Data determination of HQET parameters in inclusive charm decays

Chun Huang; Kang-Kang Shao; Qin Qin

REVIEW 3 major objections 4 minor 1 cited by

Data determination of HQET parameters in inclusive charm decays

T0 review · 3 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read The paper claims the first data-only determination of the four HQET parameters governing inclusive D meson decays.

desk verdict First data-driven HQET parameters in charm, but the 'model-independent' claim overstates the VIA treatment of four-quark operators. read the letter →

arxiv 2502.05901 v1 pith:6AVBWNAP submitted 2025-02-09 hep-ph

Kang-Kang Shao , Chun Huang , Qin Qin This is my paper · ORCID

classification hep-ph

keywords heavyquarkeffectivetheoryHQETparametersinclusivecharmdecaysoperatorproductexpansionelectronenergymomentsDmesonlifetimes1Smassscheme

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper aims to show that the parameters controlling the heavy-quark expansion of inclusive charm decays can be extracted from data instead of being borrowed from models or from beauty decays. The authors fit theoretical expressions for the total width and the first four electron-energy moments of $D^0\to Xe\nu$, $D^+\to Xe\nu$, and $D_s\to Xe\nu$ to the measured spectra and branching fractions, working in the 1S charm mass scheme where the perturbative series converges. Their result is the first data determination of the kinetic, chromomagnetic, Darwin, and spin-orbit HQET parameters; for example, $\mu_\pi^2(D^{0,+})=(0.09\pm 0.05)\,\mathrm{GeV}^2$, $\mu_G^2(D^{0,+})=(0.32\pm 0.02)\,\mathrm{GeV}^2$, and $\mu_G^2(D_s)=(0.43\pm 0.02)\,\mathrm{GeV}^2$. A sympathetic reader would care because these same hadronic matrix elements enter $D$-meson lifetime calculations, where current theory has struggled, and inclusive $B$ decays through heavy-quark symmetry.

What carries the argument

The machinery is the heavy-quark operator product expansion for inclusive decays: the total width and electron-energy moments are written as a double expansion in $\alpha_s$ and $\Lambda_{\mathrm{QCD}}/m_c$, with short-distance coefficients computed to next-to-next-to-leading order at leading power and to leading order for the $1/m_c^2$ and $1/m_c^3$ corrections. The hadronic matrix elements that survive are the HQET parameters (dimension-five kinetic and chromomagnetic terms $\mu_\pi^2$ and $\mu_G^2$; dimension-six Darwin and spin-orbit terms $\rho_D^3$ and $\rho_{LS}^3$), and the fit determines these from the measured moments. The 1S mass scheme is the load-bearing choice at the perturbative level: substituting the pole mass by the 1S mass (Eq. (6)) turns a poorly behaved expansion into one whose NLO, NNLO, and N$^3$LO corrections are roughly $-13\%$, $-5\%$, and $+2\%$ of the leading width.

What would settle it

A lattice QCD determination of the $D_s$ chromomagnetic parameter $\mu_G^2$ with uncertainty below $0.02\,\mathrm{GeV}^2$ that disagrees with the paper's $0.43\,\mathrm{GeV}^2$ would refute the extraction; likewise, a tau-charm factory measurement of $D_s\to Xe\nu$ $q^2$ moments whose fit with dimension-seven operators moves $\mu_\pi^2(D_s)$ by more than the quoted $0.05\,\mathrm{GeV}^2$ uncertainty would show the $1/m_c^3$ truncation is not sufficient.

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Extended reading notes

Core claim

The paper's central claim is that four HQET parameters--the kinetic energy $\mu_\pi^2$, the chromomagnetic energy $\mu_G^2$, and the dimension-six Darwin and spin-orbit terms $\rho_D^3$ and $\rho_{LS}^3$--for $D^{0/+}$ and $D_s$ mesons can be determined from inclusive semileptonic decay measurements alone, with no model assumption about hadronic matrix elements. The extraction uses the operator product expansion truncated at order $1/m_c^3$, with leading-power coefficients at next-to-next-to-leading order in $\alpha_s$, and selects the 1S mass scheme because the pole-mass series diverges while the 1S series converges. The adopted fit, Scenario 2 in the 1S scheme, gives $\mu_\pi^2(D^{0,+})=(0.09\pm 0.05)\,\mathrm{GeV}^2$, $\mu_\pi^2(D_s)=(0.11\pm 0.05)\,\mathrm{GeV}^2$, $\mu_G^2(D^{0,+})=(0.32\pm 0.02)\,\mathrm{GeV}^2$, $\mu_G^2(D_s)=(0.43\pm 0.02)\,\mathrm{GeV}^2$, $\rho_D^3(D^{0,+})=(-0.003\pm 0.002)\,\mathrm{GeV}^3$, $\rho_D^3(D_s)=(-0.004\pm 0.002)\,\mathrm{GeV}^3$, $\rho_{LS}^3(D^{0,+})=(0.004\pm 0.002)\,\mathrm{GeV}^3$, $\rho_{LS}^3(D_s)=(0.005\pm 0.002)\,\mathrm{GeV}^3$, and reproduces the measured widths and moments within their uncertainties.

Load-bearing premise

The whole extraction presumes that the theoretical formulas, expanded through $1/m_c^3$ with four-quark operator effects set to zero and masses in the 1S scheme, describe the true inclusive $D$ decay rates and electron spectra; if missing higher-order or four-quark terms shift the predictions, the fitted HQET values in Eq. (14) would be biased.

Editorial extensions

If this is right

The extracted $\mu_\pi^2$, $\mu_G^2$, $\rho_D^3$, and $\rho_{LS}^3$ become direct inputs to $D$-meson lifetime calculations, the place where the current theory has produced a negative $D^+$ width and a puzzling charmed-baryon lifetime ordering.
Because heavy-quark symmetry connects charm and beauty, the same parameters can be used in inclusive $B$-meson decay predictions, helping to sharpen analyses related to $V_{cb}$.
The demonstration that the 1S scheme converges for charm removes a longstanding worry about applying the operator product expansion at the charm mass scale.
With more precise data, especially rest-frame spectra, $q^2$ moments, and muonic channels, the same method can determine dimension-seven matrix elements and separately extract $V_{cs}$ and $V_{cd}$.

Reading between the lines

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

My own reading: the real test of the extraction will be a direct independent calculation of one parameter, say $\mu_G^2(D_s)$ from lattice QCD; a value outside $0.43\pm 0.02\,\mathrm{GeV}^2$ would localize the error in the dropped four-quark terms or in the $1/m_c^3$ truncation.
The paper treats the vacuum insertion approximation as a practical way to keep the fit underdetermined; an obvious extension is to free the four-quark operators using future data, which would make the model dependence itself measurable.
The small negative $\rho_D^3$ values hint that the $1/m_c^3$ truncation is already absorbing effects from higher-dimension operators; comparing with fits that include dimension-seven terms would show whether the quoted uncertainties are realistic.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First thing to know: this is a genuine first — the first data-driven extraction of charm HQET parameters (mu_pi^2, mu_G^2, rho_D^3, rho_LS^3) from inclusive semileptonic D decays, using CLEO and BESIII data. Ref. [25] only discussed the prospects; here they actually do the fit and report values. That is the new contribution, and it is useful: these parameters feed D lifetime calculations and heavy quark symmetry tests.

The paper does several things well. The theoretical setup is borrowed from Fael–Mannel–Vos (ref. [21]) and others, but they apply it carefully, testing the MS and 1S mass schemes and showing the 1S scheme gives a much more convergent perturbative expansion. The fit is transparent: they use decay widths and electron energy moments, account for correlations, and present results in two scenarios. The extracted values are plausible and the quoted uncertainties are reasonable.

Now the soft spots, in proportion. The headline claim of "model-independent" is too strong. The four-quark operators at 1/m_c^3 are dropped because their effects "vanish" under the vacuum insertion approximation — that is a model assumption, not a QCD theorem, and the authors admit the choice is pragmatic ("to enable a successful global fit"). If the true four-quark matrix elements are O(1) bag parameters off their VIA values, the fitted parameters in Eq. (14) would shift, and the quoted uncertainties do not include that shift. That is a real caveat, though not a fatal one: it is the kind of limitation that can be addressed in future work, and the paper itself flags it in the summary. Second, the adopted result is selected after comparing schemes and scenarios; the post-hoc choice of the lowest chi^2 is fine, but it means the quoted numbers carry a selection bias that is not fully propagated. Third, the experimental moments depend on an extrapolation to zero electron energy with an assumed spectral shape; that introduces model dependence on the data side. Fourth, Table III recomputes the observables from the fitted parameters and presents that as validation — that is tautological, not an independent check.

The bottom line: a solid, useful first extraction with an overstatement in the abstract. The central argument holds up; the values are conditional on the four-quark and higher-order assumptions. The paper deserves a serious referee, and I would recommend publishing after the authors soften the "model-independent" claim and add a discussion of the theory systematics. Who is this for? Anyone working on D lifetimes, inclusive heavy flavor, or HQET parameters. I would bring it to reading group and would cite it as a data-driven input with the caveats noted.

Referee Report

3 major / 4 minor

Summary. The paper extracts the HQET parameters mu_pi^2, mu_G^2, rho_D^3, and rho_LS^3 for D^0, D^+, and D_s^+ mesons from inclusive semileptonic decay data. Theoretical expressions for the total width and the first four electron energy moments are built from the OPE up to 1/m_c^3, with NNLO alpha_s corrections at leading power and LO alpha_s corrections to the power corrections. Three charm mass schemes are considered, and the 1S scheme is preferred because of better apparent convergence. Fitting to CLEO and BESIII measurements of D^0, D^+, and D_s^+ -> X e^+ nu yields the parameter values quoted in Eq. (14), which the paper presents as the first data-driven determination of these HQET parameters. The fitting setup is transparent, and the paper goes to some length to document the experimental moments and their correlations.

Significance. If the result is robust, Eq. (14) would provide genuinely useful inputs for inclusive charm and beauty calculations, including D meson lifetimes and comparisons with lattice QCD. The paper is also valuable for its detailed assembly of the experimental moments, its explicit treatment of correlations, and its demonstration that the 1S mass scheme improves the apparent convergence of the charm OPE. The central caveat is that the headline claim of a 'model-independent' determination is stronger than what the analysis actually delivers: the extraction relies on the vacuum insertion approximation for four-quark operators, on a spectral-shape extrapolation to zero electron energy, and on a post-hoc selection of the mass scheme and operator scenario. These assumptions are acknowledged in parts of the text but are not converted into systematic uncertainties. With those caveats quantified or the claims appropriately softened, the paper would be a solid contribution.

major comments (3)

[Section II, after Eq. (2), and Section IV] The treatment of dimension-six four-quark operators is the main load-bearing assumption and is at odds with the term 'model-independent' used in the abstract and in the Summary. The text states that these operators are omitted because their effects 'vanish' under the vacuum insertion approximation and because this choice 'helps avoid an excessive number of free parameters.' VIA is a factorization ansatz, not a QCD expansion, and the associated bag parameters can deviate from unity by O(1). Since these operators enter at the same 1/m_c^3 order as the retained rho_D^3 and rho_LS^3 terms, an O(1) violation of VIA would bias the fitted values in Eq. (14), and the quoted uncertainties would not include this bias. The authors should either estimate the four-quark contamination by varying bag parameters over a plausible range or add a nuisance-parameter fit, and in any case should remove or qualify 'model-independent' in the abstract and conclusions.
[Section III, Eqs. (8) and (10)] The experimental moments used as inputs depend on an assumed spectral shape for the region p_e < 0.2 GeV. The paper follows the procedure of fitting the first four measured bins to dGamma/dx = a x^2 (1 + b x)(1 - x), 'supposing a well feature of OPE' near p_e = 0. This functional form is a modeling assumption; other OPE-motivated forms or a different number of fitted bins would shift the extrapolated low-energy contribution and hence all of the moments in Eq. (10). The Monte Carlo propagation accounts for binwise statistical fluctuations and flat within-bin distributions, but it does not vary the extrapolation form or the fitting window. Because the final HQET parameters are directly determined by these moments, this neglected systematic is load-bearing. Please quantify the sensitivity to the extrapolation assumption, for example by comparing two or three alternative functional forms and fitting ranges.
[Section IV, Tables I and II, Eq. (14)] The primary result is selected after comparing two mass schemes and two operator scenarios on the same dataset. The quoted uncertainties in Eq. (14) combine the Scenario-2 fit errors with differences from Scenario 1, but they do not include the choice of the 1S scheme itself, the fixed input m_c,1S = 1.55 GeV, or the scale-setting procedure. The very low chi^2/d.o.f. = 0.33 in the adopted scenario also suggests that the experimental uncertainties may be overestimated or that the many correlated observables give the fit limited constraining power. The authors should report a scheme-selection and scale-variation uncertainty or explicitly state that Eq. (14) is conditional on the 1S scheme and Scenario 2. Without this, the quoted errors in Eq. (14) are likely underestimated.

minor comments (4)

[Section III, Eq. (8)] The units for the third and fourth lab-frame moments are inconsistent: the third moment is labeled 'GeV' and the fourth 'GeV^2', but they should be GeV^3 and GeV^4, respectively.
[Section IV, Table III] The sentence introducing Table III says the fit is 'further validated' by computing the decay widths and moments with the extracted parameters. Since these are the same observables used in the fit, this is a consistency check rather than an independent validation, and it should be described as such.
[Section III and IV] There are several typographical errors: 'Monto Carlo' should be 'Monte Carlo', 'dimention-six' should be 'dimension-six', 'partoic' should be 'partonic', and 'ﬁst order' should be 'first order'.
[Section IV] The isospin assumption that D^0 and D^+ have identical HQET parameters is stated but not discussed quantitatively. Since D^0 and D^+ lifetimes differ appreciably, a brief estimate of the expected isospin-breaking uncertainty in mu_pi^2 or mu_G^2 would be useful.

Circularity Check

1 steps flagged · score 2.0 of 10

Minor tautological validation only: Table III prediction of the same fitted observables is circular, but the central HQET parameter extraction is a genuine fit.

fitted input called prediction [Section IV, paragraph preceding Table III and Table III caption]
"To further validate the fit in Scenario 2, 1S scheme, we compute the decay widths and electron energy moments in the inclusive decays utilizing the extracted HQET parameters. ... It is evident that they are in excellent agreement with the experimental data. TABLE III. The predictions for the inclusive D decay widths and the electron energy moments in 1S scheme, Scenario 2."

The decay widths and moments in Table III are exactly the observables used as inputs in the least-squares fit: Eq. (1) and Eq. (3) contain the HQET parameters as coefficients, and the fit in Section IV matches these formulas to the measured widths (7) and moments (10)/(12). The best-fit parameters in Eq. (14) therefore reproduce those same data points by construction, since the fit minimizes the chi-squared to them. Calling this agreement a prediction and using it to validate the fit is circular: it is a restatement of the fit quality, not an independent test. This does not bias the central extraction, but the validation claim adds no evidence beyond the reported chi-squared per degree of freedom.

full rationale

The derivation chain is a standard OPE-based fit. The HQET parameters mu_pi^2, mu_G^2, rho_D^3, and rho_LS^3 enter Eqs. (1) and (3) as unknown coefficients; they are not defined in terms of the fitted observables or of each other. The experimental moments are obtained from CLEO/BESIII spectra by a documented Monte Carlo procedure and then treated as inputs; the fit determines the parameters. No equation reduces to its own input by construction, and no load-bearing premise rests on self-citation: the OPE formulas (Ref. [21]), NNLO partonic corrections (Ref. [35]), and 1S mass-scheme relations (Refs. [26-28]) are external to this paper's authors. The only circular element is the validation paragraph before Table III, where the predicted widths and moments are precisely the fitted observables, so their agreement is a tautological consequence of the fit. The vacuum insertion approximation neglect of four-quark operators and the choice of the 1S scheme are substantive model assumptions that could bias the extracted values, but they are a correctness risk, not circularity, because the parameters remain free degrees of freedom. Overall, the central result is a legitimate data determination with minor cosmetic circularity in the validation step.

Assumptions & free parameters 9 free parameters · 3 assumptions · 0 invented entities

The paper's contribution is a data fit within an existing OPE framework. The unpaid assumptions are the validity of the 1/m_c expansion at the charm scale, the neglect of four-quark operators, and the choice of the 1S mass scheme. No new dynamical entities are introduced.

free parameters (9)

mu_pi^2(D0,+) = 0.09 ± 0.05 GeV^2
Kinetic energy parameter for D0/D+, fitted to width and moments in Scenario 2, 1S scheme.
mu_pi^2(Ds) = 0.11 ± 0.05 GeV^2
Kinetic energy parameter for Ds, fitted to width and moments in Scenario 2, 1S scheme.
mu_G^2(D0,+) = 0.32 ± 0.02 GeV^2
Chromo-magnetic parameter for D0/D+, fitted in Scenario 2, 1S scheme.
mu_G^2(Ds) = 0.43 ± 0.02 GeV^2
Chromo-magnetic parameter for Ds, fitted in Scenario 2, 1S scheme.
rho_D^3(D0,+) = -0.003 ± 0.002 GeV^3
Dimension-six Darwin operator parameter for D0/D+, fitted in Scenario 2, 1S scheme.
rho_D^3(Ds) = -0.004 ± 0.002 GeV^3
Dimension-six Darwin operator parameter for Ds, fitted in Scenario 2, 1S scheme.
rho_LS^3(D0,+) = 0.004 ± 0.002 GeV^3
Dimension-six spin-orbit operator parameter for D0/D+, fitted in Scenario 2, 1S scheme.
rho_LS^3(Ds) = 0.005 ± 0.002 GeV^3
Dimension-six spin-orbit operator parameter for Ds, fitted in Scenario 2, 1S scheme.
low-energy spectrum shape parameters a,b for D0, D+, Ds = not reported
Fitted to the first four bins of each measured spectrum to extrapolate to pe=0; affects all experimental moments used in the HQET fit.

assumptions (3)

domain assumption The OPE expansion in Lambda_QCD/m_c, truncated at order 1/m_c^3, describes the inclusive D semileptonic widths and electron energy moments.
Used in Eqs. (1)-(3); if higher-order power corrections are large, all extracted parameters would be biased.
ad hoc to paper Four-quark operator contributions are negligible under the vacuum insertion approximation.
Section II, after Eq. (2): omitted because they 'vanish' under VIA and to 'avoid an excessive number of free parameters, enabling a successful global fit'.
ad hoc to paper The 1S mass scheme provides a convergent alpha_s expansion for charm.
Section II: pole scheme is divergent and MS scheme is less convergent; the 1S scheme is selected as favorable. The adopted results depend on this choice.

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Cite this review

Pith. "Pith review of Data determination of HQET parameters in inclusive charm decays." pith.science (2026). https://pith.science/paper/6AVBWNAP

@misc{pith2026250205901,
  author       = {Pith},
  title        = {Pith review of: Data determination of HQET parameters in inclusive charm decays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6AVBWNAP}},
  note         = {Machine review of arXiv:2502.05901}
}

abstract

This work delves into the phenomenology of electronic inclusive decays of $D$ mesons, encompassing $D^0, D^+, D^+_s\to Xe^{+}\nu$. The theoretical formulas for the decay widths and electron energy moments of these decays are presented as expansions with powers of $\alpha_s$ and $\Lambda_{\rm QCD}/m_c$. Remarkably, the expansion exhibits excellent convergence properties when we choose the 1S mass scheme for charm. The formulas are subsequently fitted to experimental data, and the $D$ meson matrix elements of operators in the heavy quark effective theory are hence determined by data for the first time, including \begin{align} \mu^2_\pi(D^{0,+}) &= (0.09\pm 0.05) \mathrm{GeV}^2, \qquad \qquad \mu^2_\pi(D^{+}_s) = (0.11\pm 0.05) \mathrm{GeV}^2, \nonumber \\ \mu^2_G(D^{0,+}) &= (0.32\pm 0.02) \mathrm{GeV}^2, \qquad \qquad \mu^2_G(D^{+}_s) = (0.43\pm 0.02) \mathrm{GeV}^2, \nonumber \\ \rho_D^3(D^{0,+}) &= (-0.003\pm 0.002) \mathrm{GeV}^3, \qquad\ \rho_D^3(D^{+}_s) = (-0.004\pm 0.002) \mathrm{GeV}^3, \nonumber \\ \rho_{LS}^3(D^{0,+}) &= (0.004\pm 0.002) \mathrm{GeV}^3, \qquad \ \ \ \rho_{LS}^3(D^{+}_s) = (0.005\pm 0.002) \mathrm{GeV}^3 . \nonumber \end{align} These determined parameters will play a crucial role as inputs in various physical quantities, including $D$ meson lifetimes.

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Charm physics
hep-ph 2025-06 unverdicted novelty 1.0 of 10

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

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Works this paper leans on

62 extracted references · 27 canonical work pages · cited by 1 Pith paper

[25]

Ablikim et al

M. Ablikim et al. (BESIII), Phys. Rev. Lett. 121, 251801 (2018), arXiv:1805.09060 [hep-ex]

arXiv 2018
[21]

Archilli, M

F. Archilli, M. O. Bettler, P. Owen, and K. A. Petridis, N ature 546, 221 (2017)

work page 2017
[1]

0.964628 0 .888372 0 .799743 −0.0682164 0 .964628 1

−0.0764818 −0.0682164 −0.0584038 −0.049709 −0.0764818 1 . 0.964628 0 .888372 0 .799743 −0.0682164 0 .964628 1 . 0.976053 0 .921246 −0.0584038 0 .888372 0 .976053 1 . 0.982859 −0.049709 0 .799743 0 .921246 0 .982859 1 .         , Cor(D+) =        

work page
[2]

0.959852 0 .877876 0 .784972 −0.0111696 0 .959852 1

−0.00918393 −0.0111696 −0.011663 −0.0114986 −0.00918393 1 . 0.959852 0 .877876 0 .784972 −0.0111696 0 .959852 1 . 0.974619 0 .917145 −0.011663 0 .877876 0 .974619 1 . 0.982034 −0.0114986 0 .784972 0 .917145 0 .982034 1 .         , (17) 9 Cor(D+ s ) =        

work page
[3]

0.961103 0 .877715 0 .779303 −0.0854423 0 .961103 1

−0.0948363 −0.0854423 −0.0692735 −0.0528099 −0.0948363 1 . 0.961103 0 .877715 0 .779303 −0.0854423 0 .961103 1 . 0.973193 0 .910118 −0.0692735 0 .877715 0 .973193 1 . 0.979699 −0.0528099 0 .779303 0 .910118 0 .979699 1 .         . The second set includes the decay width, the ﬁst order electron en ergy moment, the second, third and the fourth elect...

work page
[4]

−0.088841 −0.444378 −0.0618813 0.0281587 −0.088841 1

−0.0764818 0 .0281587 0 .0330765 0 .0102788 −0.0764818 1 . −0.088841 −0.444378 −0.0618813 0.0281587 −0.088841 1 . −0.00420729 0 .817582 0.0330765 −0.444378 −0.00420729 1 . −0.0351105 0.0102788 −0.0618813 0 .817582 −0.0351105 1 .         , Cor(D+) =        

work page
[5]

−0.0423819 −0.456701 −0.0390424 −0.00799742 −0.0423819 1

−0.00918393 −0.00799742 0 .00816853 −0.0107153 −0.00918393 1 . −0.0423819 −0.456701 −0.0390424 −0.00799742 −0.0423819 1 . −0.0538756 0 .809543 0.00816853 −0.456701 −0.0538756 1 . −0.0924318 −0.0107153 −0.0390424 0 .809543 −0.0924318 1 .         , (18) Cor(D+ s ) =        

work page
[6]

−0.047314 −0.40486 −0.0191632 0.0254998 −0.047314 1

−0.0948363 0 .0254998 0 .0800786 0 .00809594 −0.0948363 1 . −0.047314 −0.40486 −0.0191632 0.0254998 −0.047314 1 . 0.0763575 0 .800281 0.0800786 −0.40486 0 .0763575 1 . 0.172337 0.00809594 −0.0191632 0 .800281 0 .172337 1 .        

work page

Show all 62 references

[7]

Cao et al

L. Cao et al. (Belle), Phys. Rev. Lett. 131, 211801 (2023), arXiv:2303.17309 [hep-ex]

2023 arXiv
[8]

Aggarwal et al

L. Aggarwal et al. (Belle-II), Phys. Rev. Lett. 131, 051804 (2023), arXiv:2301.08266 [hep-ex]

2023 arXiv
[9]

Huber, T

T. Huber, T. Hurth, J. Jenkins, E. Lunghi, Q. Qin, and K. K. Vos, JHEP 10, 228 (2019), arXiv:1908.07507 [hep-ph]

2019 arXiv
[10]

Huber, T

T. Huber, T. Hurth, J. Jenkins, E. Lunghi, Q. Qin, and K. K. Vos, JHEP 10, 088 (2020), arXiv:2007.04191 [hep-ph]

2020 arXiv
[11]

Huber, T

T. Huber, T. Hurth, J. Jenkins, E. Lunghi, Q. Qin, and K. K. Vos, JHEP 11, 130 (2024), arXiv:2404.03517 [hep-ph]

2024 arXiv
[12]

M. Fael, M. Prim, and K. K. Vos, Eur. Phys. J. ST 233, 325 (2024)

2024
[13]

M. Fael, I. S. Milutin, and K. K. Vos, (2024), arXiv:2409. 15007 [hep-ph]

2024
[14]

D. King, A. Lenz, M. L. Piscopo, T. Rauh, A. V. Rusov, and C. Vlahos, JHEP 08, 241 (2022), arXiv:2109.13219 [hep-ph]

2022 arXiv
[15]

Cheng, Chin

H.-Y. Cheng, Chin. J. Phys. 78, 324 (2022), arXiv:2109.01216 [hep-ph]

2022 arXiv
[16]

Aaij et al

R. Aaij et al. (LHCb), Sci. Bull. 67, 479 (2022), arXiv:2109.01334 [hep-ex]

2022
[17]

Adachi et al

I. Adachi et al. (Belle-II), Phys. Rev. Lett. 131, 171803 (2023), arXiv:2306.00365 [hep-ex]

2023 arXiv
[18]

Gratrex, B

J. Gratrex, B. Meli´ c, and I. Niˇ sandˇ zi´ c, JHEP07, 058 (2022), arXiv:2204.11935 [hep-ph]

2022 arXiv
[19]

Cheng and C.-W

H.-Y. Cheng and C.-W. Liu, JHEP 07, 114 (2023), arXiv:2305.00665 [hep-ph]

2023 arXiv
[20]

Banerjee et al

S. Banerjee et al. (Heavy Flavor Averaging Group (HFLA V)), (2024), arXiv:241 1.18639 [hep-ex]

2024
[22]

de Boer and G

S. de Boer and G. Hiller, Phys. Rev. D 93, 074001 (2016), arXiv:1510.00311 [hep-ph]

2016 arXiv
[23]

D. M. Asner et al. (CLEO), Phys. Rev. D 81, 052007 (2010), arXiv:0912.4232 [hep-ex]

2010 arXiv
[24]

Ablikim et al

M. Ablikim et al. (BESIII), Phys. Rev. D 104, 012003 (2021), arXiv:2104.07311 [hep-ex]

2021
[26]

Ablikim et al

M. Ablikim et al. (BESIII), Phys. Rev. D 107, 052005 (2023), arXiv:2212.03753 [hep-ex]

2023
[27]

M. Fael, T. Mannel, and K. K. Vos, JHEP 12, 067 (2019), arXiv:1910.05234 [hep-ph]

2019 arXiv
[28]

Ligeti, M

Z. Ligeti, M. Luke, and A. V. Manohar, Phys. Rev. D 82, 033003 (2010), arXiv:1003.1351 [hep-ph]

2010 arXiv
[29]

Gambino and J

P. Gambino and J. F. Kamenik, Nucl. Phys. B 840, 424 (2010), arXiv:1004.0114 [hep-ph]

2010 arXiv
[30]

J. Wu, X. Lou, Y. Che, G. Li, Y. Huang, M. Ruan, and J. Ye, (2 024), arXiv:2406.16119 [hep-ph]

arXiv
[31]

Bernlochner, A

F. Bernlochner, A. Gilman, S. Malde, M. Prim, K. K. Vos, a nd G. Wilkinson, (2024), arXiv:2408.10063 [hep-ex]

2024 arXiv
[32]

A. H. Hoang, Z. Ligeti, and A. V. Manohar, Phys. Rev. Lett . 82, 277 (1999), arXiv:hep-ph/9809423

1999 arXiv
[33]

A. H. Hoang, Z. Ligeti, and A. V. Manohar, Phys. Rev. D 59, 074017 (1999), arXiv:hep-ph/9811239

1999 arXiv
[34]

A. H. Hoang and T. Teubner, Phys. Rev. D 60, 114027 (1999), arXiv:hep-ph/9904468. 10

1999 arXiv
[35]

De Fazio and M

F. De Fazio and M. Neubert, JHEP 06, 017 (1999), arXiv:hep-ph/9905351

1999 arXiv
[36]

Capdevila, P

B. Capdevila, P. Gambino, and S. Nandi, JHEP 04, 137 (2021), arXiv:2102.03343 [hep-ph]

2021 arXiv
[37]

van Ritbergen, Phys

T. van Ritbergen, Phys. Lett. B 454, 353 (1999), arXiv:hep-ph/9903226

1999 arXiv
[38]

Brucherseifer, F

M. Brucherseifer, F. Caola, and K. Melnikov, Phys. Lett . B 721, 107 (2013), arXiv:1302.0444 [hep-ph]

2013 arXiv
[39]

Bauer, B

M. Bauer, B. Stech, and M. Wirbel, Z. Phys. C 34, 103 (1987)

1987
[40]

Aquila, P

V. Aquila, P. Gambino, G. Ridolﬁ, and N. Uraltsev, Nucl. Phys. B 719, 77 (2005), arXiv:hep-ph/0503083

2005 arXiv
[41]

L. Chen, X. Chen, X. Guan, and Y.-Q. Ma, (2023), arXiv:23 09.01937 [hep-ph]

2023
[42]

J. F. Kamenik and P. Gambino, Nucl. Phys. B Proc. Suppl. 210-211, 151 (2011)

2011
[43]

Alberti, P

A. Alberti, P. Gambino, K. J. Healey, and S. Nandi, Phys. Rev. Lett. 114, 061802 (2015), arXiv:1411.6560 [hep-ph]

2015 arXiv
[44]

Gambino, K

P. Gambino, K. J. Healey, and S. Turczyk, Phys. Lett. B 763, 60 (2016), arXiv:1606.06174 [hep-ph]

2016 arXiv
[45]

Boushmelev, T

A. Boushmelev, T. Mannel, and K. K. Vos, JHEP 07, 175 (2023), arXiv:2301.05607 [hep-ph]

2023 arXiv
[46]

N. Gray, D. J. Broadhurst, W. Grafe, and K. Schilcher, Z. Phys. C 48, 673 (1990)

1990
[47]

D. J. Broadhurst, N. Gray, and K. Schilcher, Z. Phys. C 52, 111 (1991)

1991
[48]

Fleischer, F

J. Fleischer, F. Jegerlehner, O. V. Tarasov, and O. L. Ve retin, Nucl. Phys. B 539, 671 (1999), [Erratum: Nucl.Phys.B 571, 511–512 (2000)], arXiv:hep-ph/9803493

1999 arXiv
[49]

Melnikov and T

K. Melnikov and T. v. Ritbergen, Phys. Lett. B 482, 99 (2000), arXiv:hep-ph/9912391

2000 arXiv
[50]

Aoki et al

S. Aoki et al. (Flavour Lattice Averaging Group), Eur. Phys. J. C 80, 113 (2020), arXiv:1902.08191 [hep-lat]

2020 arXiv
[51]

Navas et al

S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

2024
[52]

Herren and M

F. Herren and M. Steinhauser, Comput. Phys. Commun. 224, 333 (2018), arXiv:1703.03751 [hep-ph]

2018 arXiv
[53]

Gambino, A

P. Gambino, A. Melis, and S. Simula, Phys. Rev. D 96, 014511 (2017), arXiv:1704.06105 [hep-lat]

2017 arXiv
[54]

Gambino and S

P. Gambino and S. Hashimoto, Phys. Rev. Lett. 125, 032001 (2020), arXiv:2005.13730 [hep-lat]

2020 arXiv
[55]

Gambino, S

P. Gambino, S. Hashimoto, S. M¨ achler, M. Panero, F. San ﬁlippo, S. Simula, A. Smecca, and N. Tantalo, JHEP 07, 083 (2022), arXiv:2203.11762 [hep-lat]

2022 arXiv
[56]

Nefediev, Phys

A. Nefediev, Phys. Rev. D 109, 094021 (2024), arXiv:2404.11158 [hep-lat]

2024 arXiv
[57]

L.-B. Chen, H. T. Li, Z. Li, J. Wang, Y. Wang, and Q.-f. Wu, Phys. Rev. D 109, L071503 (2024), arXiv:2309.00762 [hep-ph]

2024 arXiv
[58]

Yan, X.-G

J. Yan, X.-G. Wu, H. Zhou, H.-T. Li, and J.-H. Shan, Phys. Rev. D 109, 114026 (2024), arXiv:2404.11133 [hep-ph]

2024 arXiv
[59]

M. Fael, K. Sch¨ onwald, and M. Steinhauser, Phys. Rev. D 104, 016003 (2021), arXiv:2011.13654 [hep-ph]

2021 arXiv
[60]

Fael and J

M. Fael and J. Usovitsch, Phys. Rev. D 108, 114026 (2023), arXiv:2310.03685 [hep-ph]

2023 arXiv
[61]

M. Fael, T. Huber, F. Lange, J. M¨ uller, K. Sch¨ onwald, a nd M. Steinhauser, Phys. Rev. D 110, 056011 (2024), arXiv:2406.08182 [hep-ph]

2024 arXiv
[62]

Achasov et al

M. Achasov et al. , Front. Phys. (Beijing) 19, 14701 (2024), arXiv:2303.15790 [hep-ex]

2024

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [25]

Ablikim et al

M. Ablikim et al. (BESIII), Phys. Rev. Lett. 121, 251801 (2018), arXiv:1805.09060 [hep-ex]

arXiv 2018

[2] [21]

Archilli, M

F. Archilli, M. O. Bettler, P. Owen, and K. A. Petridis, N ature 546, 221 (2017)

work page 2017

[3] [1]

0.964628 0 .888372 0 .799743 −0.0682164 0 .964628 1

−0.0764818 −0.0682164 −0.0584038 −0.049709 −0.0764818 1 . 0.964628 0 .888372 0 .799743 −0.0682164 0 .964628 1 . 0.976053 0 .921246 −0.0584038 0 .888372 0 .976053 1 . 0.982859 −0.049709 0 .799743 0 .921246 0 .982859 1 .         , Cor(D+) =        

work page

[4] [2]

0.959852 0 .877876 0 .784972 −0.0111696 0 .959852 1

−0.00918393 −0.0111696 −0.011663 −0.0114986 −0.00918393 1 . 0.959852 0 .877876 0 .784972 −0.0111696 0 .959852 1 . 0.974619 0 .917145 −0.011663 0 .877876 0 .974619 1 . 0.982034 −0.0114986 0 .784972 0 .917145 0 .982034 1 .         , (17) 9 Cor(D+ s ) =        

work page

[5] [3]

0.961103 0 .877715 0 .779303 −0.0854423 0 .961103 1

−0.0948363 −0.0854423 −0.0692735 −0.0528099 −0.0948363 1 . 0.961103 0 .877715 0 .779303 −0.0854423 0 .961103 1 . 0.973193 0 .910118 −0.0692735 0 .877715 0 .973193 1 . 0.979699 −0.0528099 0 .779303 0 .910118 0 .979699 1 .         . The second set includes the decay width, the ﬁst order electron en ergy moment, the second, third and the fourth elect...

work page

[6] [4]

−0.088841 −0.444378 −0.0618813 0.0281587 −0.088841 1

−0.0764818 0 .0281587 0 .0330765 0 .0102788 −0.0764818 1 . −0.088841 −0.444378 −0.0618813 0.0281587 −0.088841 1 . −0.00420729 0 .817582 0.0330765 −0.444378 −0.00420729 1 . −0.0351105 0.0102788 −0.0618813 0 .817582 −0.0351105 1 .         , Cor(D+) =        

work page

[7] [5]

−0.0423819 −0.456701 −0.0390424 −0.00799742 −0.0423819 1

−0.00918393 −0.00799742 0 .00816853 −0.0107153 −0.00918393 1 . −0.0423819 −0.456701 −0.0390424 −0.00799742 −0.0423819 1 . −0.0538756 0 .809543 0.00816853 −0.456701 −0.0538756 1 . −0.0924318 −0.0107153 −0.0390424 0 .809543 −0.0924318 1 .         , (18) Cor(D+ s ) =        

work page

[8] [6]

−0.047314 −0.40486 −0.0191632 0.0254998 −0.047314 1

−0.0948363 0 .0254998 0 .0800786 0 .00809594 −0.0948363 1 . −0.047314 −0.40486 −0.0191632 0.0254998 −0.047314 1 . 0.0763575 0 .800281 0.0800786 −0.40486 0 .0763575 1 . 0.172337 0.00809594 −0.0191632 0 .800281 0 .172337 1 .        

work page