Lattice QCD calculation of $\bar{B}\to Dl\bar{\nu}$ decay form factors at zero recoil

Aida X. El-Khadra; Andreas S. Kronfeld; James N. Simone; Paul B. Mackenzie; Shoji Hashimoto; Sinead M. Ryan

REVIEW

Lattice QCD calculation of $\bar{B}\to Dl\bar{\nu}$ decay form factors at zero recoil

Shoji Hashimoto, Aida X. El-Khadra, Andreas S. Kronfeld, Paul B. Mackenzie, Sinead M. Ryan, James N. Simone

High Energy Physics - Phenomenology · Submitted 15 Jun 1999 · 36 references

Pith's verdict: The double-ratio method is the real contribution and h+(1) holds up, but the headline F(1)−1 = 0.058 comes almost entirely from h−(1), which is exactly the piece with no computed one-loop matching.

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CitationAida X. El-Khadra, Andreas S. Kronfeld, James N. Simone, Paul B. Mackenzie, Shoji Hashimoto, Sinead M. Ryan. "Lattice QCD calculation of $\bar{B}\to Dl\bar{\nu}$ decay form factors at zero recoil." arXiv:hep-ph/9906376 (1999). https://pith.science/paper/P7ZBSJQ3

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Editor's note

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The thing to know before you read this: the method is the contribution, and it is a good one. The double ratios of Eqs. (22) and (31) are built to be identically one at equal heavy quark masses, so the signal is the deviation from one and most of the statistical and normalization baggage cancels between numerator and denominator. That is a clean idea, cleanly executed. The plateau checks (Fig. 2, varying the B interpolating time slice), the d1 variation shifting h+(1) by 0.00013, and the use of six heavy-quark hopping parameters to fit the 1/mQ expansion are all careful craft. h+(1) = 1.007(6)(2)(3) is credible and I would use it without much worry. The paper is also honest: it says outright that the 1/mQ coefficients are highly correlated with no full error analysis, that rhoVi is unavailable, and that quenching and lattice spacing are not included (abstract:s7). Credit for that. But your note has the weighting backwards, and it matters. Eq. (5) with the paper's own numbers gives F(1)−1 = 0.007 + 0.051: about 88% of the headline deviation comes from h−(1), not h+(1). So the number everyone will quote is hostage to the one quantity with no computed one-loop matching, in a matching series the paper itself flags as poorly convergent (Sec. 9, citing ref. [32]). The +0.010/−0.030 band is inferred from a single d1 variation plus a 10–20% heavier-to-lighter asymmetry, not derived. Double that assumed correction and you move F(1) by the whole quoted radiative error. There is a second flag the authors raise and then leave: their c(1)− = 0.212(31) sits well above the sum-rule estimates of 0.08(2) and −0.05(10) in Sec. 10. They say a direct comparison is not yet possible, which is fair, but a factor-of-two-to-four discrepancy on the coefficient that drives the signal deserves more than a paragraph. Minor by comparison: one lattice spacing at a coarse a⁻¹ ≈ 1.16 GeV, quenched, and the claim that quenching and lattice-spacing errors scale with F(1)−1 rather than F(1) is stated as expectation, not shown. That is the right expectation, but it is an expectation. Read it for the technique and for h+(1); treat F(1) = 1.058 as a promising first pass whose error bar is not yet earned. Worth a serious referee.

Referee report

Significance

If the result holds, this is the first first-principles determination of the hadronic normalization needed to extract |Vcb| from the exclusive ¯B → D l ¯ν channel, and it is a genuine methodological advance: the double-ratio construction is a clean and reusable idea, the plateau stability checks (Figs. 1 and 2, including variation of the interpolating-field time slice) are convincing, the d1 variation is shown to shift h_+(1) by only +0.00013, and the paper is candid about which systematics are and are not in the quoted error bar. The use of the 1/m_Q expansions as interpolation Ansätze, with the physical point inside the simulated mass range (Figs. 5 and 10), is appropriate and is stated as such. The paper also ships a falsifiable cross-check: the comparison of the extracted coefficients c(2)+ and c(1)- with QCD sum-rule estimates in Sec. 10, and the explicit statement that a future one-loop calculation of ρVi will allow a direct comparison. These are real strengths and should be weighed as such.

Major objections (4)

[Sec. 11, Eq. (5), Eqs. (40)–(42)] The decomposition of the headline number is never displayed, and it matters. With the paper's own inputs, (m_B - m_D)/(m_B + m_D) ≈ 0.477, so F(1) - 1 = 0.007 + 0.051 = 0.058: roughly 88% of the quoted deviation from unity comes from the h_-(1) term, not from h_+(1). This inverts the natural reading of the abstract, where h_+(1) is presented as the high-precision result and h_-(1) as a secondary quantity, and it means the headline number is hostage to precisely the ingredient with the least controlled matching. Sec. 9 states plainly that 'the one-loop contribution to ρVi is not yet available' and cites Ref. [32] for the poor convergence of the βV series and the tiny BLM scale; the +0.010/-0.030 band is then inferred from a single d1 variation at (κ_b, κ_c) = (0.089, 0.119) (Eq. 35, shift 0.0089 ± 0.0012) plus a 10–20% heavier-to-lighter versus lighter-to-heavier asymmetry in Table 2. That is an estimate, not a calculation. The authors should state the 88%/12% decomposition explicitly in Sec. 11 and show, at least as a linear sensitivity, how a shift δ in the h_-(1) matching propagates into F(1): a factor-two underestimate of the matching correction moves h_-(1) by ~0.03 and F(1) by ~0.014, i.e. the entire quoted radiative error bar.
[Sec. 10, Eq. (39), and Sec. 11] The comparison with QCD sum rules is presented as a consistency discussion but is not propagated to the result. The lattice value c(1)- = 0.246(37) GeV is a factor of three to five larger than the sum-rule estimates quoted in the same section (0.08(2) GeV from Neubert [34] and -0.05(10) GeV from Ligeti et al. [35]). Since h_-(1) generates most of F(1) - 1, this is not a side remark: if the true c(1)- were near the sum-rule range, F(1) would sit much closer to unity. The paper's hedge that 'it is difficult to make a direct comparison' because the lattice calculation contains some radiative corrections automatically is fair, but the reader is left without any quantitative statement of what the discrepancy would imply. The authors should translate the sum-rule range of c(1)- into an implied range for h_-(1) and F(1), and say explicitly whether that range is or is not excluded by their data.
[Abstract (s7), Sec. 12] The abstract quotes F_{B→D}(1) = 1.058(+20/-17), a 1.6% total error, while stating in the same paragraph that lattice-spacing dependence and quenching are not included. The structural argument that both scale with F(1) - 1 rather than with F(1) is plausible — the double ratio is identically one at equal heavy masses, so a systematic that is smooth in the heavy-mass difference must vanish there — but the coefficient is not computed, and the numerical estimate ('a few percent and ~15%', imported from the f_B experience of Refs. [18, 19]) is an extrapolation of experience rather than a property of this observable. The authors should either fold an explicit estimate of these two systematics into Eq. (42) or state in the abstract that the quoted error is not the total error. As written, a reader who stops at the abstract will take 1.058(20) as the full uncertainty on the hadronic normalization.
[Sec. 11, Eqs. (40) and (42)] For h_+(1) the quoted central value is a cancellation between two comparable terms: the tree-level entries of Table 3 give 0.991(3), and the one-loop correction ρV0 = 1 + 0.096 α_s contributes +0.016(3), so the final 1.007 is the difference of quantities of the same order as the correction itself. The higher-order uncertainty is then fixed at 20% of the one-loop term by assumption rather than by calculation. This is defensible as a practice, but the paper should say so in the text rather than only in the error-budget sentence, and should note that the same 20% rule applied to a two-loop coefficient of unexpected sign or magnitude would move h_+(1) by more than the quoted ±0.003. This is secondary for F(1), where h_+ contributes only 0.007, but it is load-bearing for the standalone h_+(1) claim of Eq. (40).

Minor objections (8)

[Eq. (26)] The displayed expression for d̃1 appears garbled in the typeset text ('1/2 + a m̃0 - 1/2(1 + a m̃0)'), which does not reduce to the mean-field-improved tree-level value one expects from Ref. [17]. Please check the formula and, if it is correct as printed, add the intermediate step that shows it reduces to the intended limit.
[Sec. 7, after Eq. (24)] 'We do not bother with the one-loop correction to m2 [24], because it is smaller than the uncertainty from a' is informal and, more importantly, unquantified. Please give the size of the one-loop correction relative to the scale uncertainty, or drop the sentence.
[Abstract and Eq. (42)] The asymmetric error is written as 1.058(^{20}_{17}) in the abstract and as 1.058 ± 0.016 ± 0.003 (+0.014/-0.005) in Eq. (42). The parenthetical asymmetric notation is non-standard and hard to parse; please use 1.058^{+0.020}_{-0.017} in the abstract and confirm that the quadrature is indeed what produces those numbers.
[Tables 1 and 2] Both tables are symmetric but only partially filled, and the column alignment in the typeset version makes it ambiguous which entry belongs to which (κ_initial, κ_final) pair — for instance the 0.947(24) entry appears in both the 0.062 and 0.125 rows. Please add explicit column headers or a note stating that the table is symmetric and that blank entries were not calculated.
[Table 3 caption] 'Tree level estimate of the form factors at zero recoil' is misleading, since the entries already include the 1/m_Q interpolation to the physical masses. What is absent is the radiative correction. Please reword to say so.
[Sec. 11] The value α_V(4.4/a) = 0.168 should be labelled with its scheme explicitly (V-scheme, presumably, following Ref. [15]), since the numerical value of the one-loop correction depends on it.
[Reference [18]] The page number is given as 'Phys. Rev. D58 14506 (1998)'; this should read D58, 014506.
[Secs. 6 and 8, Figs. 3 and 8] The 'chiral extrapolation' spans only m_s/2 ≤ m_q ≤ m_s, so it is an interpolation over a narrow range rather than an extrapolation to the chiral limit. The text is aware of this (it notes the statistical error doubles), but the figures and their captions would be clearer if the simulated range were marked.

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The paper

The paper claims

The paper reports a lattice QCD determination of the zero-recoil $F_{B��to D}(1)=1.058^{+0.020}_{-0.017}$ from double ratios in which most statistical and matching uncertainties cancel.

The reading

The paper sets out to compute, from first principles in lattice QCD, the hadronic normalization that controls the exclusive decay $��bar B��to D��ell��bar��nu$ at zero recoil. The authors introduce double ratios of three-point correlation functions whose numerator and denominator are built so the ratio is exactly one when the initial and final heavy quarks have equal mass and in the heavy-quark symmetry limit; the signal and most systematic errors are therefore proportional to the deviation from one. They tune the heavy-quark masses through the kinetic mass and use measured $1/m_Q$ dependence to interpolate to the physical $b$ and $c$ masses, obtaining $h_+(1)=1.007(6)(2)(3)$ and $h_-(1)=-0.107(28)(04)(^{+10}_{-30})$, hence $F_{B��to D}(1)=1.058^{+0.020}_{-0.017}$. The payoff, if the method holds up, is a lattice normalization for extracting $|V_{cb}|$ from $��bar B��to D��ell��bar��nu$ and a cross-check on the more commonly used $��bar B��to D^*$ channel. The authors explicitly leave out lattice-spacing dependence and quenching, arguing that these should scale with $F_{B��to D}(1)-1$ rather than with $F_{B��to D}(1)$ itself.

What carries the argument

The machinery is the double ratio of three-point correlation functions, constructed so that the numerator and denominator share the same interpolating fields and current normalizations. Because the ratio is identically one in the degenerate-mass limit and in the static limit, the measured deviation from one carries the physical signal while most statistical and matching uncertainties cancel. Heavy-quark symmetry then restricts the expansion to even powers of $(1/m_c-1/m_b)$ for $h_+$ and to a leading linear term for $h_-$, so a few mass combinations suffice to interpolate to the physical $b$ and $c$ masses. The clover action with a tuned clover coefficient and a rotated current supplies the lattice realization of the heavy-quark expansion.

Extended reading notes

Core claim

The central claim is that the zero-recoil $��bar B��to D$ form factor can be obtained accurately from a ratio of lattice correlation functions in which the normalization of the heavy-heavy vector current cancels between numerator and denominator. For $h_+(1)$ the relevant ratio is $R^{B��to D}(t)=C^{DV_0B}C^{BV_0D}/(C^{DV_0D}C^{BV_0B})$, and in the asymptotic time-separation limit it tends to $|h_+(1)|^2$. For $h_-(1)$ a second double ratio involving spatial and temporal currents yields $1-h_-(1)/h_+(1)$ at small recoil. The authors then observe the heavy-quark mass dependence directly, fit it with constrained $1/m_Q$ expansions, and interpolate to physical masses, arriving at $F_{B��to D}(1)=1.058^{+0.020}_{-0.017}$. The paper presents this as filling the gap left by earlier lattice calculations, which could not control the current normalization and the heavy-quark mass dependence well enough to quote an absolute normalization.

Load-bearing premise

The load-bearing premise is that the omitted lattice-spacing and quenching errors scale with $F_{B��to D}(1)-1$ rather than with $F_{B��to D}(1)$ itself, so that a roughly 15 percent quenching estimate becomes a roughly 0.9 percent error on the quoted $1.058$; the paper does not compute that coefficient and imports the estimate from earlier $f_B$ work.

Editorial extensions

If this is right

It supplies a lattice normalization for extracting $|V_{cb}|$ from $��bar B��to D��ell��bar��nu$, giving an independent cross-check on the $��bar B��to D^*��ell��bar��nu$ route.
The fitted coefficients of the $1/m_Q$ expansion, such as $c_+^{(2)}=[0.20(4)\ \mathrm{GeV}]^2$, become targets for QCD sum rules and quark models.
The same double-ratio construction can be adapted to other heavy-to-heavy matrix elements once the relevant current matching is known, including the axial-vector case of $��bar B��to D^*��ell��bar��nu$.
If the lattice-spacing and quenching systematics are brought under control as the authors expect, the quoted $F_{B��to D}(1)$ precision is small enough to matter for the exclusive determination of $|V_{cb}|$.

Reading between the lines

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

Beyond the paper, the double-ratio strategy looks like a general template: any matrix element with a symmetry-protected normalization condition can be turned into a ratio whose errors are proportional to the deviation from the symmetric limit.
The most valuable next step is not more statistics but a direct nonperturbative estimate of the quenching and lattice-spacing coefficients, because the entire error budget rests on an uncomputed scaling assumption.
The tension with sum-rule estimates of $c_-^{(1)}$ may be a useful diagnostic: if the missing one-loop matching for the spatial current moves $h_-(1)$ toward the sum-rule range, that would support the paper's error estimate; if it does not, the discrepancy points to a real gap between lattice and sum-rule treatments.
If future $��bar B��to D$ and $��bar B��to D^*$ lattice normalizations both mature, a persistent difference in the extracted $|V_{cb}|$ would be a clean place to look for either underestimated lattice systematics or new physics in semileptonic decays.

Original abstract

A lattice QCD calculation of the $\bar{B}\to Dl\bar{\nu}$ decay form factors is presented. We obtain the value of the form factor $h_+(w)$ at the zero-recoil limit $w=1$ with high precision by considering a ratio of correlation functions in which the bulk of the uncertainties cancels. The other form factor $h_-(w)$ is calculated, for small recoil momenta, from a similar ratio. In both cases, the heavy quark mass dependence is observed through direct calculations with several combinations of initial and final heavy quark masses. Our results are $h_+(1) = 1.007(6)(2)(3)$ and $h_-(1)=-0.107(28)(04)(^{10}_{30})$. For both the first error is statistical, the second stems from the uncertainty in adjusting the heavy quark masses, and the last from omitted radiative corrections. Combining these results, we obtain a precise determination of the physical combination $F_{B\to D}(1)=1.058(^{20}_{17})$, where the mentioned systematic errors are added in quadrature. The dependence on lattice spacing and the effect of quenching are not yet included, but with our method they should be a fraction of $F_{B\to D}-1$.

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The abstract, sentence by sentence

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

A lattice QCD calculation of the $\bar{B}\to Dl\bar{\nu}$ decay form factors is presented. We obtain the value of the form factor $h_+(w)$ at the zero-recoil limit $w=1$ with high precision by considering a ratio of correlation functions in which the bulk of the uncertainties cancels. The other form factor $h_-(w)$ is calculated, for small recoil momenta, from a similar ratio. In both cases, the heavy quark mass dependence is observed through direct calculations with several combinations of initial and final heavy quark masses. Our results are $h_+(1) = 1.007(6)(2)(3)$ and $h_-(1)=-0.107(28)(04)(^{10}_{30})$. For both the first error is statistical, the second stems from the uncertainty in adjusting the heavy quark masses, and the last from omitted radiative corrections. Combining these results, we obtain a precise determination of the physical combination $F_{B\to D}(1)=1.058(^{20}_{17})$, where the mentioned systematic errors are added in quadrature. The dependence on lattice spacing and the effect of quenching are not yet included, but with our method they should be a fraction of $F_{B\to D}-1$.

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	A lattice QCD calculation of the $\bar{B}\to Dl\bar{\nu}$ decay form factors is presented.	contribution 1.00	0.94	0.06	asserted 0.99
s1	We obtain the value of the form factor $h_+(w)$ at the zero-recoil limit $w=1$ with high precision by considering a ratio of correlation functions in which the bulk of the uncertainties cancels.	result 0.42	0.97	0.24	asserted 1.00
s2	The other form factor $h_-(w)$ is calculated, for small recoil momenta, from a similar ratio.	method 0.88	0.96	0.03	asserted 1.00
s3	In both cases, the heavy quark mass dependence is observed through direct calculations with several combinations of initial and final heavy quark masses.	method 0.91	0.95	0.03	asserted 1.00
s4	Our results are $h_+(1) = 1.007(6)(2)(3)$ and $h_-(1)=-0.107(28)(04)(^{10}_{30})$.	result 1.00	0.97	0.48	asserted 1.00
s5	For both the first error is statistical, the second stems from the uncertainty in adjusting the heavy quark masses, and the last from omitted radiative corrections.	interpretation 0.71	0.84	0.05	asserted 1.00
s6	Combining these results, we obtain a precise determination of the physical combination $F_{B\to D}(1)=1.058(^{20}_{17})$, where the mentioned systematic errors are added in quadrature.	result 1.00	0.97	0.65	asserted 1.00
s7	The dependence on lattice spacing and the effect of quenching are not yet included, but with our method they should be a fraction of $F_{B\to D}-1$.	limitation 1.00	0.33	0.04	hedged possibility 0.85

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

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

levels run

P abstract

not run

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

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

Figures

**Figure 1.** RB→D(t) as a function of t. The heavy quark hopping parameter for the initial and final mesons are (κb, κc) = (0.089, 0.110) (diamonds), and (0.089, 0.119) (circles). The light quark corresponds to the strange quark, κl = 0.1405. The solid lines represent a constant fit with 4 ≤ t ≤ 8. suppressing radiative corrections. Here we use the definition (3) and the unit normalization of |h+(1)| in the equal mass case. Thus, we expect RB→D to be constant as a function of t, and its value represents the form factor squared. In

**Figure 2.** Check of the plateau in RB→D(t) by varying the time slice tB of the B meson interpolating field. Open diamonds, crosses and solid diamonds correspond to the results with tB = 12, 10, and 8, respectively. The heavy quark hopping parameters are (κb, κc) = (0.089, 0.110), and κl = 0.1405

**Figure 3.** Chiral extrapolation of |h+(1)| 2 . The heavy quark hopping parameters for the initial and final mesons are (κb, κc) = (0.089, 0.110) (diamonds), and (0.089, 0.119) (circles). We examine the chiral limit by computing with four values of the light quark mass (14), roughly in the range ms/2 ≤ mq ≤ ms

**Figure 4.** 1/amc dependence of |h+(1)|. The initial heavy quark mass is fixed at κb = 0.089, which corresponds to 1/amb = 0.475. The light quark corresponds to the strange quark, κl = 0.1405. are chosen nonperturbatively from the masses of the D and B mesons

**Figure 5.** [1 − |h+(1)|] /∆2 vs. 1/amc + 1/amb. The dotted vertical line indicates the physical value of 1/amc + 1/amb. The light quark corresponds to the strange quark, κl = 0.1405. where ∆ = 1/amc − 1/amb. The left-hand side is plotted in

**Figure 6.** R (B→D)/(D→D) Vi/V0 (t) for the final state momentum (1, 0, 0) (circles) and (2, 0, 0) (squares). The heavy quark hopping parameter for the initial and final mesons are (κb, κc) = (0.089, 0.119) (solid symbols) and (0.119, 0.089) (open symbols). The light quark corresponds to the strange quark, κl = 0.1405. The solid lines represent a constant fit for the momentum (1, 0, 0) with 4 ≤ t ≤ 8. 9 Heavy quark mass dependence of h−(1) As with h+(1), the heavy quark mass dependence of h−(1) can be described, in the heavy quark limit of QCD, with a 1/mQ expansion. The form of the heavy qua

**Figure 7.** Extrapolation of R (B→D)/(D→D) Vi/V0 to the zero-recoil limit. The heavy quark hopping parameter for the initial and final mesons are (κb, κc) = (0.089, 0.119) (solid circles) and (0.119, 0.089) (open circles). The light quark corresponds to the strange quark, κl = 0.1405. Note that the lattice spacing a is held fixed here. order, since the correction to the h+(1) starts at order 1/m2 Q. To take radiative corrections into account, we should note that the (lattice) ratio R (B→D)/(D→D) Vi/V0 corresponds to [1−h−/h+]/ρVi . The right-hand side of (33), on the other hand, is justified…

**Figure 8.** Chiral extrapolation of 1−h−(1)/h+(1). The heavy quark hopping parameters for the initial and final mesons are (κb, κc) = (0.089, 0.119) (solid circles) and (0.119, 0.089) (open circles). “lighter-to-heavier” transitions. The two sets of data are consistent with each other, except three points appearing well above the other points. These data involve the heaviest quark mass in our calculation, where the statistical noise is very large, and reliable fits become difficult. The data are well described by the linear form (34), and our results for its coefficients extracted with the…

**Figure 9.** 1/amc dependence of h−(1)/h+(1). The initial heavy quark mass is fixed at κb = 0.089 (solid circles), which corresponds to 1/amb = 0.475. The open circles are obtained by exchanging the initial and final states. The light quark corresponds to the strange quark, κl = 0.1405. compensates for the omitted rotation, provided we reconstitute the physical value of h−(1) using the physical values of the quark masses throughout. A bonus of this method is that the radiative correction factor ρVi will be easier to compute when d1 = 0. We have checked the influence of the rotation by repeating…

**Figure 10.** −[h−(1)/h+(1)]/∆3 vs. 1/amc + 1/amb. Filled (open) symbols represent the “heavier-to-lighter” (“lighter-to-heavier”) decay results. The solid and dashed lines are fitted results to the solid and open data points, respectively. The dotted vertical line indicates the physical value of 1/amc + 1/amb. The light quark corresponds to the strange quark, κl = 0.1405. from a change in the radiative corrections, because the change in the heavy quark expansion is, fortuitously, negligible. Thus, it provides an estimate of the uncertainty from omitting the radiative corrections. Another check…

Figures reproduced from arXiv:hep-ph/9906376 by the authors.

References

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Forward citations

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How the literature uses it

36 arXiv papers cite this in 41 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 · 11 sentences without a confident label

Builds on it 1 paper

Double ratio methods similar to what has been developed for lattice studies of $B →D l ν$ [ref] can be adapted to semileptonic $D$ meson decays [ref] .

Weak Charm Decays with Lattice QCD · Semileptonic $D$ Meson Form Factors · 0.88

Uses its method or tool 23 papers

The semileptonic form factor $h_A_1(w)$ at zero recoil (i.e. $w=1$) can be obtained with the Hashimoto ratio [ref] :

Current progress on the semileptonic form factors for $\bar{B} \to D^{\ast} \ell \bar{\nu}$ decay using the Oktay-Kronfeld action · Preliminary result on $h_A_1(w=1)/ρ_A_1$: $B →D^∗ℓν$ form factor at zero recoil · 1.00
The pioneering work of Hashimoto et al. [ref] introduced several double ratios to this end.

Update of $|V_{cb}|$ from the $\bar{B}\to D^*\ell\bar{\nu}$ form factor at zero recoil with three-flavor lattice QCD · Introduction · 0.80
We use a mostly nonperturbative method [ref] to match the $b→q$ ($q=u,c$) vector and axial vector currents from the lattice scheme to the continuum $MS$ scheme.

$\Lambda_b \to p \ell^- \bar{\nu}_\ell$ and $\Lambda_b \to \Lambda_c \ell^- \bar{\nu}_\ell$ form factors from lattice QCD with relativistic heavy quarks · Lattice actions and currents · 1.00

Compares with it 2 papers

Previous lattice calculations by the Fermilab collaboration [ref] quote the value of $G^B→D(w)$ only at zero recoil where it can be extracted with good statistical accuracy by using the so called "double ratio" technique.

Quenched lattice calculation of the B --> D l nu decay rate · Form factors and decay rate · 0.80
This result is an interesting, and fully non-perturbative, analogue of the Fermilab [ref] partially-perturbative approach to currents that are conserved in the continuum.

The decay constants ${\mathbf{f_D}}$ and ${\mathbf{f_{D_{s}}}}$ in the continuum limit of ${\mathbf{N_f=2+1}}$ domain wall lattice QCD · RI/SMOM and the axial vertex function · 0.80

Cites it as background 3 papers

Currently, there have been some studies on the semileptonic decays $B̅_s^0→D_s^+(1968,2317) l ν̅_l$ ranging from phenomenological model [ref] to QCD sum rules approach [ref] , PQCD approach [ref] and Lattice QCD [ref] .

Exclusive $B_s$ decays to the charmed mesons $D_s^+(1968,2317)$ in the standard model · Introduction · 0.98
There have existed some phenomenological studies using different approaches, including the phenomenological model [ref] , the QCD sum rules approach [ref] , PQCD approach [ref] , Lattice QCD [ref] , as well as the light-cone sum rules (LCSR) [ref] .

Charmed Scalar Meson Production in $B$ Decays · Introduction · 0.96
Theoretically, numerous effective approaches exist to make reasonable predictions for TFF of the $B→Dℓ^+ν_ℓ$ semileptonic decay process, such as the perturbative QCD (pQCD) [ref] , the QCD light-cone sum rule (LCSRs) [ref] , and the lattice QCD (LQCD) [ref] .

Footprint in fitting $B \to D$ vector form factor and determination for $D$-meson leading-twist LCDA · Introduction · 0.84

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.

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