Dispersive Bounds on the Shape of B -> D^(*) l nu Form Factors

I. Caprini (Bucharest); L. Lellouch; M. Neubert (CERN)

REVIEW

Dispersive Bounds on the Shape of B -> D^(*) l nu Form Factors

I. Caprini (Bucharest), L. Lellouch, M. Neubert (CERN)

High Energy Physics - Phenomenology · Submitted 17 Dec 1997 · 42 references

Pith's verdict: The paper that gave the field its standard one-parameter shapes for the B→D(*) form factors, and it holds up — the 2% is an honest estimate, not a theorem, and the Bc-pole subtraction is the input I'd most want an error bar on.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 4 major objections · 10 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/9712417 (version 1)

Pith IDRPAA6E2U, Pith's permanent record of this paper and its review

CitationI. Caprini (Bucharest), L. Lellouch, M. Neubert (CERN). "Dispersive Bounds on the Shape of B -> D^(*) l nu Form Factors." arXiv:hep-ph/9712417 (1997). https://pith.science/paper/RPAA6E2U

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Short version: this is the paper that gave the field its standard one-parameter shapes for the B→D(*) form factors, and it holds up. If you extract |Vcb| exclusively, this is the reference you already use whether or not you cite it by equation number. Worth a serious read even now, mostly for how the uncertainties are handled rather than for the central numbers, which have been absorbed into the collective toolkit. What is actually new relative to Refs. [9]–[20]: spin symmetry exploited across all twenty form factors and all four spin-parity channels at once, the two lowest Bc and B*c poles subtracted in Eq. (8), and the leading short-distance and 1/mQ corrections carried into the relations of Eq. (24) with their uncertainties folded in rather than ignored. The conservatism is real and deliberate — nf inflated to 2.5, correlators raised and V1(1) lowered by one sigma in Eq. (11) to weaken the bounds on purpose, and the third-order constraints in Fig. 2 widened by an explicit scan instead of quoted at face value. The cross-check between the z and z* expansions in Fig. 5 is a genuine consistency test, not decoration: different orders, different dominant channels, nearly identical shapes. Where I'd push back: the 'better than 2%' of [abstract:s3] is the width of the ellipse in Fig. 5, which traces back to K, which traces to the correlators of Eq. (11) and the δ=0.1 symmetry-breaking scan. The δ is flagged in Section 4 as a conservative estimate, so that one is acknowledged. Less well flagged is the Bc-pole subtraction in Eq. (8), which uses the quark-model decay constants of Table 1 with no error bar; those contributions are positive, so an overestimate of f_n shrinks the ellipse and flatters the 2%. The paper says only that the constants 'can be calculated rather accurately.' That is the input I'd want quantified. Minor: the truncation bound of Eq. (31) leans on assuming S1(w0) as low as (2/3)S1(1) — conservative, but an assumption. One correction to the reader's take: δ matters mostly for the third-order Section 4 analysis, much less for the second-order Section 5 result that actually produces the 2%, so the Bc subtraction is the better target. Who gets value: phenomenologists fitting recoil spectra, lattice people wanting shape priors, and anyone teaching the dispersive method — Section 6 stands alone as a summary. Send it out.

Referee report

Significance

If the results hold, this is a genuinely useful paper. It exploits spin symmetry across the full ground-state doublet rather than one form factor at a time, which is what makes the bounds competitive, and it is careful in the conservative direction in several places: nf = 2.5 over-covers SU(3) breaking, Eq. (11) simultaneously raises the correlators and lowers V1(1) by one standard deviation, and the third-order constraints are explicitly widened by the symmetry-breaking scan of Fig. 2 rather than quoted at face value. The paper also ships something experiments can use directly: simple one-parameter functions with a stated accuracy, plus explicit allowed intervals for the slopes, which are falsifiable against future measurements and against inclusive sum-rule determinations. The internal consistency check between the two expansion variables (Fig. 5, lower plot) is a real check, not a decoration, since the two expansions are truncated at different orders and dominated by different spin-parity channels. The derivation is analytic and reproducible from the stated inputs; there is no hidden fit to the semileptonic data being described.

Major objections (4)

[Abstract and Section 5] The abstract states that the one-parameter functions describe the form factors 'with an accuracy of better than 2%', and the same figure is attached to 'all twenty' form factors. In the body, however, the 2% is demonstrated explicitly only for S1 (Section 5, from the truncation argument of Eq. (31) plus the 0.2% truncation of [φ B]⁻¹) and for V1 and A1 (Fig. 5 and Eqs. (33), (39)). The remaining seventeen form factors are obtained from Eq. (24) and Tables A.1/A.2, whose coefficients carry the assumed δ = 0.1; their accuracy is therefore inherited rather than shown, and for entries with large coefficients (for example A5, with B = 0.298 and C = −0.239) the propagated band need not be 2%. Either qualify the abstract to the form factors for which the accuracy is actually verified, or add an explicit propagation of the δ = 0.1 uncertainty through Eq. (24) for a representative subset (S2, S3, A5) showing the resulting band over 1 ≤ w ≤ wmax.
[Section 4, Eq. (24) and Fig. 2] The choice δB = δC = δD = 0.1 is described as 'a conservative estimate of the uncertainties' but is not derived, and it is the dominant driver of the third-order ellipse envelope in Fig. 2 and, through K in Tables 3 and 4, of the width of the band that produces the 2% figure in Fig. 5. The paper is explicit that these uncertainties 'ultimately limit the accuracy of the dispersive approach', so the input is acknowledged; what is missing is a sensitivity statement. Please show how the ellipse parameters of Tables 3 and 4, and the width of the light-shaded bands in Fig. 5, respond to, say, δ = 0.05 and δ = 0.2. If the 2% is stable under a factor-of-two change in δ, the claim is robust and should be said so; if it scales roughly linearly in δ, the abstract should carry the qualifier.
[Section 2, Eq. (8) and Table 1] The Bc and B*c pole contributions are subtracted from the correlators in Eq. (8) using the quark-model masses and decay constants of Table 1, with the text asserting only that these constants 'can be calculated rather accurately using quark models'. No error bar is assigned, and the direction of the effect matters: because the pole terms are positive, subtracting them reduces χ and therefore tightens the bounds in Eq. (11). An overestimate of f_n would make the allowed ellipses smaller than they should be, which is the opposite of the conservative posture taken elsewhere in the paper. Please attach an uncertainty to the subtracted terms and state how much the bounds in Eq. (11), and the slope intervals quoted in Sections 4 and 6, would weaken under a ±20% variation of the decay constants. The neglect of orbitally excited states is conservative in the safe direction and needs no change.
[Section 6, Table 5 and Fig. 6] The fits to the CLEO recoil spectrum neglect correlations between data points (stated) and, more importantly, do not propagate the shape-theory uncertainty into the quoted errors on ρ²_A1, ρ²_F and |Vcb|. The errors in Table 5 are therefore statistical only, and the statement that the parametrized fits give |Vcb| 'systematically higher (by about one standard deviation)' than the linear fit should be qualified, since the theory band that defines the shape is not in that standard deviation. Either add the theory band to the fit errors or state explicitly that the comparison is between central values with statistical errors only. The stated goal of illustrating rather than establishing |Vcb| is reasonable and should be kept.

Minor objections (10)

[Eqs. (34) and (40)] As printed, the two directions of each relation are not mutual inverses: setting ρ²₁ = 1 in the first expression of (34) gives 0.44, and feeding that into the second gives about 0.81 rather than 1. This looks like a loss of denominators in typesetting rather than an error of substance, but since these relations are what a reader will use to convert a measured slope between the two schemes, please give the explicit rational forms.
[Eqs. (33) and (39)] In both equations the denominator (0.354ρ²₁* + 0.992) and (0.358ρ²_A1* + 0.984) is set on the same line as the z²* term, so it is ambiguous whether it divides the whole expression or only the last term. Please set these unambiguously.
[Section 5, Eq. (31)] The remainder bound |Δj(z)| < |z|³ (1/|fj(0)|² − 1)^{1/2} is quoted without derivation. A one-line indication of how it follows from the inequality (20) would let the reader check the truncation argument rather than take it on trust.
[Section 5, the 1.5% product-truncation estimate] The statement that the z³* and z⁴* terms of the product of the two truncated expansions 'never exceed 1.5% over the full semileptonic region' is asserted rather than shown. A small table of the maximum deviation over the semileptonic domain for each form factor would substantiate the headline 2% claim at little cost.
[Table 3, 'Combined' row] The combined K = 0.84 is smaller than either of the inputs (0.85 for 0+ and 1.08 for 0−). Averaging ellipse parameters is not the same operation as intersecting the ellipses, and the resulting row should be labelled explicitly as an average representation rather than a rigorous combined bound, with a sentence on why the averaged K can fall below both inputs.
[Section 4, the 1± channels] The claim that the 0± bounds are 'fully contained in' the 1± ones is supported visually by Fig. 1 but not quantitatively. A short numerical statement of the containment would make the decision to drop the 1± channels auditable.
[Section 7, comparison with Ref. [20]] The statement that the form factors agree with Ref. [20] 'to better than 3% for values w < 1.5' is not backed by a figure or table. Please show the comparison, or say where it can be found.
[Table 1] The 1+ column lists masses but no decay constants. A footnote stating that these vanish by construction, as the text already explains, would make the table self-contained for a reader who consults it before reading the surrounding paragraph.
[Section 6, choice of reference form factor] The remark that repeating the analysis with A1(w) as reference 'gives essentially the same results' is plausible given the small symmetry-breaking corrections, but it is stated without support. One sentence quantifying the difference, or a pointer to where it was checked, would close the loop.
[Editorial] A few typographical slips should be corrected: 'form fatcors' in footnote 3, 'explicitely' in Section 7, 'enitre' in Section 4, 'will be neglected it in what follows' in Section 5, and 'the the unitarity relations' in the Appendix introduction.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Dispersive bounds turn twenty B to D(*) form factors into one-parameter curves, accurate to about 2 percent, and bound the slope that controls the extraction of |V_cb|.

The reading

The shapes of the form factors that control the exclusive decays $B^(*) to D^(*) l nu$ are the main obstacle to a clean measurement of the quark-mixing element $|V_{cb}|$: experiments measure a recoil spectrum, and one must extrapolate it to zero recoil where the normalization is known. This paper argues that those shapes are not free. Using analyticity of current-current correlation functions, positivity of their spectral functions, and heavy-quark spin symmetry to tie all twenty form factors together, the authors derive allowed domains for the slope, curvature, and third derivative of a reference form factor, and then show that the whole set collapses onto simple one-parameter functions of a conformal variable $z$. The claimed payoff is that each form factor is fixed up to a single slope number, with a stated accuracy better than 2% over the entire semileptonic region, and that the slope itself is confined to a finite interval. If that holds, the dominant extrapolation uncertainty in $|V_{cb}|$ becomes a controlled, one-dimensional fit rather than an unconstrained shape assumption.

What carries the argument

The load-bearing device is the combination of a subtracted dispersion relation for the vacuum polarization functions $chi_{0^pm}(Q^2)$ and $chi_{1^pm}(Q^2)$ with the unitarity sum over $B^{(*)}D^{(*)}$ states, plus the positivity that lets a partial sum of the spectral function bound the whole. Two technical ingredients make it bite. The conformal map $z(w,a) = (sqrt{w+1}-sqrt{2},a)/(sqrt{w+1}+sqrt{2},a)$ sends the branch point $w=-1$ to $z=-1$ and the physical region to a small arc near the origin, so that a short Taylor series in $z$ converges rapidly; the optimized choice $a_* approx 1.067$ centers the semileptonic interval on the origin. The inner (Blaschke) functions $B_j(z)$, with zeros at the images of the $B_c$ pole positions, remove the unknown pole residues without introducing any new parameters, since they have unit modulus on the physical cut. Heavy-quark symmetry then does the work of replacing a twenty-function problem by a one-function problem, with the breaking of that symmetry carried by the ratios $R_j(w) = F_j(w)/V_1(w)$ expanded to third order in $(w-w_0)$.

Extended reading notes

Core claim

The central claim is that the twenty semileptonic form factors of the ground-state heavy-light doublet are, for practical purposes, one-parameter objects. The authors derive four unitarity inequalities, one per spin-parity channel ($0^+$, $0^-$, $1^-$, $1^+$), by bounding the hadronic spectral functions of vector and axial-vector correlation functions from below with the $BD$, $BD^*$, $B^*D$, and $B^*D^*$ intermediate states and from above with the operator-product-expansion result for the correlators in the Euclidean region. Heavy-quark symmetry, with short-distance and $1/m_Q$ corrections included, converts the sums over those states into constraints on a single reference form factor $V_1(w)$. Mapping the cut $w$ plane onto the unit disc with $z(w,a)$ and dividing out the known $B_c$ poles with Blaschke factors turns the inequalities into statements about Taylor coefficients of analytic functions, which become ellipses in the slope-curvature plane. The authors then show that expanding in the conformal variable rather than in $(w-1)$ absorbs the strong slope-curvature correlation the ellipses display, so that a second-order polynomial in an optimized variable $z_*$ reproduces each form factor to better than 2% over the full physical region, with the curvature slaved to the slope along the major axis of the allowed ellipse.

Load-bearing premise

The claimed 2% accuracy rests on assigning a fixed uncertainty of $0.1$ to each of the heavy-quark symmetry-breaking coefficients $B_j$, $C_j$, and $D_j$ in the ratio expansions; no derivation of that number is given, and the paper itself says these uncertainties ultimately limit the accuracy of the dispersive approach.

Editorial extensions

If this is right

The slope of $V_1$ at zero recoil is confined to $-0.17 < rho_1^2 < 1.51$, and the slope of $A_1$ to $-0.14 < rho_{A_1}^2 < 1.54$, so the shape of the recoil spectrum is bounded before any data are fitted.
Experimental recoil spectra in $B to D l nu$ and $B to D^* l nu$ can be fitted with a single shape parameter instead of an unconstrained linear or quadratic form, removing an assumption that had been made without an assigned error.
Refitting the available $B to D^* l nu$ data with the constrained parametrizations yields $|V_{cb}|$ values systematically about one standard deviation above the linear-fit result, with $F(1)$ and the slopes correspondingly larger.
The same construction yields parametrizations for all remaining $B^(*) to D^(*)$ form factors through the ratio expansions collected in the Appendix, so the method covers the full set of twenty rather than a chosen few.
The two independent expansions, in $z(w,1)$ around zero recoil and in $z(w,a_*)$ around the middle of the semileptonic region, produce nearly indistinguishable shapes for $1 <= w < 1.6$, and the dispersive bounds in the two cases are dominated by different spin-parity channels.

Reading between the lines

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

Because the bounds are dominated by the scalar and pseudoscalar channels while the parametrization is applied to vector and axial form factors, the agreement between the two expansions is doing more epistemic work than any single inequality: it is a cross-check between channels that the paper does not quantify as a systematic.
The framework is naturally extended by treating the slope parameter as a quantity to be extracted jointly from lattice-QCD form-factor shapes and from experimental recoil spectra, which would test the dispersive domain rather than merely use it.
The same analyticity-plus-positivity-plus-symmetry template should apply to the $B to pi l nu$ and $B to rho l nu$ form factors, where the light final-state meson makes the symmetry relations weaker but the conformal expansion still controls the shape.
If a future lattice calculation returned a slope outside the quoted intervals, that would not merely shift a parameter; it would indicate that the spectral functions carry contributions below the $B^{(*)}D^{(*)}$ thresholds larger than the neglected subthreshold cuts assumed here.

Original abstract

Dispersive constraints on the shape of the form factors which describe the exclusive decays B -> D^(*) l nu are derived by fully exploiting spin symmetry in the ground-state doublet of heavy-light mesons. The analysis includes all twenty B^(*) -> D^(*) semileptonic form factors. Heavy-quark symmetry, with both short-distance and 1/m_Q corrections included, is used to provide relations between the form factors near zero recoil. Simple one-parameter functions are derived, which describe the form factors in the semileptonic region with an accuracy of better than 2%. The implications of our results for the determination of |V_cb| are discussed.

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, 4,223 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.95 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Dispersive constraints on the shape of the form factors which describe the exclusive decays B -> D^(*) l nu are derived by fully exploiting spin symmetry in the ground-state doublet of heavy-light mesons. The analysis includes all twenty B^(*) -> D^(*) semileptonic form factors. Heavy-quark symmetry, with both short-distance and 1/m_Q corrections included, is used to provide relations between the form factors near zero recoil. Simple one-parameter functions are derived, which describe the form factors in the semileptonic region with an accuracy of better than 2%. The implications of our results for the determination of |V_cb| are discussed.

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	Dispersive constraints on the shape of the form factors which describe the exclusive decays B -> D^(*) l nu are derived by fully exploiting spin symmetry in the ground-state doublet of heavy-light mesons.	contribution 0.88	0.91	0.29	asserted 1.00
s1	The analysis includes all twenty B^() -> D^() semileptonic form factors.	contribution 0.82	0.87	0.06	asserted 1.00
s2	Heavy-quark symmetry, with both short-distance and 1/m_Q corrections included, is used to provide relations between the form factors near zero recoil.	method 0.98	0.70	0.06	asserted 1.00
s3	Simple one-parameter functions are derived, which describe the form factors in the semileptonic region with an accuracy of better than 2%.	result 0.99	0.95	0.50	asserted 1.00
s4	The implications of our results for the determination of \|V_cb\| are discussed.	interpretation 1.00	0.62	0.10	unclear 0.85

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

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

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.** Bounds on the slope and curvature of the reference form factor V1(w) obtained from the unitarity inequalities in the different spin–parity channels. Dashed curves correspond to the heavy-quark limit, while solid ones include the leading corrections to that limit. Note that the axes in the lower plots are extended by a factor of 2. ellipsoid in (ρ 2 1 , c1, d1) space, whose axes are roughly in the ratios 1 : 1/8 : 1/64. The coefficient d1 is thus determined within a rather small range: d1 = b4 + b5ρ 2 1 + b6c1 64 ± ∆ , (27) where ∆ < K/64 ≈ 0.02. We will see below that this is

**Figure 2.** Bounds on the slope and curvature of the reference form factor V1(w) obtained by including the third-derivative terms in the unitarity inequalities for the 0 ± channels, taking theoretical uncertainties in the calculation of corrections that break heavy-quark symmetry into account

**Figure 3.** For each choice of ρ 2 1∗ , the parameter c1∗ is scanned over the region allowed by the dispersive bounds. Because S is large compared with K2 , and because the term multiplying c1∗ in expression (29) for the form factor is suppressed by the small factor z 2 ∗ , the spread in the curves caused by the variation of c1∗ is very small. Therefore, to a very good accuracy, c1∗ can be replaced by ¯c1 + tanϕ (ρ 2 1∗ −ρ¯ 2 1 ). This gives the one-parameter function V1(w) V1(1) ≈ 1 − 9.105ρ 2 1∗ z∗ + (57.0ρ 2 1∗ − 7.5)z 2 ∗ 0.354ρ 2 1∗ + 0.992 , with z∗ = √ w + 1 − 1.5

**Figure 4.** Bounds on the slope and curvature of the reference form factor V1(w) obtained using an expansion in the optimized variable z∗. The solid (dashed) ellipses show the results obtained with (without) including theoretical uncertainties in the heavy-quark relations. 1/BS1 (z∗) contains the scalar poles. The fact that rconv = |z∗|max/|z∗pole| is so small guarantees that the expansion of [φS1 (z∗)BS1 (z∗)]−1 converges rapidly. We find that the first three terms in this expansion deviate by at most 0.2% from the full function over the whole semileptonic region. As a result, the form factor…

**Figure 5.** Upper plot: Allowed shapes for the function V1(w) for various values of ρ 2 1∗ (the slope at w0 ≈ 1.276) chosen such that they correspond to the values of ρ 2 1 (the slope at w = 1) of

**Figure 6.** Experimental data for the product |Vcb| F(w) as a function of w, extracted from semileptonic B¯ → D∗ ℓ ν¯ decays [34]. The solid curve is a fit using our parametrization in (38), while the (barely visible) long-dashed one refers to the parametrization of (39). The two curves are nearly indistinguishable in the semileptonic domain. The short-dashed line shows a straight-line fit, similar to the one used in the experimental analysis

Figures reproduced from arXiv:hep-ph/9712417 by the authors.

References

Works cited (42)

[9]

N.N. Meiman, Sov. Phys. JETP 17, 830 (1963)

View on Pith 1963
[20]

C.G. Boyd, B. Grinstein and R.F. Lebed, Phys. Rev. D 56, 6895 (1997)

View on Pith 1997
[1]

M. Neubert, Phys. Lett. B 264, 455 (1991); 338, 84 (1994)

View on Pith 1991
[2]

N. Isgur and M.B. Wise, Phys. Lett. B 232, 113 (1989); 237, 527 (1990)

View on Pith 1989
[3]

For a review, see: M. Neubert, Phys. Rep. 245, 259 (1994); Int. J. Mod. Phys. A 11, 4173 (1996)

View on Pith 1994
[4]

M.E. Luke, Phys. Lett. B 252, 447 (1990)

View on Pith 1990
[5]

A.F. Falk and M. Neubert, Phys. Rev. D 47, 2965 and 2982 (1993)

View on Pith 1993
[6]

M. Shifman, N.G. Uraltsev and A. Vainshtein, Phys. Rev. D 51, 2217 (1995)

View on Pith 1995
[7]

A. Czarnecki, Phys. Rev. Lett. 76, 4124 (1996)

View on Pith 1996
[8]

Z. Ligeti, Y. Nir and M. Neubert, Phys. Rev. D 49, 1302 (1994)

View on Pith 1994
[10]

S. Okubo, Phys. Rev. D 3, 2807 (1971); S. Okubo and I. Shih, Phys. Rev. D 4, 2020 (1971)

View on Pith 1971
[11]

V. Singh and A.K. Raina, Forts. der Physik 27, 561 (1979)

View on Pith 1979
[12]

C. Bourrely, B. Machet and E. de Rafael, Nucl. Phys. B 189, 157 (1981)

View on Pith 1981
[13]

E. de Rafael and J. Taron, Phys. Lett. B 282, 215 (1992)

View on Pith 1992
[14]

E. de Rafael and J. Taron, Phys. Rev. D 50, 373 (1994). 30

View on Pith 1994
[15]

I. Caprini, Z. Phys. C 61, 651 (1994)

View on Pith 1994
[16]

I. Caprini, Phys. Lett. B 339, 187 (1994); Phys. Rev. D 52, 6349 (1995)

View on Pith 1994
[17]

C.G. Boyd, B. Grinstein and R.F. Lebed, Phys. Lett. B 353, 306 (1995); Nucl. Phys. B 461, 493 (1996)

View on Pith 1995
[18]

I. Caprini and C. Macesanu, Phys. Rev. D 54, 5686 (1996)

View on Pith 1996
[19]

I. Caprini and M. Neubert, Phys. Lett. B 380, 376 (1996)

View on Pith 1996
[21]

E.J. Eichten and F. Feinberg, Phys. Rev. D 23, 2724 (1981); E.J. Eichten and C. Quigg, Phys. Rev. D 49, 5845 (1994)

View on Pith 1981
[22]

D.J. Broadhurst, Phys. Lett. B 101, 423 (1981)

View on Pith 1981
[23]

S.C. Generalis, J. Phys. G 16, 367 and 785 (1990)

View on Pith 1990
[24]

A. Djouadi and P. Gambino, Phys. Rev. D 49, 3499 (1994)

View on Pith 1994
[25]

L.J. Reinders, S. Yazaki and H.R. Rubinstein, Phys. Rep . 127, 1 (1985)

View on Pith 1985
[26]

I. Caprini, J. Phys. A: Math. Gen. 14, 1271 (1981); I. Caprini, I. Guiasu and E.E. Radescu, Phys. Rev. D 25, 1808 (1982)

View on Pith 1981
[27]

J.L. Walsh, Interpolation and Approximation by Rational Functions in t he Complex Domain (American Mathematical Society, Providence, RI, 1956)

View on Pith 1956
[28]

R.E. Cutkoski and B.B. Deo, Phys. Rev. 174, 1859 (1968)

View on Pith 1968
[29]

Z. Nehari, Conformal Mapping (Dover Publ., 1952)

View on Pith 1952
[30]

C.G. Boyd and R.F. Lebed, Nucl. Phys. B 485, 275 (1997)

View on Pith 1997
[31]

C.G. Boyd, Z. Ligeti, I.Z. Rothstein and M.B. Wise, Phys . Rev. D 55, 3027 (1997)

View on Pith 1997
[32]

CLEO Collaboration (J.E. Duboscq et al.), Phys. Rev. Le tt. 76, 3898 (1996); CLEO Collaboration (A. Anastassov et al.), Preprint CLEO CO NF 96-8, ICHEP96 PA05-079, contributed paper to the 28th International Conf erence on High Energy Physics, Warsaw, Poland, July 1996

View on Pith 1996
[33]

For a discussion of this uncertainty, see: L.K. Gibbons , Proceedings of the 28th International Conference on High-energy Physics (ICHEP 96 ), Warsaw, Poland, July 1996, p. 183 [hep-ex/9704017]

View on Pith Pith review arXiv 1996
[34]

CLEO Collaboration (B. Barish et al.), Phys. Rev. D 51, 1014 (1995). 31

View on Pith 1995
[35]

ARGUS Collaboration (H. Albrecht et al.), Z. Phys. C 57, 533 (1993); Phys. Rep. 276, 223 (1996)

View on Pith 1993
[36]

ALEPH Collaboration (D. Buskulic et al.), Phys. Lett. B 395, 373 (1997)

View on Pith 1997
[37]

DELPHI Collaboration (P. Abreu et al.), Z. Phys. C 71, 539 (1996)

View on Pith 1996
[38]

OPAL Collaboration (K. Ackerstaﬀ et al.), Phys. Lett. B 395, 128 (1997)

View on Pith 1997
[39]

J.E. Paschalis and G.J. Gounaris, Nucl. Phys. B 222, 473 (1983); F.E. Close, G.J. Gounaris and J.E. Paschalis, Phys. Lett. B 149, 209 (1984)

View on Pith 1983
[40]

A.F. Falk and B. Grinstein, Phys. Lett. B 249, 314 (1990)

View on Pith 1990
[41]

M. Neubert, Phys. Rev. D 46, 2212 (1992); Nucl. Phys. B 371, 149 (1992)

View on Pith 1992
[42]

M. Neubert, Z. Ligeti and Y. Nir, Phys. Lett. B 301, 101 (1993); Phys. Rev. D 47, 5060 (1993); Z. Ligeti, Y. Nir and M. Neubert, Phys. Rev. D 49, 1302 (1994). 32

View on Pith 1993

Forward citations

Showing 60 of 81 Pith papers that cite this

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. See all 81 Pith citations

Unitarity bounds with subthreshold and anomalous cuts for $b$-hadron decays
hep-ph 2024-12 conditional novelty 8.0 of 10

A generalized, unitarity-bounded parametrization for b-hadron decay form factors that incorporates subthreshold and anomalous branch cuts is constructed.
$B \rightarrow D^*$ vector, axial-vector and tensor form factors for the full $q^2$ range from lattice QCD
hep-lat 2023-04 accept novelty 7.0 of 10

Lattice QCD form factors for B to D* and Bs to Ds* across the full kinematic range give Vcb = 39.03(56)exp(67)latt x 10^-3 and a lattice-only R(D*) = 0.273(15).
Test of Lepton Flavor Universality by the measurement of the $B^0 \to D^{*-} \tau^+ \nu_{\tau}$ branching fraction using three-prong $\tau$ decays
hep-ex 2017-11 accept novelty 7.0 of 10

Using three-prong tau decays, LHCb measures R(D*) = 0.291 +/- 0.019 (stat) +/- 0.026 (syst) +/- 0.013 (ext), consistent with the Standard Model within about one standard deviation.
Hilbert Series of Pseudoscalar Mesons: Operators and Sum Rules
hep-ph 2026-08 conditional novelty 6.0 of 10

A Hilbert series construction yields the complete four-meson, two-derivative operator basis with CKM spurions, from which all leading-order B to pseudoscalar decay sum rules follow as null vectors.
Decay constants of the $B_c$ mesons with vector and tensor currents
hep-ph 2026-06 conditional novelty 6.0 of 10

QCD sum-rule computation of vector/axial-vector and tensor/axial-tensor decay constants for B_c, B_c*, B_c0*, B_c1 mesons, with refined power corrections and first tensor results.

Show 55 more citing papers

$V_{cb}$ puzzle in semi-leptonic $B\to D^*$ decays revisited
hep-ph 2024-12 conditional novelty 6.0 of 10

Using the latest Belle and Belle II data, CLN, BGL, and HQET fits give consistent exclusive |Vcb| values near 39.7 times 10^-3, confirming the persistent 2 to 3 sigma gap with the inclusive value.
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.
Lepton-flavour non-universality of $\bar{B}\to D^*\ell \bar\nu$ angular distributions in and beyond the Standard Model
hep-ph 2021-04 conditional novelty 6.0 of 10

Belle's 2018 B to D* lepton-neutrino angular data, recast into the four independent angular observables it actually contains, shows a roughly 4-sigma electron-muon non-universality in the forward-backward asymmetry, t...
$B_c \rightarrow J/\psi$ Form Factors for the full $q^2$ range from Lattice QCD
hep-lat 2020-07 accept novelty 6.0 of 10

The first lattice QCD determination of the B_c to J/psi form factors across the full q-squared range yields a total semileptonic rate of 1.73(12)e13 per second and a branching fraction of 0.0150(11)(10)(3).
Theory determination of $\bar{B}\to D^{(*)}\ell^-\bar\nu$ form factors at $\mathcal{O}(1/m_c^2)$
hep-ph 2019-08 accept novelty 6.0 of 10

A full heavy-quark expansion to order 1/m_c^2 for all B to D and D* form factors gives a consistent theory determination of |V_cb| = (40.3 ± 0.8) x 10^-3 and sharp predictions for R(D^(*)).
Model-independent method for measuring the angular coefficients of $B^0 \to D^{*-} \tau^+ \nu_{\tau}$ decays
hep-ph 2019-08 conditional novelty 6.0 of 10

A multidimensional template fit recovers the B0 to D*- tau+ nu_tau angular coefficients unbiasedly and model-independently despite missing neutrino information.
$B_s\to D_s \ell\nu$ Form Factors for the full $q^2$ range from Lattice QCD with non-perturbatively normalized currents
hep-lat 2019-06 accept novelty 6.0 of 10

The Bs to Ds scalar and vector form factors are computed over the full q-squared range with a non-perturbatively normalized lattice current, yielding R(Ds) = 0.2987(46) in the Standard Model.
Measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^{\ast})$ with a semileptonic tagging method
hep-ex 2019-04 accept novelty 6.0 of 10

With 772 million B-meson pairs and a semileptonic tag, Belle measures R(D) = 0.307 +/- 0.037 +/- 0.016 and R(D*) = 0.283 +/- 0.018 +/- 0.014, both consistent with Standard Model predictions.
$B\to P$ 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.
The pressure distribution and shear forces inside the proton
nucl-th 2018-10 conditional novelty 6.0 of 10

Combining lattice-QCD quark and gluon energy-momentum tensor form factors yields the first full pressure and shear distributions inside the proton, with gluons dominating the shear at 2 GeV.
It's all right(-handed neutrinos): a new $W'$ model for the $R_{D^{(*)}}$ anomaly
hep-ph 2018-04 conditional novelty 6.0 of 10

A W' that couples only to right-handed quarks and leptons, plus a light right-handed neutrino, can explain both R_D and R_D* while evading flavor-changing, electroweak-precision, and Z'-to-tau-tau collider bounds.
Constraining new physics in $b\to c\ell\nu$ transitions
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^-...
Measurement of the ratio of the $B^0 \to D^{*-} \tau^+ \nu_{\tau}$ and $B^0 \to D^{*-} \mu^+ \nu_{\mu}$ branching fractions using three-prong $\tau$-lepton decays
hep-ex 2017-08 accept novelty 6.0 of 10

Using 3 fb^-1 of LHCb data and a new three-pion tau final state, the ratio R(D*) = 0.291 +/- 0.019 (stat) +/- 0.026 (syst) +/- 0.013 (ext) is measured, about 1.1 sigma above the Standard Model.
$R(D^*)$, $|V_{cb}|$, and the Heavy Quark Symmetry relations between form factors
hep-ph 2017-07 conditional novelty 6.0 of 10

Using heavy quark symmetry to strengthen unitarity bounds on B to D* form factors, the authors obtain |Vcb| between 40.6 and 41.5 times 10^-3 and R(D*) = 0.260(8), about 2.6 sigma below the experimental average.
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.
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.
A closer look at the $R_D$ and $R_{D^*}$ anomalies
hep-ph 2016-10 conditional novelty 6.0 of 10

Within a dimension-6 effective field theory, the authors show that binned R_D*, tau polarization, and tau forward-backward asymmetry together can separate the operator structures that could explain the R_D and R_D* anomalies.
Deuterium target data for precision neutrino-nucleus cross sections
hep-ph 2016-03 conditional novelty 6.0 of 10

A model-independent reanalysis of neutrino-deuterium data gives an axial radius r_A^2 = 0.46(22) fm^2, several times less precise than dipole-based extractions, and a neutrino-neutron quasielastic cross section of 10....
New physics in the kinematic distributions of $\bar B\to D^{(*)}\tau^-(\to\ell^-\bar\nu_\ell\nu_\tau)\bar\nu_\tau$
hep-ph 2016-02 conditional novelty 6.0 of 10

The three-fold differential rate for B to D(*) tau (to lepton neutrino neutrino) neutrino factorizes into three angular coefficients, and the forward-backward asymmetry coefficient is a new observable that changes sig...
The $B \to D \ell \nu$ form factors at nonzero recoil and $|V_{cb}|$ from $2+1$-flavor lattice QCD
hep-lat 2015-03 conditional novelty 6.0 of 10

Fourteen lattice ensembles give the B to D form factors across the full recoil range, fixing |Vcb| = 39.6(1.7)(0.2) x 10^-3 and R(D) = 0.299(11) in the Standard Model.
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...
Measurement of an Excess of B -> D(*) Tau Nu Decays and Implications for Charged Higgs Bosons
hep-ex 2013-03 conditional novelty 6.0 of 10

BaBar's full-dataset measurement finds R(D) = 0.440 and R(D*) = 0.332, exceeding Standard Model expectations at a combined 3.4 sigma and excluding a type II charged Higgs.
Refining new-physics searches in B -> D tau nu decay with lattice QCD
hep-ph 2012-06 conditional novelty 6.0 of 10

A full lattice-QCD calculation gives R(D) = 0.316(12)(7) and P_L(D) = 0.325(4)(3), about one sigma above earlier estimates and 1.7 sigma below the BaBar measurement.
Model independent extraction of the proton charge radius from electron scattering
hep-ph 2010-08 conditional novelty 6.0 of 10

Expanding the proton form factor in a conformally mapped variable with bounded coefficients yields a charge radius of 0.870 to 0.880 fm from scattering data without assuming a functional form.
Semitauonic $b$-hadron decays: A lepton flavor universality laboratory
hep-ex 2021-01 accept novelty 5.5 of 10

The paper reviews semitauonic b-decay measurements and shows that the R(D(*)) world-average tension with the Standard Model depends on how D** background uncertainties are correlated across experiments.
Unitarity bounds and form-factor predictions for $B$-meson decays
hep-ph 2026-05 unverdicted novelty 5.0 of 10

Reviews unitarity bounds for B-meson form factors, shows standard methods apply rigorously only to B→π, develops GG parametrization for general cases, and delivers combined-analysis predictions with public supplementa...
$B \to D^*\ell\nu_\ell$ semileptonic form factors from lattice QCD with M\"obius domain-wall quarks
hep-lat 2023-06 conditional novelty 5.0 of 10

Lattice QCD with Möbius domain-wall quarks gives R(D*) = 0.252(22) in the Standard Model and, fitted jointly with Belle data, |Vcb| = 39.19(91) x 10^-3.
Measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$ with a semileptonic tagging method
hep-ex 2019-10 accept novelty 5.0 of 10

Belle reports R(D) = 0.307 +/- 0.037 +/- 0.016 and R(D*) = 0.283 +/- 0.018 +/- 0.014, the most precise measurements to date and consistent with Standard Model predictions.
Lepton Flavor Universality tests through angular observables of $\overline{B}\to D^{(\ast)}\ell\overline{\nu}$ decay modes
hep-ph 2019-07 unverdicted novelty 5.0 of 10

Angular observables in B→D(*)ℓν decays can distinguish Lorentz structures of new physics contributions fitted to measured R(D(*)) ratios, even when those ratios agree with the Standard Model.
Global fit to $b \to c \tau \nu$ transitions
hep-ph 2019-04 conditional novelty 5.0 of 10

A global effective-field-theory fit to b to c tau nu data leaves two viable new-physics solutions and finds the measured D* longitudinal polarization in tension with all of them.
Anatomy of $b \to c \, \tau \, \nu$ anomalies
hep-ph 2018-05 conditional novelty 5.0 of 10

Meson-mixing constraints force the partial-compositeness scale needed to explain the R_D and R_D* anomalies down to about 650 GeV, in tension with electroweak precision observables.
Scrutinizing $\bar B \to D^*(D \pi) \ell^- \bar \nu_\ell$ and $\bar B \to D^*(D \gamma) \ell^- \bar \nu_\ell$ in search of new physics footprints
hep-ph 2018-01 conditional novelty 5.0 of 10

Angular coefficients in B → D*(→ Dπ, Dγ) ℓ ν decays provide form-factor-independent observables and a handle on tensor-type new physics.
One constraint to kill them all?
hep-ph 2017-12 conditional novelty 5.0 of 10

Updated lattice inputs raise the Standard Model B_s mixing prediction to 20.0 ps^-1 against a measured 17.76 ps^-1, tightening Z-prime and leptoquark mass bounds by roughly a factor of five.
Lattice QCD calculation of the ${{B}_{(s)}\to D_{(s)}^{*}\ell{\nu}}$ form factors at zero recoil and implications for ${|V_{cb}|}$
hep-lat 2017-11 accept novelty 5.0 of 10

Independent lattice determinations of the zero-recoil B to D* and Bs to Ds* form factors give 0.895(26) and 0.883(31), and combined with BGL/BCL fits to unfolded Belle data imply |Vcb| = 41.3(2.2) x 10^-3.
Extraction of $|V_{cb}|$ from $B\to D^{(*)}\ell\nu_\ell$ and the Standard Model predictions of $R(D^{(*)})$
hep-ph 2017-07 conditional novelty 5.0 of 10

Combined fits to B→Dℓν and B→D*ℓν data give |Vcb| = 39.77×10^-3 (CLN) and 40.90×10^-3 (BGL), with SM predictions R(D*) = 0.259 (CLN) and 0.257 (BGL).
A fresh look at the determination of |V_cb| from B-> D^* l nu
hep-ph 2017-03 conditional novelty 5.0 of 10

The CLN and BGL form-factor parameterizations applied to the same new Belle B to D* l nu data yield |Vcb| values differing by 9 percent, and the shift traces to CLN's fixed HQET slopes for the ratios R1 and R2.
Precise determination of the CKM matrix element $\left| V_{cb}\right|$ with $\bar B^0 \to D^{*\,+} \, \ell^- \, \bar \nu_\ell$ decays with hadronic tagging at Belle
hep-ex 2017-02 conditional novelty 5.0 of 10

Belle determines |Vcb| = (37.4 ± 1.3) × 10^-3 from hadronically tagged B0 → D*+ ℓ- ν decays, consistent with the world average, and reports unfolded differential decay rates.
Probing new physics in $\bar{B}^0 \to D^{(\ast)} \tau^- \bar\nu_{\tau}$ using the longitudinal, transverse, and normal polarization components of the tau lepton
hep-ph 2017-01 conditional novelty 5.0 of 10

The tau lepton's transverse and normal spin components in B to D(*) tau neutrino are shown to be sensitive probes of new physics, with the normal component reaching order 0.2 to 0.8 under complex new-physics couplings.
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 lifetime of the $B_c^-$ meson and the anomalies in $B\to D^{(*)}\tau\nu$
hep-ph 2016-11 accept novelty 5.0 of 10

The Bc meson lifetime excludes scalar-operator explanations of the R_D* anomaly and leaves only left-handed or tensor new physics.
LHC constraints and prospects for $S_1$ scalar leptoquark explaining the $\bar B \to D^{(*)} \tau \bar\nu$ anomaly
hep-ph 2016-03 conditional novelty 5.0 of 10

Simulated 14 TeV LHC searches in the (b nu)(b nu) and (c tau)(c tau) channels can exclude or discover the S1 leptoquark that explains the B to D(*) tau nu anomaly up to masses of roughly 0.8 to 1.1 TeV.
Probing New Physics with $q^2$ distributions in $\bar{B} \to D^{(*)} \tau \bar\nu$
hep-ph 2014-12 conditional novelty 5.0 of 10

Ratios of tauonic to light-lepton B decay rates binned in momentum transfer separate competing new-physics explanations of the B to D(*) tau nu excess, and Belle II could test most of them with 1 to 6 inverse attobarns.
Testing leptoquark models in $\bar B \to D^{(*)} \tau \bar\nu$
hep-ph 2013-09 conditional novelty 5.0 of 10

Three leptoquark models (scalar S1, scalar R2, vector U1) can reproduce the measured R(D) and R(D*) ratios with order-one couplings at a 1 TeV mass, and their predictions for tau and D* polarization differ enough to d...
B -> K^* Form Factors from Flavor Data to QCD and Back
hep-ph 2013-08 accept novelty 5.0 of 10

Form factor ratios extracted from B to K-star dilepton angular data at low recoil, combined with heavy-quark symmetry and LCSR input, yield Standard-Model-consistent predictions for A_FB and P'_5.
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-...
On the anomalous enhancement observed in $B \to D^{(*)} \, \tau \, {\bar \nu}_\tau $ decays
hep-ph 2013-02 conditional novelty 5.0 of 10

A tensor operator added to the standard weak Hamiltonian can reproduce the measured B to D(*) tau neutrino excess without altering B to tau neutrino, and it predicts shifted forward-backward asymmetries and enhanced r...
New physics in the weak interaction of $\bar B\to D^{(*)}\tau\bar\nu$
hep-ph 2012-12 accept novelty 5.0 of 10

Using the most general four-fermion Lagrangian for b to c tau nu, the authors show that scalar and tensor operators can explain the measured R(D) and R(D*) excess, while 2HDM type II without FCNC and R-parity-violatin...
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.
$\bar B\to D\tau\bar \nu_\tau$ vs. $\bar B\to D\mu\bar \nu_\mu$
hep-ph 2012-06 conditional novelty 5.0 of 10

A hybrid experimental-plus-lattice extraction gives R(D) = 0.31 ± 0.02, roughly 1.7σ below the BaBar measurement, and shows the Standard Model test needs only the lattice ratio of scalar to vector form factors.
Constraints on the charged scalar effects using the forward-backward asymmetry on $B\to D^{(*)}\tau\bar{\nu_{\tau}}$
hep-ph 2012-05 conditional novelty 5.0 of 10

Forward-backward asymmetries built from the tau's hadronic decay products can distinguish the four allowed regions of charged-scalar couplings that B to D(*) tau nu branching ratios leave degenerate.
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...
Measurement of the form factors of the decay B0 -> D*- ell+ nu and determination of the CKM matrix element |Vcb|
hep-ex 2010-10 conditional novelty 5.0 of 10

Belle's 711 fb^-1 analysis of B0 to D-star lepton neutrino decays yields the most precise HQET form factor parameters and F(1)|Vcb| at the time, with |Vcb| = 37.5 ± 0.2 ± 1.1 ± 1.0 × 10^-3.
Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays
hep-ph 2010-04 accept novelty 5.0 of 10

Two-term series expansions, constrained by newly computed NLO tensor-current dispersive bounds, describe B to K, rho, K* and phi form factors across the whole decay region and reproduce lattice points not used in the fits.
An introduction to Hammer v2: Helicity Amplitude Module for Matrix Element Reweighting
hep-ph 2026-07 unverdicted novelty 4.0 of 10

Hammer v2 updates the helicity amplitude reweighting library with near-linear scaling for high-dimensional tensor operations in BSM and form-factor spaces plus improved Python bindings.
$|V_{cb}|$ 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.

See all 81 Pith citations

How later papers used it

186 later papers cite it

Evidence: substantial. 182 of the citing papers share no author with it, and 88 of those carry a confident label from Pith's citation classifier.

Pith read 26 of the 346 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 and 1 compared its own results with it. 1 of them appears under more than one label.

Uses its method or tool 4 of 70 papers with this label

Adopted expressions derived by Caprini, Lellouch and Neubert in this paper.

Measurement of the form factors of the decay B^+\to\bar D^{*0}\ell^+\nu_\ell and determination of the CKM matrix element |V_{cb}| (2009) · 0.98 · paraphrased: the licence does not allow quoting
Adopted expressions derived by Caprini, Lellouch and Neubert in this paper.

Measurement of the form factors of the decay B0 -> D*- ell+ nu and determination of the CKM matrix element |Vcb| (2010) · 1.00 · paraphrased: the licence does not allow quoting
Used the parametrization defined in this paper, which introduces three free parameters to govern the shape of the form factors.

Semileptonic Decays at Belle (2008) · 0.99 · paraphrased: the licence does not allow quoting
Adopted expressions derived by Caprini, Lellouch and Neubert in this paper.

Measurement of the form factors of the decay B^0 -> D^{*-} l^+ nu_l and determination of the CKM matrix element |V_{cb}| (2008) · 0.97 · paraphrased: the licence does not allow quoting

Compares with it 1 of 8 papers with this label

Computed a numerical measure of the agreement between its own two dimensional fit result and the functions predicted by this paper's parameterization.

Measurement of the form factors of the decay B0 -> D*- ell+ nu and determination of the CKM matrix element |Vcb| (2010) · 0.83 · paraphrased: the licence does not allow quoting

How the literature uses it

168 arXiv papers cite this in 315 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 · 180 sentences without a confident label

Contests it 4 papers

This supports the approach used in Ref. [ref] ; (iii) The slope-curvature relation developed by Ref. [ref] is in tension with the data, and leads to large upward biases in $R(D)$; (iv) The VC limit, in contrast to the RC expansion, produces poor fits because of its structure at zero recoil, but using only shape information yields good fits.

Constrained second-order power corrections in HQET: $R(D^{(*)})$, $|V_{cb}|$, and new physics · Introduction · contest 0.78
Since the approximations made in Ref. [ref] are no longer sufficiently justified in view of the current precision, the latter has been extended by including higher-order radiative and power corrections [ref] .

$|V_{cb}|$ determinations from $\bar{B} \to D^{(*)} \ell \bar\nu$ decays within the SM and beyond · Introduction · contest 0.76
The form factor $F_0(q^2)$ is given as [ref] [In Ref. [ref] , $f_0(w)$ was transcribed there in Eq. (11b) with a typo [$+ ρ_0^2 (w - 1)$ instead of $-ρ_0^2 (w - 1)$], but the correct expression ([ref]) was used in the calculations there.]

Exploring CP-violation, via heavy neutrino oscillations, in rare B meson decays at Belle II · Decay width $Γ(B →D ℓ_1 N)$ · contest 0.80

Uses its method or tool 63 papers

A fit to the theoretical expression for the four-dimensional differential decay width (Eq. [ref]), assuming the parameterization of the helicity amplitude given by Caprini et al. [ref] yields a measurement of $|V_cb|$ times the form factor normalization at zero recoil, $ℱ(1)|V_cb|=(35.0±0.4±2.2)×10^-3$.

Measurement of the form factors of the decay B^+\to\bar D^{*0}\ell^+\nu_\ell and determination of the CKM matrix element |V_{cb}| · Summary and discussion · 0.98
We adopt the following expressions derived by Caprini, Lellouch and Neubert [ref] , [equation] where $z=(√(w+1)-√(2))/(√(w+1)+√(2))$.

Measurement of the form factors of the decay B0 -> D*- ell+ nu and determination of the CKM matrix element |Vcb| · Form factor parameterization · 1.00
[equation] where $i$ and $j$ denote the indices of the bins in the observables , and $ΔΓ_i^pre/Γ^pre$ and $Γ^pre$ are the predicted values expressed as functions of the form-factor parameters and [ref] .

Determination of $|V_{cb}|$ using $\overline{B}^0\to D^{*+}\ell^-\bar\nu_\ell$ decays with Belle II · Results · 0.97

Uses its data or values 8 papers

Here $h_±(ω(q^2) )$ are the HQET form factors taken from the Ref. [ref] .

Explaining the $R_{K}$ and $R_{D^{(*)}}$ anomalies with vector leptoquarks · $B →D τν̅_l$ form factors · 0.99
For these renormalized subleading Isgur-Wise functions, we use [equation] These central values reproduce $L̂_1…6$ in Ref. [ref] , often used to predict $R_1,2$ and $R(D^(*))$.

Combined analysis of semileptonic $B$ decays to $D$ and $D^*$: $R(D^{(*)})$, $|V_{cb}|$, and new physics · QCD sum rule inputs · 0.96
* $B̅→D^∗τν̅_τ$ [equation] where all the $B→D$ and $B→D^∗$ form factors are taken from Refs. [ref] , except for $S_1(w)$, for which we use the form given by Eq. (A6) in Ref. [ref] .

Revisiting the one leptoquark solution to the $R(D^{(\ast)})$ anomalies and its phenomenological implications · Hadronic amplitudes in $B̅→D^(∗)τν̅_τ$ decays · 0.91

Compares with it 8 papers

Finally we compute a numerical measure of the agreement between the result obtained from this two dimensional fit with the functions predicted by the parameterization of Caprini, Lellouch and Neubert [ref] .

Measurement of the form factors of the decay B0 -> D*- ell+ nu and determination of the CKM matrix element |Vcb| · Results · 0.83
We find it is very close comparing our results without $𝒪(ε_c^2)$ terms to [ref] along with the updated one in [ref] , however these corrections have non-negligible effects. $A_j,B_j,C_j,D_j$ within the tables are defined by [equation] where $F_j,V_1$ are form factors defined in [ref] , and $ω_0=1$ in our calculation.

Exclusive Determination of $|V_{cb}|$ from Semileptonic Decays $B\to D^{(*)}\ell \nu_{\ell}$ · Strong unitary bound · 1.00
A direct, model-independent determination of the form factor shapes has also been carried out and shows good agreement with the HQET based form factor parametrization by Caprini et al. [ref] .

Measurement of the form factors of the decay B^+\to\bar D^{*0}\ell^+\nu_\ell and determination of the CKM matrix element |V_{cb}| · Summary and discussion · 0.94

Cites it as support 1 paper

As argued in Ref. [ref] , the ground-state contributions $χ_0^+^(gs)$ and $χ_1^-^(gs)$ are expected to be small and they can be conservatively ignored.

Constraints for the semileptonic $B \to D^{(*)}$ form factors from lattice QCD simulations of two-point correlation functions · Subtraction of the ground-state contribution · 0.97

Cites it as background 26 papers

In the framework of Heavy Quark Effective Theory (HQET), this decay is described by three form factor parameters, $ρ^2$, $R_1(1)$ and $R_2(1)$ [ref] along with a form factor normalization $ℱ(1)$ derived from lattice QCD [ref] .

Measurement of the form factors of the decay B^+\to\bar D^{*0}\ell^+\nu_\ell and determination of the CKM matrix element |V_{cb}| · Introduction · 0.89
In the years most of the analyses used two popular parameterisations called Boyd-Grinstein-Lebed (BGL) [ref] or Caprini-Lellouch-Neubert (CLN) [ref] after the name of the authors.

Unitarity Bounds for Semileptonic Decays in Lattice QCD · Introduction · 0.99
The most popular parametrizations for this decay are BGL [ref] and CLN [ref] .

$B\to D^\ast\ell\nu$ at non-zero recoil · Notation and definitions · 0.80

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [9]

N.N. Meiman, Sov. Phys. JETP 17, 830 (1963)

View on Pith 1963

[2] [20]

C.G. Boyd, B. Grinstein and R.F. Lebed, Phys. Rev. D 56, 6895 (1997)

View on Pith 1997

[3] [1]

M. Neubert, Phys. Lett. B 264, 455 (1991); 338, 84 (1994)

View on Pith 1991

[4] [2]

N. Isgur and M.B. Wise, Phys. Lett. B 232, 113 (1989); 237, 527 (1990)

View on Pith 1989

[5] [3]

For a review, see: M. Neubert, Phys. Rep. 245, 259 (1994); Int. J. Mod. Phys. A 11, 4173 (1996)

View on Pith 1994

[6] [4]

M.E. Luke, Phys. Lett. B 252, 447 (1990)

View on Pith 1990

[7] [5]

A.F. Falk and M. Neubert, Phys. Rev. D 47, 2965 and 2982 (1993)

View on Pith 1993

[8] [6]

M. Shifman, N.G. Uraltsev and A. Vainshtein, Phys. Rev. D 51, 2217 (1995)

View on Pith 1995

[9] [7]

A. Czarnecki, Phys. Rev. Lett. 76, 4124 (1996)

View on Pith 1996

[10] [8]

Z. Ligeti, Y. Nir and M. Neubert, Phys. Rev. D 49, 1302 (1994)

View on Pith 1994

[11] [10]

S. Okubo, Phys. Rev. D 3, 2807 (1971); S. Okubo and I. Shih, Phys. Rev. D 4, 2020 (1971)

View on Pith 1971

[12] [11]

V. Singh and A.K. Raina, Forts. der Physik 27, 561 (1979)

View on Pith 1979

[13] [12]

C. Bourrely, B. Machet and E. de Rafael, Nucl. Phys. B 189, 157 (1981)

View on Pith 1981

[14] [13]

E. de Rafael and J. Taron, Phys. Lett. B 282, 215 (1992)

View on Pith 1992

[15] [14]

E. de Rafael and J. Taron, Phys. Rev. D 50, 373 (1994). 30

View on Pith 1994

[16] [15]

I. Caprini, Z. Phys. C 61, 651 (1994)

View on Pith 1994

[17] [16]

I. Caprini, Phys. Lett. B 339, 187 (1994); Phys. Rev. D 52, 6349 (1995)

View on Pith 1994

[18] [17]

C.G. Boyd, B. Grinstein and R.F. Lebed, Phys. Lett. B 353, 306 (1995); Nucl. Phys. B 461, 493 (1996)

View on Pith 1995

[19] [18]

I. Caprini and C. Macesanu, Phys. Rev. D 54, 5686 (1996)

View on Pith 1996

[20] [19]

I. Caprini and M. Neubert, Phys. Lett. B 380, 376 (1996)

View on Pith 1996

[21] [21]

E.J. Eichten and F. Feinberg, Phys. Rev. D 23, 2724 (1981); E.J. Eichten and C. Quigg, Phys. Rev. D 49, 5845 (1994)

View on Pith 1981

[22] [22]

D.J. Broadhurst, Phys. Lett. B 101, 423 (1981)

View on Pith 1981

[23] [23]

S.C. Generalis, J. Phys. G 16, 367 and 785 (1990)

View on Pith 1990

[24] [24]

A. Djouadi and P. Gambino, Phys. Rev. D 49, 3499 (1994)

View on Pith 1994

[25] [25]

L.J. Reinders, S. Yazaki and H.R. Rubinstein, Phys. Rep . 127, 1 (1985)

View on Pith 1985

[26] [26]

I. Caprini, J. Phys. A: Math. Gen. 14, 1271 (1981); I. Caprini, I. Guiasu and E.E. Radescu, Phys. Rev. D 25, 1808 (1982)

View on Pith 1981

[27] [27]

J.L. Walsh, Interpolation and Approximation by Rational Functions in t he Complex Domain (American Mathematical Society, Providence, RI, 1956)

View on Pith 1956

[28] [28]

R.E. Cutkoski and B.B. Deo, Phys. Rev. 174, 1859 (1968)

View on Pith 1968

[29] [29]

Z. Nehari, Conformal Mapping (Dover Publ., 1952)

View on Pith 1952

[30] [30]

C.G. Boyd and R.F. Lebed, Nucl. Phys. B 485, 275 (1997)

View on Pith 1997

[31] [31]

C.G. Boyd, Z. Ligeti, I.Z. Rothstein and M.B. Wise, Phys . Rev. D 55, 3027 (1997)

View on Pith 1997

[32] [32]

CLEO Collaboration (J.E. Duboscq et al.), Phys. Rev. Le tt. 76, 3898 (1996); CLEO Collaboration (A. Anastassov et al.), Preprint CLEO CO NF 96-8, ICHEP96 PA05-079, contributed paper to the 28th International Conf erence on High Energy Physics, Warsaw, Poland, July 1996

View on Pith 1996

[33] [33]

For a discussion of this uncertainty, see: L.K. Gibbons , Proceedings of the 28th International Conference on High-energy Physics (ICHEP 96 ), Warsaw, Poland, July 1996, p. 183 [hep-ex/9704017]

View on Pith Pith review arXiv 1996

[34] [34]

CLEO Collaboration (B. Barish et al.), Phys. Rev. D 51, 1014 (1995). 31

View on Pith 1995

[35] [35]

ARGUS Collaboration (H. Albrecht et al.), Z. Phys. C 57, 533 (1993); Phys. Rep. 276, 223 (1996)

View on Pith 1993

[36] [36]

ALEPH Collaboration (D. Buskulic et al.), Phys. Lett. B 395, 373 (1997)

View on Pith 1997

[37] [37]

DELPHI Collaboration (P. Abreu et al.), Z. Phys. C 71, 539 (1996)

View on Pith 1996

[38] [38]

OPAL Collaboration (K. Ackerstaﬀ et al.), Phys. Lett. B 395, 128 (1997)

View on Pith 1997

[39] [39]

J.E. Paschalis and G.J. Gounaris, Nucl. Phys. B 222, 473 (1983); F.E. Close, G.J. Gounaris and J.E. Paschalis, Phys. Lett. B 149, 209 (1984)

View on Pith 1983

[40] [40]

A.F. Falk and B. Grinstein, Phys. Lett. B 249, 314 (1990)

View on Pith 1990

[41] [41]

M. Neubert, Phys. Rev. D 46, 2212 (1992); Nucl. Phys. B 371, 149 (1992)

View on Pith 1992

[42] [42]

M. Neubert, Z. Ligeti and Y. Nir, Phys. Lett. B 301, 101 (1993); Phys. Rev. D 47, 5060 (1993); Z. Ligeti, Y. Nir and M. Neubert, Phys. Rev. D 49, 1302 (1994). 32

View on Pith 1993