two ratios receiving no correction at all at this order. The payoff is a proposed use: the point where the forward-backward asymmetry in $B to V ell^+ ell^-$ vanishes becomes a nearly hadron-free handle on the loop-induced Wilson coefficient $C_9$.

What carries the argument

The load-bearing device is the tentative factorisation formula of Eq. (27), $f_i = C_i xi + Phi_B otimes T_i otimes Phi_P$, together with the scheme choice of Eq. (29) that defines the soft functions $xi_P$, $xi_perp$, $xi_parallel$ as three particular physical form factors to all orders. Everything else follows from inserting the one-loop vertex correction, Eq. (28), into the trace representation of the soft matrix element, Eq. (11), and then adding the hard-spectator convolution, Eq. (41), built from the light-cone projectors for pseudoscalar mesons (Eq. 83), vector mesons (Eq. 91) and the $B$ meson (Eq. 45). The argument that endpoint-singular pieces of the hard-spectator graph respect the symmetry, and can therefore be absorbed into $xi$ rather than breaking it, is what keeps the bookkeeping honest; the surviving symmetry breaking is carried by two moments, $langle l_+^{-1} rangle_+$ of the $B$ meson distribution amplitude and $langle bar u^{-1} rangle$ of the light meson amplitude, collected into the quantities $Delta F_P$, $Delta F_perp$, $Delta F_parallel$.

Extended reading notes

Core claim

The paper's claim is that the large-recoil symmetry relations among heavy-to-light $B$ form factors survive radiative corrections in a controlled way. The authors compute the order-$alpha_s$ corrections to the ten form factors and organise them as a factorisation formula, $f_i(q^2) = C_i xi_P(E) + Phi_B otimes T_i otimes Phi_P$, in which the soft, symmetry-respecting part is separated from a hard kernel convoluted with the light-cone distribution amplitudes of the $B$ meson and the light meson. They fix the scheme by declaring three form factors to be the soft functions by definition, $f_+ equiv xi_P$, $V equiv (M+m_V)/M, xi_perp$, $A_0 equiv (E/m_V), xi_parallel$, so that every other form factor is predicted as a ratio up to explicit corrections. The resulting ratios, their Eqs. (62)-(67), show that two relations, between $A_1$ and $V$ and between $T_1$ and $T_2$, are untouched at this order, while the others shift by roughly ten percent, with one ratio potentially moving by thirty percent. Applied to the forward-backward asymmetry zero in $B to V ell^+ ell^-$, the same machinery turns a measured zero $s_0$ into $C_9 = -(2M m_b / s_0), C_7$ times a correction of about $(6.5 pm 5)$ percent, Eq. (78).

Load-bearing premise

The authors explicitly adopt, as a default power counting rather than a derived result, the assumption that the soft term $C_i xi$ dominates the hard-spectator term by one power of $alpha_s$; if a Sudakov form factor suppresses the soft term instead, the symmetry relations become irrelevant and the whole framework loses its footing.

Editorial extensions

If this is right

Form factor ratios for $B to pi$ and $B to rho$ transitions become predictions with quantified corrections, so a measured ratio that departs from Eqs. (62)-(67) by far more than the quoted sixty percent would signal physics outside the soft-plus-hard-scattering picture.
The relations between $A_1$ and $V$, and between $T_1$ and $T_2$, hold to order $alpha_s$ without correction, which makes them the cleanest available cross-checks among the vector form factors.
A measured zero $s_0$ of the forward-backward asymmetry in $B to K^* ell^+ ell^-$ converts into a determination of the Wilson coefficient $C_9$ that is largely free of hadronic modelling, once $C_7$ is fixed from inclusive $b to s gamma$.
Because the largest uncertainty is a single $B$-meson moment, the same quantity that appears in $B to ell nu gamma$ and in hard spectator corrections to $B to pi pi$, an independent determination of that moment would sharpen all of these predictions at once.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's own framing makes the scheme definition, not the loop calculation, the real pivot: declaring three form factors to be the soft functions by fiat means the numerical content lives entirely in the ratios, so a future lattice determination of $f_+$, $V$ and $A_0$ would let the predicted ratios be tested without ever computing $xi$ itself.
The acknowledged disagreement with QCD sum rule results for $T_1/V$ and $T_2/V$ is the most informative loose end, since those are exactly the two ratios the paper says receive no order-$alpha_s$ correction; resolving it would either confirm the symmetry argument or expose a missing contribution.
If the soft term really is Sudakov-suppressed, as the authors allow, then the same hard-scattering machinery would become the leading description rather than a correction, which would convert this paper's error budget into a leading-order calculation and change what has to be trusted.
The forward-backward zero is only as clean as the omitted four-quark and chromomagnetic operator corrections, so the natural next test is whether those corrections shift $s_0$ by more or less than the five percent presently quoted.

Original abstract

Recently it has been shown that symmetries emerging in the heavy quark and large recoil energy limit impose various relations on form factors that parametrise the decay of B mesons into light mesons. These symmetries are broken by perturbative effects. In this paper we discuss the structure of heavy-to-light form factors including such effects and compute symmetry-breaking corrections to first order in the strong coupling. As an application of our results we consider the forward-backward asymmetry zero in the rare decay B -> V l^+ l^- and the possibility to constrain potential new physics contributions to the Wilson coefficient C_9.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,620 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.14 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Recently it has been shown that symmetries emerging in the heavy quark and large recoil energy limit impose various relations on form factors that parametrise the decay of B mesons into light mesons. These symmetries are broken by perturbative effects. In this paper we discuss the structure of heavy-to-light form factors including such effects and compute symmetry-breaking corrections to first order in the strong coupling. As an application of our results we consider the forward-backward asymmetry zero in the rare decay B -> V l^+ l^- and the possibility to constrain potential new physics contributions to the Wilson coefficient C_9.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Recently it has been shown that symmetries emerging in the heavy quark and large recoil energy limit impose various relations on form factors that parametrise the decay of B mesons into light mesons.	background 1.00	0.05	0.04	asserted 1.00
s1	These symmetries are broken by perturbative effects.	background 0.96	0.06	0.04	asserted 1.00
s2	In this paper we discuss the structure of heavy-to-light form factors including such effects and compute symmetry-breaking corrections to first order in the strong coupling.	contribution 1.00	0.94	0.27	asserted 0.97
s3	As an application of our results we consider the forward-backward asymmetry zero in the rare decay B -> V l^+ l^- and the possibility to constrain potential new physics contributions to the Wilson coefficient C_9.	contribution 0.74	0.72	0.23	hedged possibility 0.91

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.90.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Different contributions to the B → P(V ) transition. (a) Soft contribution (soft interactions with the spectator antiquark ¯q ′ are not drawn). (b) Hard vertex renormalisation. (c,d) Hard spectator interaction. lagrangian), such as the one shown in Fig. 1b. (The disconnected spectator quark line in Figs. 1a and 1b is meant to indicate that it is connected to the other lines only via soft exchanges. Fig. 1a therefore stands for the leading term in the heavy quark mass limit.) The symmetry-breaking effects are caused only by the short-distance part of Fig. 1b. They are accounted for by

**Figure 2.** Corrections to symmetry relations as a function of q 2 (three solid lines, see text). Figs. (a)–(g) correspond to the form factor ratios in Eqs. (62)-(67) with overall scaling factors divided out, such that the symmetry limit (dotted lines) corresponds to a ratio equal to 1 independent on q 2 . For illustration we show also results from QCD sum rules [30, 26] (dashed lines). Tensor form factors are renormalized at µ = mb. 18

**Figure 3.** Various next-to-leading order contributions to the B → K∗γ ∗ matrix elements. sufficient accuracy. (For completeness we note that the form factor ratios required for the present analysis are exactly those where there exists a discrepancy with the QCD sum rule result. From Fig. 2d, we also deduce that the QCD sum rule calculation of the relevant form factor ratios leads to a 3% reduction of s0. This adds importance to clarifying the origin of this discrepancy.) We should emphasize that Eq. (78) is not a complete result at order αs even after replacing the Wilson coefficients C7,9 by…

Figures reproduced from arXiv:hep-ph/0008255 by the authors.

References

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hep-ph 2026-10 accept novelty 6.0 of 10

In dark SMEFT, one-loop matching of top-flavoured dark matter shows that only tree-level operators can explain the Belle II B+→K+ννbar excess with O(1) couplings at Λ=1 TeV, with B0→K*0+inv giving the strongest constraint.
More than a Lifetime: Towards Precision Predictions for $B$-Meson Decays in the Standard Model and Beyond
hep-ph 2026-10 accept novelty 6.0 of 10

The thesis computes the complete leading-order dimension-seven two-quark contributions to inclusive non-leptonic B decays and extends the HQE Darwin term to a general BSM effective Hamiltonian.
Electromagnetic tails of $B$-meson light-cone distribution amplitudes
hep-ph 2026-09 accept novelty 6.0 of 10

The paper derives model-independent asymptotic expressions for the QED-induced negative-momentum tail of B-meson light-cone distribution amplitudes in terms of pure-QCD distribution amplitudes.
Soft Collinear Effective Theory for Heavy QCD Axions
hep-ph 2026-08 conditional novelty 6.0 of 10

A new dimension-seven operator is generated by the gluon equation of motion in the presence of the axion-gluon coupling, and its spectator-scattering contribution to B to K a is roughly 25 percent of the soft-overlap ...
$B_c \to \eta_c$ form factors at large recoil: SCET analysis and a three-loop consistency check
hep-ph 2026-05 unverdicted novelty 6.0 of 10

SCET factorization confirms the double-logarithmic resummation for B_c to eta_c form factors up to three loops and derives the iterative structure from RG equations of light-cone distribution amplitudes with cutoff re...
$\bar{B}_{s,d}^{0} \to J/\psi \mu^{+}\mu^{-}$ Decays in QCD Factorization
hep-ph 2025-10 unverdicted novelty 6.0 of 10

Computes branching ratios of order 10^{-10} for Bs and 10^{-11} for Bd decays after NLO vertex corrections in QCD factorization, plus dimuon distributions and J/psi polarization.
SCET sum rules for $\Lambda_b \to \Lambda \ell^+\ell^-$, $\Lambda \gamma$ decays
hep-ph 2025-06 conditional novelty 6.0 of 10

SCET light-cone sum rules give NLO soft form factors and small non-factorizable corrections for Λ_b → Λ decays, with a Λ_b → Λ γ branching fraction consistent with data.
Precision calculations of $B\to K^*$ form factors from SCET sum rules beyond leading-power contributions
hep-ph 2024-12 conditional novelty 6.0 of 10

New subleading-power corrections to B to K* form factors from SCET sum rules yield SM branching fractions BR(Bbar0 to Kbar*0 nu nubar)=8.09(96)e-6 and F_L=0.44(4).
Transition form factors of the $\Lambda_b \rightarrow \Lambda(1520)$ in QCD light-cone sum rules
hep-ph 2024-12 conditional novelty 6.0 of 10

First light-cone sum rule calculation of the Lambda_b to Lambda(1520) transition form factors, with rare decay predictions consistent with LHCb within large uncertainties.
Dispersive Analysis of $B\to K^{(*)}$ and $B_s\to \phi$ Form Factors
hep-ph 2023-05 accept novelty 6.0 of 10

Including below-threshold B_s pi0 and B_s pi0 pi0 branch cuts in a joint dispersive fit of the B to K(*), B_s to phi form factors produces parametrizations whose truncation error is bounded rather than guessed.
$B$-meson light-cone distribution amplitude from the Euclidean quantity
hep-ph 2019-08 conditional novelty 6.0 of 10

The paper derives a hard-collinear factorization formula with a one-loop matching coefficient connecting the B-meson quasi-distribution amplitude to the physical light-cone distribution amplitude.
$B\to P$ and $B\to V$ Form Factors from $B$-Meson Light-Cone Sum Rules beyond Leading Twist
hep-ph 2018-11 conditional novelty 6.0 of 10

Complete twist-four two-particle and three-particle corrections to all B to P and B to V form factors are computed, and the higher-twist two-particle terms turn out to dominate the three-particle ones.
Radiative leptonic decay $B\to \gamma \ell \nu_\ell$ with subleading power corrections
hep-ph 2018-04 conditional novelty 6.0 of 10

Including 1/E_gamma and 1/m_b corrections, the predicted B to gamma lepton neutrino form factors depend as strongly on the shape parameter sigma_1 of the B-meson LCDA as on the inverse moment lambda_B.
Towards the discovery of new physics with lepton-universality ratios of $b\to s\ell\ell$ decays
hep-ph 2017-04 conditional novelty 6.0 of 10

LHCb's muon-to-electron ratios in B decays deviate from the Standard Model at 3.7 sigma, and effective-field-theory fits favour new physics in the O9/O10 operators, with a proposed new observable to isolate the O10 co...
Perturbative corrections to $B \to D$ form factors in QCD
hep-ph 2017-01 accept novelty 6.0 of 10

One-loop hard and jet functions for the vacuum-to-B correlation function with a D interpolating current are computed under the counting mc ~ sqrt(Lambda m_b), yielding NLL sum rules for B to D form factors.
Factorization and dispersion relations for radiative leptonic $B$ decay
hep-ph 2016-06 accept novelty 6.0 of 10

The one-loop soft two-particle correction to the B to gamma form factors is computed via dispersion relations and found to reduce the leading-power prediction by 10 to 30 percent at lambda_B = 354 MeV.
Building Blocks for Subleading Helicity Operators
hep-ph 2016-01 conditional novelty 6.0 of 10

A complete-in-SCET-I set of scalar helicity building blocks, plus an angular momentum selection rule, lets subleading-power SCET operators be enumerated by simple multiplication instead of Lorentz and Dirac index contraction.
Perturbative Corrections to $\Lambda_b \to \Lambda$ Form Factors from QCD Light-Cone Sum Rules
hep-ph 2015-11 accept novelty 6.0 of 10

One-loop QCD corrections reduce the light-cone-sum-rule predictions for all ten Lambda_b to Lambda form factors by about a factor of two, with the hard-collinear jet function, not the hard matching coefficients, suppl...
Phenomenology of semileptonic B-meson decays with form factors from lattice QCD
hep-ph 2015-10 accept novelty 6.0 of 10

With new lattice-QCD form factors, Standard Model predictions for B to pi/K mu mu run 1 to 2 sigma above LHCb measurements, and the same inputs give |Vtd| and |Vts| with uncertainties competitive with meson mixing.
QCD corrections to $B \to \pi$ form factors from light-cone sum rules
hep-ph 2015-06 conditional novelty 6.0 of 10

The authors compute the O(alpha_s) corrections to B to pi form factors in the B-meson distribution-amplitude light-cone sum rule, prove one-loop factorization with the method of regions, and extract |Vub| = 3.05 x 10^-3.
Exclusive Radiative Higgs Decays as Probes of Light-Quark Yukawa Couplings
hep-ph 2015-05 accept novelty 6.0 of 10

Next-to-leading-order QCD factorization plus a ratio to h to gamma gamma turns rare h to V gamma decays into a quantitatively controlled probe of the charm, bottom and strange Yukawa couplings.
Differential branching fraction and angular analysis of $\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^-$ decays
hep-ex 2015-03 conditional novelty 6.0 of 10

LHCb measures the differential branching fraction of Lambda_b to Lambda mu+ mu- and reports the first forward-backward asymmetries in the dimuon and proton-pion systems, finding A_FB^h = -0.29 +/- 0.07 +/- 0.03 in 15 ...
$B\to V\ell^+\ell^-$ in the Standard Model from Light-Cone Sum Rules
hep-ph 2015-03 accept novelty 6.0 of 10

Updated light-cone sum rule form factors for B to V l+ l- decays, with correlated uncertainties and combined lattice fits, sharpen Standard Model predictions for rare B decays and the extraction of |Vub|.
Exclusive Radiative Decays of W and Z Bosons in QCD Factorization
hep-ph 2015-01 accept novelty 6.0 of 10

QCD factorization with one-loop corrections and resummed logarithms yields branching ratios between roughly 10^-12 and 10^-7 for exclusive radiative W and Z decays into a single meson plus a photon.
Reassessing the discovery potential of the $B \to K^{*} \ell^+\ell^-$ decays in the large-recoil region: SM challenges and BSM opportunities
hep-ph 2014-12 conditional novelty 6.0 of 10

Allowing power corrections to the heavy-quark limit to float reduces the B to K* mu mu angular anomaly from 3.7 sigma to below 2 sigma, and new muon-to-electron angular ratios are proposed as clean lepton-universality tests.
Angular Analysis of the Decay $\Lambda_b \to \Lambda (\to N \pi) \ell^+\ell^-$
hep-ph 2014-10 accept novelty 6.0 of 10

The full angular distribution of Lambda_b to Lambda(-> N pi) l+ l- yields ten angular observables, two of which (X1, X2) probe right-handed b to s couplings that B to K* l+ l- cannot access.
On the impact of power corrections in the prediction of B->K*mu+mu- observables
hep-ph 2014-07 conditional novelty 6.0 of 10

Using a scheme-dependent treatment of soft form factors and a fit to light-cone sum rule inputs, the authors find that factorisable power corrections to B to K* mu+ mu- angular observables are under control at the rou...
An Exclusive Window onto Higgs Yukawa Couplings
hep-ph 2014-06 conditional novelty 6.0 of 10

Rare Higgs decays h -> M V (M a vector meson, V = photon, W or Z) are shown to be calculable and, at future hadron colliders, sensitive to first- and second-generation quark Yukawa couplings.
Disentangling the Decay Observables in $B^- \to \pi^+\pi^-\ell^-\bar\nu_\ell$
hep-ph 2013-10 accept novelty 6.0 of 10

The paper derives the complete angular decomposition of B- to pi+ pi- l- nu-bar and a set of algebraic null tests that would reveal non-standard (V+A, scalar, or tensor) structure in b to u transitions.
Light-Cone Distribution Amplitudes for Heavy-Quark Hadrons
hep-ph 2013-08 accept novelty 6.0 of 10

The authors find Bessel-function dual representations that diagonalize the Lange-Neubert evolution kernel for B-meson and Lambda_b-baryon light-cone distribution amplitudes, and construct momentum-space projector mode...
Isospin asymmetries in $B\to (K^*,\rho) \gamma/ l^+ l^-$ and $B \to K l^+ l^-$ in and beyond the Standard Model
hep-ph 2013-05 conditional novelty 6.0 of 10

Standard Model isospin asymmetries in B to K, K*, rho plus lepton pairs are computed to be below 1.5 percent at low dilepton mass, and a ratio of the rho-gamma and K*-gamma asymmetries is proposed as a quasi-null test...
On B -> V l l at small dilepton invariant mass, power corrections, and new physics
hep-ph 2012-12 conditional novelty 6.0 of 10

The positive-helicity amplitudes in B to K* lepton pairs are suppressed by the V-A structure even including non-factorizable charm and light-quark corrections, leaving P1 and P3^CP as clean null tests sensitive to C'_...
Complete Anatomy of B -> K*ll and its angular distribution
hep-ph 2012-02 accept novelty 6.0 of 10

A complete basis of angular observables for B -> K* l+ l- is constructed, with six form-factor-independent observables in the massless case plus two for lepton masses and two for scalars.
B meson distribution amplitude from B --> \gamma l \nu
hep-ph 2011-10 conditional novelty 6.0 of 10

Including NLL radiative and 1/mb power corrections roughly halves the predicted B to gamma lepton neutrino branching fraction, lowering the BABAR-derived lower bound on lambda_B from about 670 MeV to about 310 MeV.
Theory of B -> K(*)l+l- decays at high q^2: OPE and quark-hadron duality
hep-ph 2011-01 conditional novelty 6.0 of 10

The high-q^2 region of B -> K(*) l+ l- is shown to be calculable from standard form factors alone, with nonperturbative corrections and quark-hadron duality violation each estimated below a few percent.
New physics reach of the decay mode $\bar{B} \to \bar{K}^{*0}\ell^+\ell^-$
hep-ph 2010-05 accept novelty 6.0 of 10

The angular distribution of B to K*0 l+ l- has four symmetries in the massless-lepton limit, not three, and this yields one exact constraint among the angular coefficients plus a new form-factor-free observable.
Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes
hep-ph 2009-12 accept novelty 6.0 of 10

In the minimal Randall-Sundrum model, tree-level Kaluza-Klein exchange makes Delta F=2 observables relatively model-independent while Delta F=1 rare decays depend strongly on right-handed top quark localization and th...
Symmetries and Asymmetries of B -> K* mu+ mu- Decays in the Standard Model and Beyond
hep-ph 2008-11 accept novelty 6.0 of 10

A complete basis of CP-averaged and CP-violating angular observables for B -> K* mu+ mu- is defined, computed in the Standard Model with full form factors, and shown to discriminate among new-physics scenarios.
New observables in the decay mode anti-B --> anti-K*0 l+ l-
hep-ph 2008-07 accept novelty 6.0 of 10

Two new form-factor-independent angular observables, A_T^(3) and A_T^(4), are constructed for B_d to K*0 l+ l- and shown to probe right-handed currents, while the previously proposed A_T^(1) is shown to be experimenta...
CP Asymmetries in bar B -> bar K* (-> bar K pi) l+ l- and Untagged bar B_s,B_s -> phi (-> K+ K-) l+ l- Decays at NLO
hep-ph 2008-05 accept novelty 6.0 of 10

Seven angular CP asymmetries in B -> K* l+ l- are computed at NLO in QCD factorization; all sit at or below the percent level in the Standard Model, while the three T-odd ones can reach order one with new physics.
Angular Distributions of B -> K ll Decays
hep-ph 2007-09 accept novelty 6.0 of 10

In the Standard Model the flat term in the B -> K l+ l- angular distribution scales as the lepton mass squared and the muon-to-electron rate ratio R_K equals one to 10^-4, giving two clean null tests of new physics.
QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
hep-ph 2001-04 accept novelty 6.0 of 10

QCD factorization at next-to-leading order reproduces the observed B to pi K and pi pi branching ratios and yields constraints on the Wolfenstein parameters without phenomenological models at leading power.
Semileptonic neutral current decays of $\Xi_b$ with dileptons or dineutrinos in the final state
hep-ph 2025-12 unverdicted novelty 5.0 of 10

Perturbative QCD calculations find that branching fractions for Ξ_b to Ξ lepton-pair decays lie within LHCb reach and that angular observables plus a specific ratio can constrain Wilson coefficients and extract |V_td/...
Improved Theory Predictions and Global Analysis of Exclusive $\boldsymbol{b\to s\mu^+\mu^-}$ Processes
hep-ph 2022-06 conditional novelty 5.0 of 10

A global analysis of rare B to K(*) mu+mu- and Bs to phi mu+mu- decays with parametrized non-local form factors finds a 5.7 sigma tension with the Standard Model in B to K mu+mu- and BSM shifts Re C9 approximately -1....
Precision calculations of $B \to V$ form factors in QCD
hep-ph 2019-07 conditional novelty 5.0 of 10

Light-cone sum rules with B-meson distribution amplitudes, computed at next-to-leading order and up to twist-six, yield B to vector form factors and give |Vub| = (3.05 +0.67-0.52) x 10^-3 from B to rho l nu and (2.54 ...
QCD calculations of $B \to \pi, K$ form factors with higher-twist corrections
hep-ph 2018-10 conditional novelty 5.0 of 10

Adding twist-five and twist-six B-meson distribution-amplitude corrections shifts the B to pion vector form factor by 20 to 30 percent and gives |Vub| = (3.23 +0.66-0.48) x 10^-3.
New Physics effect on $B_c \to J/\psi \tau\bar\nu$ in relation to the $R_{D^{(*)}}$ anomaly
hep-ph 2017-09 conditional novelty 5.0 of 10

Fitting six new-physics operator scenarios to R_D, R_D*, and the new R_J/psi measurement, the author finds chi-squared values of 2 to 4.3 versus about 22 for the Standard Model, with the scalar S2 solution excluded by...

See all 84 Pith citations

How later papers used it

143 later papers cite it

Evidence: substantial. 130 of the citing papers share no author with it, and 35 of those carry a confident label from Pith's citation classifier.

Pith read 17 of the 258 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

4 later papers by other authors are listed below: 4 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool.

Uses its method or tool 5 of 31 papers with this label · 1 by the same authors

Used this paper's QCD factorization approach to write the leading-power heavy-to-light form factor as a hard function times a soft form factor.

$\Lambda_{b}\rightarrow P \ell$ factorization in QCD (2024) · 0.80 · paraphrased: the licence does not allow quoting
Wrote the explicit form of the B-meson light-cone projector, neglecting three-particle distribution amplitudes and implementing the equation-of-motion constraint, as given by this paper.

$\bar{B}_{s,d}^{0} \to J/\psi \mu^{+}\mu^{-}$ Decays in QCD Factorization (2025) · 0.92 · paraphrased: the licence does not allow quoting
Expressed the semileptonic B to pion decay distribution in the large energy limit in terms of a single form factor following this paper.

Probing New Physics with $\bar B \to \rho(770) \, \ell^- \bar \nu_\ell$ and $\bar B \to a_1(1260) \, \ell^- \bar \nu_\ell$ (2019) · 0.96 · paraphrased: the licence does not allow quoting
Defined the light-cone distribution amplitude as given by this paper and parameterized it with twist wave functions.

Search for Majorana Neutrino Signal in $B_c$ Meson Rare Decay (2012) · 0.94 · paraphrased: the licence does not allow quoting

By the same authors

Gave the B-meson projector up to twist-3 under the Wandzura-Wilczek approximation as given by this paper.

QED factorization of non-leptonic $B$ decays (2020) (same authors) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

135 arXiv papers cite this in 251 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We show that these corrections are perturbatively calculable, and present results to first order in the strong coupling constant alpha_s.

Heavy-to-light form factors: Symmetries at large recoil and calculation of alpha_s corrections · 0.95

Papers citing it · 165 sentences without a confident label

Builds on it 1 paper

With these results the symmetry-breaking corrections to the heavy-to-light form factor relations [ref] that were first computed at $𝒪(α_s)$ in [ref] , can be extended to $𝒪(α_s^2)$.

Soft-collinear factorization in B decays · Form-factor relations · 0.98

Uses its method or tool 30 papers

The matrix elements of the leptoquark operators are calculated in the QCD factorization approach [ref] , which is widely used in the semi-leptonic and non-leptonic decays of $B$ mesons.

$\Lambda_{b}\rightarrow P \ell$ factorization in QCD · Introduction · 0.91
We use the framework of QCD factorization (QCDF) valid in the low-$q^2$ region [ref] and exploit the symmetries of QCD in the large recoil limit of heavy-to-light transitions [ref] .

Angular Distributions of B -> K ll Decays · Introduction · 1.00
The hadronic matrix elements of the operators $O_i$ between the $B$- and $π$-meson states are expressed in terms of three independent form factors $f_+ (q^2)$, $f_0 (q^2)$ and $f_T (q^2)$ as follows [ref] :

Precise Calculation of the Dilepton Invariant-Mass Spectrum and the Decay Rate in $B^\pm \to \pi^\pm \mu^+ \mu^-$ in the SM · The $B^+ →π^+ ℓ^+ ℓ^-$ Decay · 0.90

Uses its data or values 5 papers

We obtain [equation] where the corresponding endpoint-divergent contributions in $ξ_π^(HSA)(E_2)$ have been calculated in [ref] and can be found in Eq. ([ref]) in the appendix.

QCD Factorization for $B \to \pi\pi\ell\nu$ Decays at Large Dipion Masses · Endpoint-divergent terms · 0.86
The FFs for the vector and axial-vector currents have been investigated in Ref. [ref] with the use of perturbative QCD [ref] and then the following parametrizations are given: [equation] where the values for the $q^2=0$ point are obtained by the fit; $V^c(0) = 0.42 ±0.01 ±0.01$, $A_0^c(0) = 0.52 ±0.02 ±0.01$, $A_1^c(0) = 0.46 ±0.02 ±0.01$, and $A_2^c(0) = 0.64 ±0.02 ±0.01$ [ref] .

New Physics effect on $B_c \to J/\psi \tau\bar\nu$ in relation to the $R_{D^{(*)}}$ anomaly · Description of hadronic amplitude and form factors · 0.89
The perturbative corrections were computed in the heavy-quark and large recoil energy limit in [ref] with the result (in the NDR scheme with $MS$ subtraction) [equation] where $μ=O(m_b)$, $μ_h=O(√(Λm_b))$, and $E_K=O(m_b)$ depends on $s=q^2/m^2_B$ through ([ref]).

Precision Flavour Physics with $B\to K\nu\bar\nu$ and $B\to Kl^+l^-$ · Relation between form factors $f_T$ and $f_+$ · 0.83

Compares with it 8 papers

However, upon neglecting the power correction term $m_K_0^*^2/m_B^2$, one finds that the results reported in [ref] are recovered.

Symmetry-Breaking Effects on Form Factors and Observables in $B \to K_0^*(1430)\mu^+\mu^-$ Decay · Matrix elements and form factors · 0.96
The $q^2$-dependence of the soft form factors is shown in Fig. [ref] and compared to the naive scaling behaviour [equation] which follows in the framework of SCET/QCDF at tree level [ref] .

$D \to \rho \,\ell^+\ell^-$ Decays in the QCD Factorization Approach · Naive factorization · 0.90
The expressions for $C_P^(f)$ and $T_P,+^(f)$ in eq:C:and:T agree with $- C_∥^(f)$ and $- T_∥,+^(f)$ given in [ref] , respectively, where a different definition of the longitudinal form factor $ξ_∥$ with respect to the one used in previous works [ref] is employed.

Angular Distributions of B -> K ll Decays · $T_P$ for $B̅ →K$ · 0.99

Cites it as background 25 papers

According to the standard Lorentz decomposition of the bilinear quark currents, the $B→K^*$ form factors are defined in the standard way [ref] [equation] with the convention $ϵ_0123=-1$.

Precision calculations of $B\to K^*$ form factors from SCET sum rules beyond leading-power contributions · NLL correction to the form factors at leading power · 0.89
In the limit of large recoil energy, $E ∼𝒪(m_B)$, these are related at leading power in the heavy-quark expansion up to calculable factorizable corrections [ref] .

$B_c \to \eta_c$ form factors at large recoil: SCET analysis and a three-loop consistency check · Introduction · 0.86
The $B$-meson LCDA $ϕ_+(ω)$ [ref] is the Fourier transform of the HQET matrix element [equation] where $[t, 0]$ denotes a straight soft Wilson line connecting the light-like separated points 0 and $t$.

$B_{d,s}\to\gamma\ell\bar{\ell}$ decay with an energetic photon · Hard-collinear function · 0.81

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