Pith. sign in

REVIEW 3 major objections 6 minor 65 references

The D_s → K*0 semileptonic decay keeps lepton flavor universality: electron and muon branching fractions agree within error, with R_{μ/e}=0.950.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 18:33 UTC pith:EAYPHNYT

load-bearing objection A competent LCSR calculation of D_s -> K*0 form factors with plausible new numbers, but the missing Borel stability analysis and the imported experimental correlation coefficients keep it from being fully certified. the 3 major comments →

arxiv 2607.17253 v1 pith:EAYPHNYT submitted 2026-07-19 hep-ph

Scrutinizing lepton flavor universality and transition form factor correlation from charmed meson semileptonic decay into light strange vector K^* meson

Sheng-Bo Wu , Dong Huang , Fang-Ping Peng , Hai-Bing Fu , Long-Zeng This is my paper
classification hep-ph
keywords semileptonic decayD_s mesonK* vector mesontransition form factorslight-cone sum ruleslepton flavor universalitydistribution amplitudesCKM matrix element
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper computes the strong-interaction form factors that govern the semileptonic decay of the D_s meson into the light strange vector meson K*0, using QCD light-cone sum rules with a harmonic-oscillator model for the K*0's internal quark-antiquark distribution. At zero momentum transfer it finds A1(0)=0.579, A2(0)=0.414, V(0)=0.830, and after extrapolating to the full kinematic range it obtains branching fractions of 2.05×10^{-3} (electron channel) and 1.95×10^{-3} (muon channel). The ratio of these two branching fractions, R=0.950 with tiny errors, is consistent with lepton flavor universality — the Standard Model assumption that electrons and muons couple identically. The same calculation yields the CKM matrix element |V_cd| and forward-backward asymmetries. The paper's broader point is that the form factors are not independent inputs but correlate through the underlying meson distribution, and those correlations offer a sharper test of the theory than any single decay rate.

Core claim

The central claim is that a parameter-free (in the sense of being fixed by normalization and a few moments) construction of the K*0 twist-2 light-cone distribution amplitudes, inserted into a standard light-cone sum-rule correlation function, reproduces the measured electron-mode branching fraction and predicts the muon-mode branching fraction so that the ratio R^{K*0}_{μ/e} = 0.950_{-0.002}^{+0.004}, in line with lepton flavor universality. The zero-recoil form factors are A1(0)=0.579_{-0.028}^{+0.024}, A2(0)=0.414_{-0.023}^{+0.021}, V(0)=0.830_{-0.020}^{+0.020}; the ratios r_V=V/A1=1.433 and r_2=A2/A1=0.715. The paper also stresses that A1, A2 and V are correlated because they arise from t

What carries the argument

The engine of the calculation is the light-cone harmonic oscillator (LCHO) model for the twist-2 light-cone distribution amplitudes (LCDAs) φ^{⊥}_{2;K*0}(x,μ) and φ^{∥}_{2;K*0}(x,μ). These functions encode the probability of finding the quark and antiquark of the K*0 carrying momentum fraction x and transverse momentum k⊥. The model's parameters are fixed by the normalization of each LCDA, by the average transverse momentum squared ⟨k⊥²⟩^{1/2}=0.37 GeV, and by the first Gegenbauer moments a_⊥1=0.04, a_∥1=0.03. These LCDAs are then fed into the correlation function whose operator product expansion yields the sum rules for the form factors A1, A2, V and A0; the twist-2 pieces dominate the theo

Load-bearing premise

The load-bearing assumption is that the K*0 twist-2 distribution amplitudes are exactly represented by the harmonic-oscillator model with only the first Gegenbauer moment; if higher Gegenbauer moments (a_2, a_3, ...) are not negligible, the quoted form factors, branching fractions, and R_{μ/e}=0.950 would shift.

What would settle it

Measure the D_s→K*0 μ ν branching fraction to a precision such that R_{μ/e} is known to better than ±0.005 and compare with the predicted 0.950; a measured ratio below 0.945 or above 0.960 would falsify the prediction. Alternatively, a lattice calculation of the second Gegenbauer moment of the K* twist-2 distribution amplitude that clearly differs from zero would invalidate the model input.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The predicted R_{μ/e}=0.950 means lepton flavor universality holds in this decay within the stated uncertainties, so no new physics is required.
  • The extracted |V_cd| values from the electron and muon channels, 0.225 and 0.227, are mutually consistent and consistent with CKM unitarity.
  • The ratio predictions r_V=1.433 and r_2=0.715 sit inside the experimentally favored correlation region, so the hadronic input is not just tuned to one number.
  • The forward-backward asymmetry averages, around -0.21 (electron) and -0.24 (muon), provide a second observable for upcoming precision measurements.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A precise future measurement of R_{μ/e} at the per-mille level would directly test the small phase-space suppression that produces 0.950 instead of 1, distinguishing Standard Model dynamics from a possible lepton-flavor-violating contribution.
  • The LCHO model's truncation at the first Gegenbauer moment is testable: a lattice calculation of the second Gegenbauer moment of the K* twist-2 LCDA, if nonzero, would shift the central form factors and could be compared directly with the predicted distribution shape.
  • The same correlation-based reasoning could be applied to other charmed semileptonic decays, such as D_s→φ, where the analogous R_{μ/e} may be more sensitive to model input.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper uses QCD light-cone sum rules (LCSR) to compute the D_s^+ -> K^{*0} transition form factors A_1(q^2), A_2(q^2), and V(q^2). The twist-2 light-cone distribution amplitudes of the K^{*0} are constructed with the light-cone harmonic oscillator (LCHO) model, with parameters fixed by normalization, the transverse-momentum scale, and the first Gegenbauer moments. The LCSR results at q^2=0 are then extrapolated to the full kinematic region using a simplified z-series expansion, and are used to predict the semileptonic decay widths and branching fractions, the LFU ratio R^{K*0}_{\mu/e}, the CKM element |V_cd|, and the forward-backward asymmetries. The central numerical results are A_1(0)=0.579^{+0.024}_{-0.028}, A_2(0)=0.414^{+0.021}_{-0.023}, V(0)=0.830^{+0.020}_{-0.020}, B(D_s^+->K^{*0}e^+\nu_e)=(2.05^{+0.13}_{-0.16})\times10^{-3}, B(D_s^+->K^{*0}\mu^+\nu_\mu)=(1.95^{+0.13}_{-0.15})\times10^{-3}, and R^{K*0}_{\mu/e}=0.950^{+0.004}_{-0.002}, consistent with lepton flavor universality.

Significance. If the results are robust, the paper provides an independent LCSR-based determination of all D_s^+->K^{*0} form factors, together with updated predictions for the branching fractions, the LFU ratio, and the CKM element |V_cd|. The appendix gives explicit expressions for the LCSR coefficients, which is a strength for reproducibility. The comparison with the 2026 BESIII data is timely and the predicted branching fractions agree within errors. However, the sum-rule window is not validated, and the claimed TFF/BR correlations are partly constructed using experimental correlation coefficients rather than derived from the theory, so the full strength of the 'correlation prediction' claim is not yet established.

major comments (3)
  1. [Section III, before Table II] The Borel masses and continuum thresholds are stated as s0^{A1}=s0^{A2}=8.5±0.5 GeV^2, s0^V=14±0.5 GeV^2, M^2_{A1}=15±1 GeV^2, M^2_{A2}=12±1 GeV^2, M^2_V=15±1 GeV^2, with the single sentence that they follow the 'self-consistency criteria of QCDSR'. No Borel plateau, no s0-variation curve, and no OPE-convergence or ground-state-dominance check is shown. For m_Ds=1.968 GeV, these parameters correspond to e^{-s0/M^2}~0.4–0.6, so continuum contributions are not strongly suppressed. Since all TFFs and all downstream observables (branching fractions, R_{μ/e}, |V_cd|) inherit these choices, the central numerical claims require the standard LCSR validation plots. This omission is load-bearing and should be fixed.
  2. [Section II, Eq. (23) and Table I] The LCHO model for the twist-2 LCDAs is truncated at the C_1^{3/2}(ξ) term, and the model parameters are fixed using only the first Gegenbauer moments a_⊥1=0.04(3) and a_∥1=0.03(2). If the true K^{*0} twist-2 LCDAs have non-negligible a_2 or higher moments, the resulting TFFs will shift. The quoted uncertainties are parametric uncertainties within the model and do not include this truncation systematic. The authors should quantify the sensitivity by adding a C_2^{3/2} term with a range guided by lattice or QCDSR estimates, or otherwise justify why the first-moment truncation is sufficient. This directly affects the uncertainty budget of A_1(0), A_2(0), and V(0), and hence of the branching fractions and R_{μ/e}.
  3. [Section III, Figs. 3 and 6] The paper states in the abstract and text that it 'predicts the correlation of TFFs and their corresponding ratios', but the correlation ellipses in Fig. 3 use correlation coefficients 'respectively set to 0.2 and -0.28 [8]', and the branching-fraction ellipse in Fig. 6 takes the coefficient as 0.15 from BESIII [8]. These are experimental correlations, not derived from the LCSR formalism or the LCHO model. Thus the correlation prediction is partly an import from experiment. The TFF values themselves do not depend on these coefficients, but the correlation claim does. The authors should either derive the theoretical correlations from the common parameter variations (e.g., by propagating the correlated LCHO and LCSR uncertainties) or clearly reframe Figs. 3 and 6 as comparisons that use the BESIII correlation coefficients.
minor comments (6)
  1. [Introduction, paragraph 2] The sentence 'Therefore, further studies of this muonic channel will help comprehensively test lepton flavor universality (LFU)' is duplicated verbatim.
  2. [Section II, before Eq. (5)] Typo: 'facyor' should be 'factor'.
  3. [Section III, before Eq. (27)] The branching-fraction uncertainties are propagated from the TFFs, but Table I lists the LCHO parameters A_λ, B_λ, b_λ without uncertainties even though they are fitted to inputs with errors (a_1, ⟨k_⊥^2⟩). Clarify how the parameter uncertainties are obtained and propagated.
  4. [Section III, Eq. (25)] The simplified series expansion parameters β_{k,i} are introduced but the fit procedure and fit quality are not described. Please specify the input q^2 points, the number of fitted parameters, and the resulting uncertainties/correlation matrix, since these affect the extrapolated TFFs.
  5. [Section III, Fig. 7 and text] Reference [63] (ATLAS top-squark search) appears to be cited for the AFB theoretical comparison range; this seems to be an incorrect reference. Please verify.
  6. [Throughout] Several typos and grammatical issues: 'rum rules' (Eq. (14) discussion), 'helicality' (Eq. (11) discussion), 'farther determined' (Introduction), 'our prediction prefers a single-peak behavior, while are consistent' (Section III, Fig. 2 discussion).

Circularity Check

2 steps flagged

Core LCSR derivation is self-contained, but two load-bearing inputs are imported rather than derived: the claimed correlation ellipses use BESIII correlation coefficients as inputs, and the sum-rule window is justified by a same-group citation without in-paper stability checks.

specific steps
  1. fitted input called prediction [Section III, Fig. 6 caption and text (also Fig. 3)]
    "Meanwhile, we also provided the correlation degree predictions for the branching fractions of two decay channels, D+s → K∗0e+νe and D+s → K∗0µ+νµ, and presented them in Fig. 6. The correlation coefficient is taken as 0.15 from the most recent BESIII result [8]."

    The ellipse in Fig. 6 is the claimed 'prediction' of the B(e)-B(µ) correlation, but its central quantitative input is the experimental coefficient ρ=0.15 from BESIII [8]. No LCSR-based correlated error propagation is shown to produce a different coefficient; the predicted correlation degree is therefore the imported experimental value by construction. Fig. 3 uses the same device: the caption states 'The correlation coefficients are respectively set to 0.2 and −0.28 [8]' while the text calls the resulting ellipses 'theoretical predictions for the correlations.'

  2. self citation load bearing [Section III, paragraph on continuum threshold and Borel parameter]
    "These parameters can be determined according to the self-consistency criteria of QCDSR [51]. Based on this, the continuum threshold s0 and Borel parameter M2 corresponding to TFFs can be further obtained, and the results are sA1_0 = sA2_0 = 8.5 ± 0.5 GeV2, sV_0 = 14±0.5 GeV2, M2_A1 = 15.0±1.0 GeV2, M2_A2 = 12.0±1.0 GeV2 and M2_V = 15.0 ± 1.0 GeV2"

    Ref. [51] (Tian, Fu, Zhong, Luo, Hu, Yang) shares authors with the present work (H.B. Fu et al.). The values of s0 and M^2 enter every LCSR expression, Eqs. (16)-(19), and therefore set A1(0)=0.579, A2(0)=0.414, V(0)=0.830, the branching fractions, and R_{μ/e}. No Borel plateau, s0-variation, OPE-convergence, or ground-state-dominance check is shown in this paper; the quantitative choice is justified solely by citing [51]. Thus a load-bearing numerical input reduces to a same-group citation rather than to demonstrated stability.

full rationale

The central derivation is not circular: the LCHO parameters (Aλ, Bλ, bλ) are fixed by normalization, ⟨k⊥²⟩^{1/2}=0.37(2) GeV, and the first Gegenbauer moments a⊥1=0.04(3), a∥1=0.03(2) from Refs. [37,41,45]; none of the target outputs (A1,2(0), V(0), branching fractions, R_{μ/e}) is used to fix them. Eqs. (16)-(19) are genuine LCSR convolutions, and the decay rates follow from them via Eqs. (11)-(12); the headline numbers are benchmarked against external experiments and models in Tables II-IV. The circular content is therefore partial. First, the 'prediction' of the correlation ellipses in Figs. 3 and 6 uses experimental correlation coefficients (0.15, -0.28, 0.2) taken from BESIII [8] as inputs, so those specific predictions are imported rather than derived. Second, the sum-rule window (s0, M^2) is justified only by citing same-group Ref. [51], with no stability plots in the paper; although this is partly a validation omission, it makes a load-bearing numerical choice rest on self-citation. These issues warrant a score of 4 rather than 0-2, but do not reduce the main TFF/BR/R derivation to a fit or a renaming; I see no circularity at the 6+ level.

Axiom & Free-Parameter Ledger

10 free parameters · 7 axioms · 0 invented entities

No new particles or forces are introduced. The main free parameters are the six LCHO model parameters (A,B,b for λ=⊥,∥), the Borel masses, continuum thresholds, and the correlation coefficients imported from BESIII. The crucial model assumptions are the LCHO ansatz, the truncation at the first Gegenbauer moment, the WW approximation, and the external twist-4 LCDAs.

free parameters (10)
  • A⊥; K*0 (transverse LCHO normalization) = 34.1354 at μ=1.5 GeV
    Fixed by ∫φ⊥ dx = 1; normalization constraint for transverse LCDA.
  • B⊥; K*0 (first Gegenbauer coefficient) = -0.0593
    Fixed by a⊥1(1 GeV)=0.04(3) from QCDSR [37].
  • b⊥; K*0 (transverse-size parameter) = 0.6846 GeV^-1
    Fixed by ⟨k⊥²⟩^{1/2}_{K*}=0.37(2) GeV.
  • A∥; K*0 (longitudinal LCHO normalization) = 31.5511 at μ=1.5 GeV
    Fixed by ∫φ∥ dx = 1.
  • B∥; K*0 (first Gegenbauer coefficient) = -0.0702
    Fixed by a∥1(1 GeV)=0.03(2) from QCDSR [37].
  • b∥; K*0 (transverse-size parameter) = 0.6851 GeV^-1
    Fixed by ⟨k⊥²⟩^{1/2}_{K*}=0.37(2) GeV.
  • Borel masses M² = M²_A1=15.0, M²_A2=12.0, M²_V=15.0 GeV² (±1)
    Chosen by QCDSR self-consistency criteria [51]; no stability plots shown in the paper.
  • Continuum thresholds s0 = s0(A1)=s0(A2)=8.5, s0(V)=14 GeV² (±0.5)
    Chosen by sum-rule criteria; V threshold differs sharply from A1/A2.
  • Correlation coefficients for TFF/BR ellipses = ρ(A2,A1)=0.2; ρ(r2,rV)=-0.28; ρ(BR)=0.15
    Imported from BESIII [8] and used to draw the 'predicted' ellipses in Figs. 3 and 6.
  • Constituent quark masses in LCHO model = mq=0.300 GeV, ms=0.450 GeV
    Adopted from ref [44] for the Wigner-Melosh factor Y=x̄ms+xmq.
axioms (7)
  • standard math QCD light-cone sum rule machinery: OPE for correlation function (13), quark-hadron duality ρ_H = ρ_QCD θ(s0-s), Borel transform in (p+q)^2.
    Section II, after Eq. (14)-(15); unproved background used to convert correlation function to TFFs.
  • standard math Standard factorization of semileptonic amplitude into hadronic matrix element parameterized by A1,A2,A3,A0,V (Eq. (6)) and leptonic tensor.
    Section II, Eq. (6)-(12).
  • domain assumption LCHO/BHL ansatz for the K*0 light-cone wave function (Eqs. (21)-(24)), including Wigner-Melosh spin factor and exponential transverse-momentum dependence.
    Section II; this is a model for nonperturbative LCDAs, not derived from QCD.
  • ad hoc to paper Truncation of the Gegenbauer expansion at the C_1^{3/2} term (only Bλ first moment; no a2,a3 terms) in Eq. (23).
    The paper fixes Bλ using a1 only and introduces no higher moments; this controls the LCDA shape and hence the TFF central values.
  • domain assumption Wandzura-Wilczek approximation expressing twist-3 LCDAs through twist-2 LCDAs.
    Used for twist-3 contributions in the TFF sum rules; stated at end of Section II and in Appendix.
  • domain assumption Twist-4 LCDAs taken from Ball-Braun-Lenz [37].
    External parameterization assumed for twist-4 contributions; referenced in Sections II-III and Appendix.
  • domain assumption SSE z-series (Eq. (25)) with β_k coefficients determined from LCSR points in the low-q² region.
    Needed to extrapolate TFFs to the full physical region; assumes the z-expansion form and pole factor.

pith-pipeline@v1.3.0-alltime-deepseek · 27858 in / 14766 out tokens · 123114 ms · 2026-08-01T18:33:40.148076+00:00 · methodology

0 comments
read the original abstract

In this paper, we calculate the transition form factors (TFFs) $A_{1,2}(q^2)$ and $V(q^2)$ of $D_s^+ \to K^{*0}$ decays by using the QCD light-cone sum rule (QCD LCSR) and constructing a correlation function containing the usual current, in which the twist-2 transverse and longitudinal light-cone distribution amplitudes (LCDAs) $\phi^\lambda_{2;K^{*0}}(x,\mu_0)$ with $\lambda=(\bot,\|)$ of the $K^{*0}$ meson constitute the main source of theoretical uncertainty. Based on this, we construct these LCDAs using the light-cone harmonic oscillator model. Subsequently, the TFFs obtained in the large recoil region are $A_{1}(0)=0.579_{-0.028}^{+0.024}$, $A_{2}(0)=0.414_{-0.023}^{+0.021}$, and $V(0)=0.830_{-0.020}^{+0.020}$, and the corresponding ratios are obtained to be $r_V=1.433_{-0.090}^{+0.110}$ and $r_2=0.715_{-0.067}^{+0.075}$. Furthermore, we predict the correlation of TFFs and their corresponding ratios. Then, we extrapolate the TFFs over the whole physical $q^2$-region and calculate the decay widths and branching fractions for the semileptonic decays $D_s^+\to K^{*0}\ell^+\nu_{\ell}$. The results are $\mathcal{B}(D_s^+\to K^{*0}e^+\nu_{e})=(2.05_{-0.16}^{+0.13})\times 10^{-3}$ and $\mathcal{B}(D_s^+\to K^{*0}\mu^+\nu_{\mu})=(1.95_{-0.15}^{+0.13})\times 10^{-3}$. Meanwhile, we calculated the branching fraction ratio $\mathcal{R}_{\mu/e}^{K^{*0}}$ to be $0.950_{-0.002}^{+0.004}$. In addition, we extract values of the CKM matrix element, obtaining $|V_{cd}|_{(e\text{-Channel})} = 0.225_{-0.005}^{+0.005}$ and $|V_{cd}|_{(\mu\text{-Channel})} = 0.227_{-0.004}^{+0.011}$. Finally, we calculated the forward-backward asymmetry parameters for the $D_s^+\to K^{*0} \ell^+\nu_{\ell}$ decay.

Figures

Figures reproduced from arXiv: 2607.17253 by Dong Huang, Fang-Ping Peng, Hai-Bing Fu, Long-Zeng, Sheng-Bo Wu.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: In addition, the average values of Aℓ FB are given as ⟨Ae FB⟩ = −0.212+0.01 −0.03 and ⟨A µ FB⟩ = −0.243+0.008 −0.003, respectively. These results indicate that no significant violation of LFU is observed in the semileptonic decay D + s → K ∗0 ℓ + νℓ . V. ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China under Grant No.12265010, the Project of Guizhou Provincial Dep… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

65 extracted references · 56 linked inside Pith

  1. [1]

    Antonelli, D

    M. Antonelli, D. M. Asner, D. Bauer, T. G. Becher, M. Beneke, A. J. Bevan, M. Blanke, C. Bloise, M. Bona and A. E. Bondar, et al. Flavor Physics in the Quark Sector, Phys. Rept. 494, 197- 414 (2010) [arXiv:0907.5386]

    Pith/arXiv arXiv 2010

  2. [2]

    J. D. Richman and P . R. Burchat, Leptonic and semileptonic decays of charm and bottom hadrons, Rev. Mod. Phys. 67, 893- 976 (1995) [arXiv:hep-ph/9508250]

    Pith/arXiv arXiv 1995

  3. [3]

    Kobayashi and T

    M. Kobayashi and T. Maskawa, CP Violation in the Renormal- izable Theory of Weak Interaction, Prog. Theor. Phys. 49, 652- 657 (1973)

    1973

  4. [4]

    Navas et al

    S. Navas et al. [Particle Data Group], Review of particle physics, Phys. Rev. D 110 no.3, 030001 (2024)

    2024

  5. [5]

    Y eltonet al

    J. Y eltonet al. [CLEO], Absolute Branching Fraction Measure- ments for Exclusive Ds Semileptonic Decays, Phys. Rev. D 80, 052007 (2009) [arXiv:0903.0601]

    Pith/arXiv arXiv 2009

  6. [6]

    Hietala, D

    J. Hietala, D. Cronin-Hennessy, T. Pedlar and I. Shipsey, Exclu- sive Ds semileptonic branching fraction measurements, Phys. Rev. D 92, no.1, 012009 (2015) [arXiv:1505.04205]

    Pith/arXiv arXiv 2015

  7. [7]

    Ablikim et al

    M. Ablikim et al. [BESIII], First Measurement of the Form Fac- tors in D+ s → K0e+νe and D+ s → K∗0e+νe Decays, Phys. Rev. Lett. 122, no.6, 061801 (2019) [arXiv:1811.02911]

    Pith/arXiv arXiv 2019

  8. [8]

    Ablikim et al

    M. Ablikim et al. [BESIII], First Measurement of the D+ s → K∗(892)0+ Decay, Study of Dynamics and Test of Lepton Uni- versality with D+ s → K∗(892)0ℓ+ℓ Decays, [arXiv:2605.07176]

    Pith/arXiv arXiv

  9. [9]

    M. A. Ivanov, J. G. Körner, J. N. Pandya, P . Santorelli, N. R. Soni and C. T. Tran, Exclusive semileptonic decays of D and Ds mesons in the covariant confining quark model, Front. Phys. (Beijing) 14 no.6, 64401 (2019) [arXiv:1904.07740]

    Pith/arXiv arXiv 2019

  10. [10]

    N. R. Soni, M. A. Ivanov, J. G. Körner, J. N. Pandya, P . San- torelli and C. T. Tran, Semileptonic D(s)-meson decays in the light of recent data, Phys. Rev. D 98, no.11, 114031 (2018) [arXiv:1810.11907]

    Pith/arXiv arXiv 2018

  11. [11]

    Sekihara and E

    T. Sekihara and E. Oset, Investigating the nature of light scalar mesons with semileptonic decays of D mesons, Phys. Rev. D 92 no.5, 054038 (2015) [arXiv:1507.02026]

    Pith/arXiv arXiv 2015

  12. [12]

    H. Y . Cheng and X. W. Kang, Branching fractions of semilep- tonic D and Ds decays from the covariant light-front quark model, Eur. Phys. J. C 77 no.9, 587 (2017) [arXiv:1707.02851]

    Pith/arXiv arXiv 2017

  13. [13]

    Fajfer and J

    S. Fajfer and J. F. Kamenik, Charm meson resonances and D → V semileptonic form-factors, Phys. Rev. D 72, 034029 (2005) [arXiv:hep-ph/0506051]

    Pith/arXiv arXiv 2005

  14. [14]

    Melikhov and B

    D. Melikhov and B. Stech, Weak form-factors for heavy me- son decays: An Update, Phys. Rev. D 62, 014006 (2000) [arXiv:hep-ph/0001113]

    Pith/arXiv arXiv 2000

  15. [15]

    Y . L. Wu, M. Zhong and Y . B. Zuo, B(s), D(s) → π, K,η,ρ, K∗,ω,ϕ Transition Form Factors and Decay Rates with Extraction of the CKM parameters |V(ub)|, |V(cs)|, |V(cd)|, Int. J. Mod. Phys. A 21, 6125-6172 (2006) [arXiv:hep- ph/0604007]

    arXiv 2006

  16. [16]

    W. Lin, X. E. Huang, S. Cheng and D. L. Y ao, Semileptonic de- cays of D →ρℓ+ν and D(s) → K∗ℓ+ν from light-cone sum rules, Phys. Rev. D 111, no.11, 113005 (2025) [arXiv:2505.01329]

    Pith/arXiv arXiv 2025

  17. [17]

    Palmer and J

    T. Palmer and J. O. Eeg, Form factors for semileptonic D de- cays, Phys. Rev. D 89, no.3, 034013 (2014) [arXiv:1306.0365]

    Pith/arXiv arXiv 2014

  18. [18]

    Zhang, X

    L. Zhang, X. W. Kang, X. H. Guo, L. Y . Dai, T. Luo and C. Wang, A comprehensive study on the semileptonic decay of heavy flavor mesons, JHEP 02, 179 (2021) [arXiv:2012.04417]

    Pith/arXiv arXiv 2021

  19. [19]

    R. C. V erma, Decay constants and form factors ofs-wave and p- wave mesons in the covariant light-front quark model, J. Phys. G 39, 025005 (2012) [arXiv:1103.2973]

    Pith/arXiv arXiv 2012

  20. [20]

    Y ang, S

    H. Y ang, S. Q. Guo and Z. Q. Zhang, Systematic analysis ofD(s) meson semi-leptonic decays in the covariant light-front quark model, Eur. Phys. J. C 86, no.4, 363 (2026) [arXiv:2511.14165]

    Pith/arXiv arXiv 2026

  21. [21]

    Wang and Y

    W. Wang and Y . L. Shen,Ds → K, K∗,ϕ form factors in the Co- variant Light-Front Approach and Exclusive Ds Decays, Phys. Rev. D 78, 054002 (2008)

    2008

  22. [22]

    R. N. Faustov, V . O. Galkin and X. W. Kang, Semileptonic de- cays of D and Ds mesons in the relativistic quark model, Phys. Rev. D 101, no.1, 013004 (2020) [arXiv:1911.08209]

    Pith/arXiv arXiv 2020

  23. [23]

    H. A. Ahmed, Y . Chen and M. Huang, D(s)-mesons semilep- tonic form factors in four-flavor holographic QCD, Phys. Rev. D 109, no.2, 026008 (2024) [arXiv:2309.06156]

    Pith/arXiv arXiv 2024

  24. [24]

    R. H. Li, C. D. Lu and W. Wang, Transition form fac- tors of B decays into p-wave axial-vector mesons in the per- turbative QCD approach, Phys. Rev. D 79, 034014 (2009) [arXiv:0901.0307]

    Pith/arXiv arXiv 2009

  25. [25]

    S. J. Brodsky, T. Huang and G. P . Lepage, Hadronic wave functions and high momentum transfer interactions in quan- tum chromodynamics, Conf. Proc. C 810816, 143-199 (1981) SLAC-PUB-16520

    1981

  26. [26]

    F. g. Cao and T. Huang, Large corrections to asymptotic Fηcγ and Fηbγ in the light-cone perturbative QCD, Phys. Rev. D 59, 15 093004 (1999) [arXiv:hep-ph/9711284]

    Pith/arXiv arXiv 1999

  27. [27]

    Huang and X

    T. Huang and X. G. Wu, A Model for the twist-3 wave function of the pion and its contribution to the pion form-factor, Phys. Rev. D 70, 093013 (2004) [arXiv:hep-ph/0408252]

    Pith/arXiv arXiv 2004

  28. [28]

    D. D. Hu, X. G. Wu, L. Zeng, H. B. Fu and T. Zhong, An im- proved light-cone harmonic oscillator model for the ϕ-meson longitudinal leading-twist light-cone distribution amplitude and its e ffects to D+ s → ϕℓ+νℓ. Phys. Rev. D 110 no.5, 056017 (2024) [arXiv:2403.10003]

    Pith/arXiv arXiv 2024

  29. [29]

    H. B. Fu, X. G. Wu, W. Cheng and T. Zhong, ρ -meson longi- tudinal leading-twist distribution amplitude within QCD back- ground field theory, Phys. Rev. D 94 no.7, 074004 (2016) [arXiv:1607.04937]

    Pith/arXiv arXiv 2016

  30. [30]

    Y . L. Y ang, Y . L. Song, F. P . Peng, H. B. Fu, T. Zhong and S. Ullah, Exploring the exclusive decay B+ → ωℓ+ν with light-cone sum rules, Phys. Rev. D 112 no.1, 016002 (2025) [arXiv:2504.05650]

    Pith/arXiv arXiv 2025

  31. [31]

    H. M. Choi and C. R. Ji, Distribution amplitudes and decay constants for ( π, K,ρ, K∗) mesons in light-front quark model, Phys. Rev. D 75, 034019 (2007) [arXiv:hep-ph/0701177]

    Pith/arXiv arXiv 2007

  32. [32]

    J. Xu, Q. A. Zhang and S. Zhao, Light-cone distribution am- plitudes of vector meson in a large momentum e ffective theory, Phys. Rev. D 97 no.11, 114026 (2018) [arXiv:1804.01042]

    Pith/arXiv arXiv 2018

  33. [33]

    Zhong, Y

    T. Zhong, Y . H. Dai and H. B. Fu, ρ-meson longitudinal leading-twist distribution amplitude revisited and the D → ρ semileptonic decay, Chin. Phys. C 48, no.6, 063108 (2024) [arXiv:2308.14032]

    Pith/arXiv arXiv 2024

  34. [34]

    Y . X. Wang, D. D. Hu, W. B. Luo, T. Zhong and H. B. Fu, Status of the D+ s →ϕℓ+νℓ decay with a chiral-odd ϕ-meson light-cone distribution amplitude, Phys. Rev. D 112, no.5, 056008 (2025) [arXiv:2505.15014]

    arXiv 2025

  35. [35]

    Be ˇcirevi´c, F

    D. Be ˇcirevi´c, F. Ja ffredo, A. Peñuelas and O. Sumensari, New Physics e ffects in leptonic and semileptonic decays, JHEP 05, 175 (2021) [arXiv:2012.09872]

    Pith/arXiv arXiv 2021

  36. [36]

    Huang and Z

    T. Huang and Z. H. Li, B → K∗γ in the light-cone QCD sum rule, Phys. Rev. D 57, 1993-1996 (1998)

    1993

  37. [37]

    P . Ball, V . M. Braun and A. Lenz, Twist-4 distribution ampli- tudes of the K∗ and ϕ mesons in QCD, JHEP 08,090 (2007) [arXiv:0707.1201]

    Pith/arXiv arXiv 2007

  38. [38]

    P . Ball, V . M. Braun, Y . Koike and K. Tanaka, Higher twist dis- tribution amplitudes of vector mesons in QCD: Formalism and twist-three distributions, Nucl. Phys. B 529, 323-382 (1998) [arXiv:hep-ph/9802299]

    Pith/arXiv arXiv 1998

  39. [39]

    Ball and R

    P . Ball and R. Zwicky, Bd,s → ρ,ω, K∗,ϕ decay form-factors from light-cone sum rules revisited, Phys. Rev. D 71, 014029 (2005) [arXiv:hep-ph/0412079]

    Pith/arXiv arXiv 2005

  40. [40]

    X. G. Wu and T. Huang, Constraints on the Light Pseu- doscalar Meson Distribution Amplitudes from Their Meson- Photon Transition Form Factors, Phys. Rev. D 84, 074011 (2011) [arXiv:1106.4365]

    Pith/arXiv arXiv 2011

  41. [41]

    X. G. Wu and T. Huang, An Implication on the Pion Distribu- tion Amplitude from the Pion-Photon Transition Form Factor with the New BABAR Data, Phys. Rev. D 82, 034024 (2010) [arXiv:1005.3359]

    Pith/arXiv arXiv 2010

  42. [42]

    Huang, B

    T. Huang, B. Q. Ma and Q. X. Shen, Analysis of the pion wave function in light cone formalism, Phys. Rev. D 49, 1490-1499 (1994) [arXiv:hep-ph/9402285]

    Pith/arXiv arXiv 1994

  43. [43]

    X. G. Wu and T. Huang, Pion electromagnetic form-factor in the K(T ) factorization formulae, Int. J. Mod. Phys. A 21, 901- 904 (2006) [arXiv:hep-ph/0507136]

    Pith/arXiv arXiv 2006

  44. [44]

    X. G. Wu, T. Huang and Z. Y . Fang, SU(f)(3)-symmetry breaking e ffects of the B → K transition form-factor in the QCD light-cone sum rules, Phys. Rev. D 77, 074001 (2008) [arXiv:0712.0237]

    Pith/arXiv arXiv 2008

  45. [45]

    Huang, T

    T. Huang, T. Zhong and X. G. Wu, Determination of the pion distribution amplitude, Phys. Rev. D 88, 034013 (2013) [arXiv:1305.7391]

    Pith/arXiv arXiv 2013

  46. [46]

    Ball and V

    P . Ball and V . M. Braun, Use and misuse of QCD sum rules in heavy to light transitions: The Decay B → ρeν reexamined, Phys. Rev. D 55, 5561-5576 (1997) [arXiv:hep-ph/9701238]

    Pith/arXiv arXiv 1997

  47. [47]

    Ablikim et al

    M. Ablikim et al. [BESIII], Measurement of the Absolute Branching Fraction of D+ s →τ+ντ viaτ+ → e+νe ¯ντ, Phys. Rev. Lett. 127, no.17, 171801 (2021) [arXiv:2106.02218]

    arXiv 2021

  48. [48]

    Hua et al

    J. Hua et al. [Lattice Parton], Distribution Amplitudes of K∗ and ϕ at the Physical Pion Mass from Lattice QCD, Phys. Rev. Lett. 127 no.6, 062002 (2021) [arXiv:2011.09788]

    Pith/arXiv arXiv 2021

  49. [49]

    Ahmady, A

    M. Ahmady, A. Leger, Z. Mcintyre, A. Morrison and R. San- dapen, Probing transition form factors in the rare B → K∗ν¯ν de- cay, Phys.Rev.D 98, no.5, 053002 (2018) [arXiv:1805.02940]

    Pith/arXiv arXiv 2018

  50. [50]

    Ahmady and R

    M. Ahmady and R. Sandapen, Predicting the isospin asym- metry in B → K∗γ using holographic AdS /QCD Distribu- tion Amplitudes for the K∗, Phys.Rev.D88, 014042 (2013) [arXiv:1305.1479]

    Pith/arXiv arXiv 2013

  51. [51]

    H. J. Tian, H. B. Fu, T. Zhong, X. Luo, D. D. Hu and Y . L. Y ang, Investigating theD+ s →π0ℓ+νℓ decay process within the QCD sum rule approach, Phys. Rev. D 108 no.7, 076003 [arXiv:2306.07595]

    Pith/arXiv arXiv

  52. [52]

    Bazavov et al

    A. Bazavov et al. [Fermilab Lattice and MILC], D- meson semileptonic decays to pseudoscalars from four- flavor lattice QCD, Phys. Rev. D 107, no.9, 094516 (2023) [arXiv:2212.12648]

    Pith/arXiv arXiv 2023

  53. [53]

    Lubiczet al

    V . Lubiczet al. [ETM], Scalar and vector form factors of D → π(K)ℓν decays with N f = 2 + 1 + 1 twisted fermions, Phys. Rev. D 96, no.5, 054514 (2017) [arXiv:1706.03017]

    Pith/arXiv arXiv 2017

  54. [54]

    H. Na, C. T. H. Davies, E. Follana, J. Koponen, G. P . Lepage and J. Shigemitsu, D → π,ℓν Semileptonic Decays, |Vcd| and 2nd Row Unitarity from Lattice QCD, Phys. Rev. D 84, 114505 (2011) [arXiv:1109.1501]

    Pith/arXiv arXiv 2011

  55. [55]

    B. C. Ke, J. Koponen, H. B. Li and Y . Zheng, Recent Progress in Leptonic and Semileptonic Decays of Charmed Hadrons, Ann. Rev. Nucl. Part. Sci. 73, 285-314 (2023) [arXiv:2310.05228]

    Pith/arXiv arXiv 2023

  56. [56]

    Riggio, G

    L. Riggio, G. Salerno and S. Simula, Extraction of |Vcd| and |Vcs| from experimental decay rates using lattice QCD D → π(K)ℓν form factors, Eur. Phys. J. C 78, no.6, 501 (2018) [arXiv:1706.03657]

    Pith/arXiv arXiv 2018

  57. [57]

    Aoki et al

    Y . Aoki et al. [Flavour Lattice Averaging Group (FLAG)], FLAG review 2024, Phys. Rev. D 113, no.1, 014508 (2026) [arXiv:2411.04268]

    Pith/arXiv arXiv 2024

  58. [58]

    Ablikim et al

    M. Ablikim et al. [BESIII], Study of Dynamics of D0 → K−e+νe and D0 → π−e+νe Decays, Phys. Rev. D 92, no.7, 072012 (2015) [arXiv:1508.07560]

    Pith/arXiv arXiv 2015

  59. [59]

    Ablikim [BESIII], First Observation of D+ → ηµ+νµ and Measurement of Its Decay Dynamics, Phys

    M. Ablikim [BESIII], First Observation of D+ → ηµ+νµ and Measurement of Its Decay Dynamics, Phys. Rev. Lett. 124, no.23, 231801 (2020) [arXiv:2003.12220]

    arXiv 2020

  60. [60]

    Ablikim et al

    M. Ablikim et al. [BESIII], Precision measurements of B(D+ → µ+νµ), the pseudoscalar decay constant fD+ , and the quark mix- ing matrix element |Vcd|, Phys. Rev. D 89, no.5, 051104 (2014) [arXiv:1312.0374]

    Pith/arXiv arXiv 2014

  61. [61]

    Besson et al

    D. Besson et al. [CLEO], Improved measurements of D me- son semileptonic decays to π and K mesons, Phys. Rev. D 80, 032005 (2009) [arXiv:0906.2983]

    Pith/arXiv arXiv 2009

  62. [62]

    J. P . Leeset al. [BaBar], Measurement of the D0 →π−e+νe dif- ferential decay branching fraction as a function of q2 and study of form factor parameterizations, Phys. Rev. D 91, no.5, 052022 (2015) [arXiv:1412.5502]

    Pith/arXiv arXiv 2015

  63. [63]

    Aad et al

    G. Aad et al. [A TLAS], A search for top-squark pair production, in final states containing a top quark, a charm quark and miss- ing transverse momentum, using the 139 fb −1 of pp collision 16 data collected by the A TLAS detector, JHEP 07, 250 (2024) [arXiv:2402.12137]

    Pith/arXiv arXiv 2024

  64. [64]

    H. B. Fu, X. G. Wu and Y . Ma,B → K∗ Transition Form Factors and the Semileptonic Decay B → K∗µ+µ−, J. Phys. G 43 no.1, 015002 (2016) [arXiv:1411.6423]

    Pith/arXiv arXiv 2016

  65. [65]

    Cheng, X

    W. Cheng, X. G. Wu and H. B. Fu, Reconsideration of the B → K∗ transition form factors within the QCD light-cone sum rules, Phys. Rev. D 95 no.9, 094023 (2017) [arXiv:1703.08677]

    Pith/arXiv arXiv 2017