Second Order Power Corrections in the Heavy Quark Effective Theory I. Formalism and Meson Form Factors

Adam F. Falk; Matthias Neubert

REVIEW

Second Order Power Corrections in the Heavy Quark Effective Theory I. Formalism and Meson Form Factors

Adam F. Falk, Matthias Neubert

High Energy Physics - Phenomenology · Submitted 23 Sep 1992 · 39 references

Pith's verdict: The 1/m_Q^2 bookkeeping is solid and worth having on the shelf; the 'few percent' number in the abstract is an estimate built from mixed inputs, and the paper mostly says so.

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CitationAdam F. Falk, Matthias Neubert. "Second Order Power Corrections in the Heavy Quark Effective Theory I. Formalism and Meson Form Factors." arXiv:hep-ph/9209268 (1992). https://pith.science/paper/F3OBJ25N

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Two things to know. First, this is the reference construction of the 1/m_Q^2 expansion for ground-state meson form factors, and the structural part holds up: the operator enumeration, the trace algebra in Appendices A and B, and the two zero-recoil theorems all follow from HQET Feynman rules plus vector current conservation. Second, the headline number in the abstract — that the zero-recoil corrections are 'unlikely to exceed the level of a few percent' — is an estimate, not a derivation, and it is the one place where I would slow down before quoting it in a talk. The paper is honest about this, which matters for how you read it. It flags that λ1 could be zero, in which case h_A1(1)−1 flips to about −3% instead of +2%. It argues the double chromo-magnetic terms D4, D5, D6 are small via the vanishing-field-strength limit. What it does not do is put an error bar on ℓ1(1)=ℓ2(1)≈−0.75 GeV^2, which comes from ISGW with the light constituent mass identified with Λ̄. That is a model value sitting next to sum-rule λ1 and λ2 from a different framework, and the two are not mutually constrained. If |ℓ(1)| were a factor of three larger, the net correction would approach 10%. The dismissal of Ref. [36]'s −10% as 'unacceptable' is a judgment, not a derivation, though it is backed by a citation to Ref. [25] and I don't read it as a red flag. Minor point: the renormalization-improved version of the normalization conditions (4.39) is deferred to 'elsewhere', so the tree-level conditions are what you actually get here. Also worth knowing that the whole analysis is tree level, stated plainly. Who should read it: anyone doing exclusive semileptonic B decays or extending HQET to higher orders; the appendices are the useful part, since every ℓ_i and m_i is written out explicitly. It deserves referees — the derivation is checkable line by line and the phenomenology is properly hedged. I'd cite it for the formalism and quote the 2% only with the caveat attached.

Referee report

Significance

This is a careful and, as far as I can check, correct piece of bookkeeping that fills a genuine gap: the 1/m_Q^2 terms of the heavy quark expansion for meson form factors had not previously been organized into a complete basis. The paper's real strengths are the completeness of the operator enumeration, the explicit closed-form expressions in Appendix A (Eqs. A4–A7) and Appendix B, which make every step checkable line by line, and the two zero-recoil theorems, which are derived from the equation of motion and vector current conservation rather than assumed. The vanishing-chromo-magnetic limit of Sec. V.D is a useful structural check: 34 functions collapse to five, with one combination vanishing at zero recoil, which is a nontrivial consistency test of the counting. The numerical statement h_A1(1) − 1 ≈ 2% is a falsifiable prediction of the framework, and the paper is candid that λ_1 = 0 would flip the sign and give ≈ −3%.

Major objections (1)

[Sec. V.B, Eqs. (5.6)–(5.8) and footnote 2] The abstract's headline claim [abstract:s5] — that the zero-recoil 1/m_Q^2 corrections are 'unlikely to exceed the level of a few percent' — rests entirely on the numerical estimate (5.8), and that estimate is not accompanied by any error band. Two inputs are combined without being mutually constrained: the ISGW value ℓ_1(1) = ℓ_2(1) = −3m_q^2 ≈ −0.75 GeV^2 from Eq. (5.2), in which the light constituent mass is identified with Λ̄, and the sum-rule values λ_1 ≈ 1 GeV^2, λ_2 ≈ 0.15 GeV^2. The D_4, D_5, D_6 terms in Eq. (5.7) are dropped on the strength of the vanishing-chromo-magnetic argument of Sec. V.D, but their magnitude is never bounded. The paper should state explicitly what range of ℓ_1(1), ℓ_2(1) and of the D-term combination would still leave |h_A1(1) − 1| below, say, 5%, and should say how much of the quoted 2% is attributable to each of the three inputs. As written, the reader cannot tell whether 'a few percent' is a derived bound or an order-of-magnitude expectation, and the sentence in Sec. V.B that a factor-of-three larger ℓ(1) would be 'unacceptable' is a judgment rather than a quantitative argument. The same applies to the dismissal of the −10% estimate of Ref. [36] in the paragraph following (5.8) and in footnote 2: the disagreement is resolved by assertion, and it would be far more useful to show what values of ℓ_1(1), ℓ_2(1) and the D terms would be required to reproduce −10%, so that the reader can judge which set of inputs is more plausible. This does not affect the structural results of Sec. IV, but it is load-bearing for the abstract's phenomenological conclusion.

Minor objections (8)

[Sec. IV.D and Appendix A] The normalization conditions (4.39) are derived only at tree level, and the paper states that more restrictive relations could be obtained by matching the logarithmic m_Q dependence, with the results 'presented elsewhere'. Since the abstract advertises the zero-recoil normalization conditions as a derived result [abstract:s3], a sentence in the main text stating plainly that (4.39) is a tree-level statement, and indicating which of the 34 functions are expected to acquire anomalous dimensions, would prevent over-reading.
[Appendix A, Eqs. (A4)–(A7)] The ℓ_i and m_i are given without any statement of their renormalization scale, and the text notes only in passing that μ-dependence is omitted. A short sentence at the head of Appendix A stating that these are tree-level, scale-independent quantities, and that the μ-dependence enters only through the coefficients once radiative corrections are included, would make the appendix self-contained.
[Sec. V.A, Eq. (5.4)] The numerical form '1 − 0.7% − 1.3% × [ℓ_4(1)/Λ̄^2]' is opaque: the reader cannot tell what value of ℓ_4(1) was inserted, in what units, or how the quoted 1.3% follows from L_4(1) ≈ −Λ̄/3 of Ref. [25]. Giving the intermediate numbers explicitly would make the estimate reproducible.
[Sec. V.A, Eq. (5.2)] The identification of the light constituent quark mass with Λ̄ in the ISGW estimate should be flagged as an assumption with its numerical consequence stated, since the constituent mass usually quoted in ISGW-type models is closer to 0.3 GeV than to the 0.5 GeV sum-rule value of Eq. (2.9). The sensitivity of ℓ_1(1) to this choice should be noted.
[References [25], [28], [37]] Several numerical and qualitative inputs used in Sec. V — L_4(1) ≈ −Λ̄/3, λ_1 ≈ 1 GeV^2, and the smallness of A_2 and A_3 that motivates the vanishing-chromo-magnetic limit of Sec. V.D — are taken from preprints or papers listed as unpublished. Since these enter the phenomenological conclusions directly, the relevant status should be updated at proof stage if possible.
[Sec. III, Eq. (3.16) and Sec. IV, Eq. (4.34)] The ellipses in (3.16) and (4.34) suppress terms of order 1/m_Q^3 and higher; this should be stated explicitly at each occurrence, since the equations are otherwise easy to misread as exact. Similarly, the 'bar' operation in (4.34) is defined only in words, and a single worked example (for instance for the P→P case) would remove any ambiguity about the velocity, polarization and mass exchanges involved.
[Eq. (3.17) and Eqs. (B2), (B5)] Argument conventions are inconsistent in places: h_8 is written without a (w) argument in (3.17) while h_7 carries one, and the relation h_8 = h_2 in (B5) is stated without comment. A uniform convention for the w-dependence of all fourteen form factors would help the reader checking Appendix B against Eq. (3.17).
[Figs. 1 and 2] The figure captions identify the operator insertions but not the vertex or momentum labelling conventions, so the correspondence between the diagrams and the individual terms of Eqs. (3.10), (4.16), (4.17), (4.19) and (4.24) has to be inferred. One sentence per caption mapping each diagram to its equation would be sufficient.

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The paper

The paper claims

Heavy-quark symmetry breaking at second order is catalogued, and the zero-recoil B→D* rate survives it at the few-percent level.

The reading

Heavy quark symmetry says that in the limit of infinite heavy-quark mass, all the hadronic form factors describing a transition between two ground-state heavy mesons collapse into one universal function of the velocity transfer $w = v·v'$, normalized to 1 at zero recoil. That limit is never exact, so the question that decides whether it is useful for extracting $V_{cb}$ is how fast the expansion in $1/m_Q$ converges. This paper pushes the expansion of meson form factors to second order, $1/m_Q^2$, and does the bookkeeping: it defines a minimal set of universal, mass-independent functions in terms of matrix elements of higher-dimension operators, and derives the constraints that vector-current conservation imposes on them at zero recoil. The payoff is a numerical argument that the second-order corrections to the zero-recoil rates for $B→Dℓν$ and $B→D^*ℓν$ are only a few percent, which is what makes the heavy-quark route to $V_{cb}$ credible rather than merely formal.

What carries the argument

The carrying device is the 'modified wave function': the spin wave function of a heavy meson is split into a large component, built on the on-shell projector $P_+$, and an induced small component, built on $P_-$, with the $1/m_Q$ and $1/m_Q^2$ corrections absorbed into scalar coefficient functions. Corrections to the effective Lagrangian and to the current enter different projector combinations, so the trace over spin wave functions can be evaluated once and reused for every form factor. The equation of motion $iv·Dh = 0$ and integration by parts then generate relations among the coefficient functions, which is how the thirty-four functions collapse to the handful that actually appear in $P→P$ and $P→V$ transitions, and how the two zero-recoil theorems are proved without relying on the structure of the perturbative coefficients.

Extended reading notes

Core claim

The paper constructs the $1/m_Q^2$ terms of the heavy-quark expansion of current matrix elements between ground-state pseudoscalar and vector mesons, and shows that they can be organized into a minimal set of thirty-four universal form factors: four from corrections to the current, twenty-five from corrections to the effective Lagrangian, and five from mixed corrections. Two theorems do the structural work. First, at zero recoil the second-order current corrections reduce to expressions in the two mass parameters $λ_1$ and $λ_2$ that already appear in the meson mass shifts. Second, all mixed current–Lagrangian corrections vanish at zero recoil. Together with the mass-renormalization counterterm for the meson wave functions, these give the zero-recoil normalization conditions of Eq. (4.39), which tie the Lagrangian form factors to $λ_1$ and $λ_2$. Applied to the phenomenologically decisive case, the authors find $h_{A_1}(1) - 1 ≈ 2$ percent, arising from a partial cancellation between a term scaling as $(1/2m_c - 1/2m_b)^2$ and a term scaling as $1/(4m_c m_b)$, so that the zero-recoil $B→D^*ℓν$ rate remains a clean handle on $V_{cb}$.

Load-bearing premise

The claim that the second-order correction is only a few percent rests on a constituent quark model estimate $ℓ_1(1) = ℓ_2(1) ≈ -0.75$ GeV$^2$ and on dropping the double chromo-magnetic insertions $D_4, D_5, D_6$; the authors note that with $λ_1 = 0$ the correction would instead be about $-3$ percent.

Editorial extensions

If this is right

Extraction of $V_{cb}$ from the zero-recoil endpoint of $B→D^*ℓν$ carries a theoretical uncertainty of a few percent rather than an unknown $O(1)$ correction, since $h_{A_1}(1)$ is protected at first order by Luke's theorem and now shown to move by only about 2 percent at second order.
The same holds for $B→Dℓν$, which is not protected by Luke's theorem but is suppressed by the Voloshin-Shifman factor; the paper estimates the combined first- and second-order shift at roughly 2 percent.
The thirty-four universal functions give a common language for comparing models: once a model fixes $ℓ_1(1)$ and $ℓ_2(1)$, heavy-quark symmetry propagates that information to every other form factor.
In the fictitious limit of vanishing chromo-magnetic interaction the thirty-four functions collapse to five, with one combination vanishing at zero recoil, providing a simplified template for estimating the dominant corrections.
The framework extends directly to heavy baryons, which the companion paper treats.

Reading between the lines

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

If the second-order correction to $h_{A_1}(1)$ really sits near 2 percent, then the dominant uncertainty in the exclusive route to $V_{cb}$ shifts from power corrections to the perturbative matching and to the experimental extrapolation of the spectrum to zero recoil — a shift that would make the exclusive and inclusive determinations a meaningful cross-check on each other rather than two loosely
The paper's estimate of the correction is dominated by a single hadronic number, $ℓ_1(1) = ℓ_2(1)$, which a lattice calculation of the elastic Isgur-Wise-like form factor could in principle supply directly; that would convert the 'few percent' claim from a model-based expectation into a computed result.
The partial cancellation between the $(1/2m_c - 1/2m_b)^2$ and $1/(4m_c m_b)$ terms is a numerical accident of the bottom-to-charm ratio rather than a symmetry, so the same expansion applied to a bottom-to-bottom or charm-to-charm transition would not enjoy the same suppression.
The thirty-four-function catalogue is a natural target for model builders: any model that claims to capture heavy-quark symmetry breaking can now be checked against the zero-recoil conditions of Eq. (4.39) before it is used to predict rates.

Original abstract

In the heavy quark effective theory, hadronic matrix elements of currents between two hadrons containing a heavy quark are expanded in inverse powers of the heavy quark masses, with coefficients that are functions of the kinematic variable $v\cdot v'$. For the ground state pseudoscalar and vector mesons, this expansion is constructed at order $1/m_Q^2$. A minimal set of universal form factors is defined in terms of matrix elements of higher dimension operators in the effective theory. The zero recoil normalization conditions following from vector current conservation are derived. Several phenomenological applications of the general results are discussed in detail. It is argued that at zero recoil the semileptonic decay rates for $B\to D\,\ell\,\nu$ and $B\to D^*\ell\,\nu$ receive only small second order corrections, which are unlikely to exceed the level of a few percent. This supports the usefulness of the heavy quark expansion for a reliable determination of $V_{cb}$.

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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, 5,591 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.34 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.12 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

In the heavy quark effective theory, hadronic matrix elements of currents between two hadrons containing a heavy quark are expanded in inverse powers of the heavy quark masses, with coefficients that are functions of the kinematic variable $v\cdot v'$. For the ground state pseudoscalar and vector mesons, this expansion is constructed at order $1/m_Q^2$. A minimal set of universal form factors is defined in terms of matrix elements of higher dimension operators in the effective theory. The zero recoil normalization conditions following from vector current conservation are derived. Several phenomenological applications of the general results are discussed in detail. It is argued that at zero recoil the semileptonic decay rates for $B\to D\,\ell\,\nu$ and $B\to D^*\ell\,\nu$ receive only small second order corrections, which are unlikely to exceed the level of a few percent. This supports the usefulness of the heavy quark expansion for a reliable determination of $V_{cb}$.

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	In the heavy quark effective theory, hadronic matrix elements of currents between two hadrons containing a heavy quark are expanded in inverse powers of the heavy quark masses, with coefficients that are functions of the kinematic variable $v\cdot v'$.	background 1.00	0.12	0.04	asserted 1.00
s1	For the ground state pseudoscalar and vector mesons, this expansion is constructed at order $1/m_Q^2$.	contribution 0.78	0.82	0.05	asserted 1.00
s2	A minimal set of universal form factors is defined in terms of matrix elements of higher dimension operators in the effective theory.	contribution 0.75	0.84	0.05	asserted 1.00
s3	The zero recoil normalization conditions following from vector current conservation are derived.	result 0.60	0.91	0.05	asserted 1.00
s4	Several phenomenological applications of the general results are discussed in detail.	contribution 0.97	0.78	0.04	asserted 0.90
s5	It is argued that at zero recoil the semileptonic decay rates for $B\to D\,\ell\,\nu$ and $B\to D^*\ell\,\nu$ receive only small second order corrections, which are unlikely to exceed the level of a few percent.	result 0.71	0.77	0.62	hedged possibility 0.92
s6	This supports the usefulness of the heavy quark expansion for a reliable determination of $V_{cb}$.	interpretation 1.00	0.47	0.39	hedged possibility 0.67

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

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

levels run

P abstract

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S sections
T body sentences
C citations
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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

References

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hep-ph 2018-01 accept novelty 6.0 of 10

Including B to D* angular observables in a global fit to b to c lepton neutrino data sharply constrains scalar, tensor, right-handed and electron-muon non-universal new physics, and yields Vcb = (3.96 +/- 0.09) x 10^-...
Tensions and correlations in $|V_{cb}|$ determinations
hep-ph 2017-08 conditional novelty 6.0 of 10

Bootstrapping the Belle unfolded B to D* lepton neutrino spectra shows the four |Vcb| extractions are 69 to 97 percent correlated, cutting the apparent tension from over 5 sigma to under 3 sigma.
Combined analysis of semileptonic $B$ decays to $D$ and $D^*$: $R(D^{(*)})$, $|V_{cb}|$, and new physics
hep-ph 2017-03 accept novelty 6.0 of 10

Fitting light-lepton B to D(*) decay data with heavy-quark symmetry yields R(D)=0.299±0.003 and R(D*)=0.257±0.003, keeping the roughly 4-sigma tension with measurements.
Minimally flavored colored scalar in $\bar B \to D^{(*)} \tau \bar \nu$ and the mass matrices constraints
hep-ph 2013-06 conditional novelty 6.0 of 10

A color-triplet weak-doublet scalar with a minimal three-parameter Yukawa texture reproduces the measured B to D(*) tau neutrino branching ratios and, when embedded in SU(5), fixes most fermion mixing angles and predi...
Theory of Charmless Inclusive B Decays and the Extraction of V_{ub}
hep-ph 2005-04 conditional novelty 6.0 of 10

A unified next-to-leading-order QCD factorization plus OPE framework gives triple-differential B to X_u l nu rates and the B to X_s gamma spectrum with no explicit b-quark mass, enabling |V_{ub}| extraction at the 5 t...
Revisiting lifetimes of doubly charmed baryons
hep-ph 2023-05 unverdicted novelty 5.0 of 10

Updated predictions within the heavy quark expansion confirm the lifetime hierarchy τ(Ξ_cc^+) < τ(Ω_cc^+) < τ(Ξ_cc^++) with τ(Ξ_cc^++) = 0.32 ± 0.05 +0.08/-0.07 ps matching LHCb data and provide ratios for the other states.
Lattice QCD form factor for $B_s\to D_s^* l\nu$ at zero recoil with non-perturbative current renormalisation
hep-lat 2019-04 accept novelty 5.0 of 10

The Bs to Ds* axial form factor at zero recoil is computed to 1.5% total precision with all-HISQ quarks, removing the perturbative matching error that dominated earlier lattice results.
Scalar contributions to $b\to c (u) \tau \nu$ transitions
hep-ph 2016-12 accept novelty 5.0 of 10

Scalar interactions with simultaneous left- and right-handed quark couplings can account for the R(D) and R(D*) anomalies and the measured q-squared distributions, with a slight tension from the Bc total width.
The Full $B \to D^{*} \tau^{-} \bar{\nu_\tau}$ Angular Distribution and CP violating Triple Products
hep-ph 2013-02 conditional novelty 5.0 of 10

The full angular distribution of B to D* tau neutrino is derived with general new-physics couplings, and the triple-product asymmetries that vanish in the Standard Model are shown to be sensitive only to vector/axial-...
Sensitivity to charged scalars in $B\to D^{(*)}\tau\nu_\tau$ and $B\to\tau\nu_\tau$ decays
hep-ph 2012-10 conditional novelty 5.0 of 10

The BaBar excess in B → D(*)τν can be accommodated in the Aligned Two-Higgs-Doublet Model, but the required parameter region conflicts with leptonic charm decays.
On the B to D* tau nu Sensitivity to New Physics
hep-ph 2012-03 conditional novelty 5.0 of 10

Within a general effective-operator framework, current B to D(*) tau nu rate measurements still allow new-physics shifts of up to about 30% in the D*-tau opening-angle asymmetry and up to about 80% in the tau helicity...
$|V_{cb}|$ determinations from $\bar{B} \to D^{(*)} \ell \bar\nu$ decays within the SM and beyond
hep-ph 2026-06 unverdicted novelty 4.0 of 10

Fits to B to D(*) l nu form factors with BSZ, BGL and HQET yield |V_cb| matching PDG average for BGL but smaller for HQET, while data still allows non-zero new physics contributions.
The Azimuthal $B \to D^{*} \tau^{-} \bar{\nu_\tau}$ Angular Distribution with Tensor Operators
hep-ph 2014-05 conditional novelty 4.0 of 10

Adding a tensor operator to the B → D* τ ν effective Hamiltonian produces azimuthal asymmetries whose patterns differ enough between vector, scalar, and leptoquark scenarios to discriminate among them.
Update of $|V_{cb}|$ from the $\bar{B}\to D^*\ell\bar{\nu}$ form factor at zero recoil with three-flavor lattice QCD
hep-lat 2014-03 conditional novelty 4.0 of 10

Improved three-flavor lattice QCD gives the zero-recoil form factor F(1) = 0.906(4)(12) and |Vcb| = (39.04 +/- 0.49 +/- 0.53 +/- 0.19) x 10^-3, leaving a 3.0 sigma gap with the inclusive determination.
Effective theory approach to new physics in $b \to u$ and $b \to c$ leptonic and semileptonic decays
hep-ph 2013-07 conditional novelty 4.0 of 10

A combined effective-theory fit to b→u and b→c B decay data finds that four simple new-physics scenarios can accommodate the measured anomalies and predicts ranges for Bc→τν, B→πτν, and their ratios.
Diagnosing New Physics in $b \to c \, \tau \, \nu_\tau$ decays in the light of the recent BaBar result
hep-ph 2012-06 conditional novelty 4.0 of 10

Constraining vector, axial-vector, scalar and pseudoscalar new-physics couplings against the BaBar R(D) and R(D*) measurements, the paper predicts forward-backward asymmetries and tau and D* polarization fractions tha...
Charm physics
hep-ph 2025-06 unverdicted novelty 1.0 of 10

A review chapter summarizing the theoretical framework and experimental status of charm hadron lifetimes, D0 mixing, CP violation, and rare decays.

How later papers used it

50 later papers cite it

Evidence: substantial. 48 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 23 of the 85 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

1 later paper by other authors is listed below: 1 used its method or tool.

Uses its method or tool 1 of 5 papers with this label

Based its analysis on the HQET formula for the heavy-light meson mass given in this paper.

Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD (2018) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

51 arXiv papers cite this in 86 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 citing it · 69 sentences without a confident label

Contests it 1 paper

We note apparent sign errors or inconsistencies for several $𝒪(1/m_cm_b)$ wavefunctions derived in Ref. [ref] .

Constrained second-order power corrections in HQET: $R(D^{(*)})$, $|V_{cb}|$, and new physics · Introduction · contest 0.90

Uses its method or tool 6 papers

Following Ref. [ref] , our analysis is based on the HQET formula for the heavy-light meson mass [ref] [equation] where $M_H^(*)$ is the pseudoscalar (vector) meson mass; $m_h$ is the heavy-quark mass; and $$, $μ_π^2$, and $μ_G^2(m_h)$ are matrix elements of HQET operators with dimension 4 and 5.

Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD · Introduction · 0.95
The corresponding form factor parameters are extracted from data [ref] , apart from the form factor ratio $R_3(1)$, which is obtained using a HQET relation to order $α_s,1/m_b,c$ [ref] and enhancing the related uncertainty to account for higher-order effects [ref] .

Scalar contributions to $b\to c (u) \tau \nu$ transitions · Hadronic input parameters and statistical treatment · 0.89
To apply the correction we exploit information from heavy-quark effective theory (HQET); the form factor at zero-recoil has the heavy-quark expansion [ref]

Update of $|V_{cb}|$ from the $\bar{B}\to D^*\ell\bar{\nu}$ form factor at zero recoil with three-flavor lattice QCD · Heavy-quark mass tuning · 0.90

Compares with it 2 papers

This is unlike the case of the meson ground state $j^P = 1 2^-$ which involves instead three independent Lagrangian perturbation functions, coming from both $ℒ_kin,v$ and $ℒ_mag,v$ and denoted by $χ_i(w)$ (i = 1,2,3) [ref] .

New results on the baryon decay Lambda_b -> Lambda_c ell nu in Heavy Quark Effective Theory · Baryon leading and subleading IW functions · 0.88
As a point of comparison to the RC expansion, we also consider the vanishing chromomagnetic (VC) interaction limit [ref] , which also dramatically simplifies the number of subleading and subsubleading Isgur-Wise functions.

Constrained second-order power corrections in HQET: $R(D^{(*)})$, $|V_{cb}|$, and new physics · Introduction · 0.87

Cites it as support 1 paper

One additional point of importance is that in this expansion the $𝒪(θ^3)$ terms at second order—the terms corresponding to mixed current and Lagrangian corrections $∼_1 ℒ_1$—vanish at zero recoil [ref] .

Constrained second-order power corrections in HQET: $R(D^{(*)})$, $|V_{cb}|$, and new physics · Modified heavy quark expansion · 0.97

Cites it as background 4 papers

The $w$-dependent $1…61$ functions have well-known expressions (see e.g. Ref. [ref] ) [equation] in terms of the standard definitions of subleading Isgur-Wise functions $χ̂_i(w)$ and $η̂(w)$ (see below).

Constrained second-order power corrections in HQET: $R(D^{(*)})$, $|V_{cb}|$, and new physics · $→$ first and second-order power corrections · 0.94
In HQET, the mass of the $B_x$ (or $B^*_x$) meson is [ref] [equation] to first order in $1/m_Q$.

Relations between Heavy-light Meson and Quark Masses · Introduction · 0.89
$M_B$ and $M_D$ In HQET the mass of a heavy-light system $H=B^(*), D^(*)$ is given as an expansion in $1/m_h$ ($h=b,c$) as [ref] M_H=m_h + Λ̅ + μ_π^2/2m_h + w(s)μ_G^2/2m_h +O(m_h^-2) .

New method for renormalon subtraction using Fourier transform · Introduction · 0.96

Discussion

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