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Semileptonic and nonleptonic $\bar{B}_{s}\to D_{sJ}$ decays in covariant light-front approach

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Pith's one-line read The paper argues that covariant light-front quark-model form factors predict sizable $\bar{B}_s\to D_{sJ}\pi$ branching fractions for $J=0,1',2$, and semileptonic rates that match the measured $D_s$ and $D_s^*$ channels.

desk verdict Competent LFQM re-derivation of B̄s→DsJ rates, anchored by the s-wave semileptonic data, but the interesting p-wave numbers—especially the factor-of-four D′s1 excess—rest on an untested mixing assumption and a single shared beta, with no error bars. read the letter →

arxiv 2504.15056 v1 pith:6F2KGQHO submitted 2025-04-21 hep-ph hep-ex

Wu Enqi , Run-Hui Li , Zhen-Xing Zhao This is my paper · ORCID
classification hep-phhep-ex
keywords B_smesondecaysD_sJmesonscovariantlight-frontquarkmodeltransitionformfactorssemileptonicnonleptonicaxial-vectormixingbranchingfractions
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

The paper aims to show that the covariant light-front quark model can compute the full set of $\bar{B}_s\to D_{sJ}$ transition form factors, for $D_{sJ}=D_s,D_s^*,D_{s0},D_{s1},D'_{s1},D_{s2}$, and that the resulting semileptonic and nonleptonic branching fractions are reliable enough to guide searches. The s-wave semileptonic predictions match the measured $\bar{B}_s\to D_s\mu\bar{\nu}_\mu$ and $\bar{B}_s\to D_s^*\mu\bar{\nu}_\mu$ rates, while the p-wave pionic channels $\bar{B}_s\to D_{sJ}\pi$ with $J=0,1',2$ come out near $10^{-3}$, which the authors argue puts them within reach of the LHC and future $e^+e^-$ colliders. The most striking number is $\mathcal{B}(\bar{B}_s\to D'_{s1}\mu\bar{\nu}_\mu)=11.1\times10^{-3}$, about four times the measured value, a discrepancy the paper attributes to the need for a remeasurement rather than to a failure of the model. If these predictions hold, the decays become a useful laboratory for non-perturbative QCD and for the internal structure of the $D_{sJ}$ states.

What carries the argument

The engine of the calculation is the covariant light-front quark model, in which a meson is described by a momentum-space Gaussian wave function whose width (shape parameter $\beta$) is fixed by fitting the meson decay constant; the relativistic spin structure is handled through the Melosh rotation, which keeps the wave functions Lorentz invariant. The paper uses $f_{\bar{B}_s}=230.3$ MeV, $f_{D_s}=249.9$ MeV, $f_{D_s^*}=272$ MeV, and $f_{D_{s0}}=74.4$ MeV to obtain $\beta_{\bar{B}_s}=0.6209$ GeV and a shared $\beta=0.3483$ GeV for all four p-wave mesons. The transition matrix elements are reduced to form factors parametrized by the fitted forms of Eq. (24) or Eq. (25). For the two axial-vector mesons, the paper imposes the heavy-quark-limit identification of Eq. (20), treating $D_{s1}$ as the $j^P=1/2^+$ state and $D'_{s1}$ as the $3/2^+$ state, with the $^3P_1$-$^1P_1$ mixing angles fixed at their heavy-quark-limit values. That identification, together with the shared p-wave $\beta$, carries the p-wave predictions.

What would settle it

Measure $\mathcal{B}(\bar{B}_s\to D'_{s1}\mu\bar{\nu}_\mu)$ and $\mathcal{B}(\bar{B}_s\to D_{s1}\mu\bar{\nu}_\mu)$ at the LHC or a future $e^+e^-$ collider. If the $D'_{s1}$ rate stays near the current $(2.7\pm0.7)\times10^{-3}$ while $D_{s1}$ comes out near the paper's $2.67\times10^{-3}$, the pure-eigenstate identification of the axial-vector mesons is ruled out; a recomputation with a nonzero $^3P_1$-$^1P_1$ mixing angle fitted to both channels would then settle which form factors are correct.

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Extended reading notes

Core claim

Within the covariant light-front quark model, the paper derives form factors for all six $\bar{B}_s\to D_{sJ}$ transitions from a single set of constituent quark masses and Gaussian wave functions, fixes each meson's shape parameter from its decay constant, and then feeds the form factors into semileptonic and factorized nonleptonic decay amplitudes. The central quantitative claims are that the s-wave semileptonic rates $\mathcal{B}(\bar{B}_s\to D_s\mu\bar{\nu}_\mu)=2.66\times10^{-2}$ and $\mathcal{B}(\bar{B}_s\to D_s^*\mu\bar{\nu}_\mu)=5.11\times10^{-2}$ agree with the measured central values, that the pionic modes $\bar{B}_s\to D_{sJ}\pi$ with $J=0,1',2$ have branching fractions around $10^{-3}$ and should be observable, and that $\bar{B}_s\to D'_{s1}\mu\bar{\nu}_\mu$ is predicted at $11.1\times10^{-3}$, far above the current experimental $(2.7\pm0.7)\times10^{-3}$. The paper treats the axial-vector states $D_{s1}(2460)$ and $D_{s1}(2536)$ as pure heavy-quark-limit eigenstates $|P_1^{1/2}\rangle$ and $|P_1^{3/2}\rangle$, respectively, and notes that this approximation is the most likely source of error for the $D'_{s1}$ channel.

Load-bearing premise

The load-bearing premise is that the two axial-vector mesons are exactly the unmixed heavy-quark-limit states $|P_1^{1/2}\rangle$ and $|P_1^{3/2}\rangle$, with no $^3P_1$-$^1P_1$ mixing; the paper itself concedes that the charm quark may not be heavy enough for this to hold.

Editorial extensions

If this is right

  • The s-wave semileptonic channels $\bar{B}_s\to D_s\mu\bar{\nu}_\mu$ and $\bar{B}_s\to D_s^*\mu\bar{\nu}_\mu$ are predicted at $2.66\times10^{-2}$ and $5.11\times10^{-2}$, matching the measured values.
  • The pionic nonleptonic modes $\bar{B}_s\to D_{sJ}\pi$ with $J=0,1',2$ have branching fractions near $10^{-3}$, making them promising for observation at the LHC and future $e^+e^-$ colliders.
  • The prediction $\mathcal{B}(\bar{B}_s\to D'_{s1}\mu\bar{\nu}_\mu)=11.1\times10^{-3}$ exceeds the measured $(2.7\pm0.7)\times10^{-3}$, which the paper argues warrants repeating the measurement.
  • The p-wave form factors come out close to the corresponding $B\to D_J$ form factors in the heavy-quark limit, supporting the underlying spectator-quark picture.
  • For the four measured s-wave nonleptonic channels $\bar{B}_s\to D_s^{(*)+}\pi^-/K^-$, the predictions overshoot the data, which the paper interprets as a sign of deviation from naive factorization.

Reading between the lines

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

  • The paper leaves implicit that a nonzero $^3P_1$-$^1P_1$ mixing angle would shift both the $D_{s1}$ and $D'_{s1}$ form factors; fitting that angle to the two measured semileptonic channels is a direct extension that could resolve the $D'_{s1}$ discrepancy.
  • Because a single shared $\beta=0.3483$ GeV is imposed on all four p-wave mesons, the paper's underpredicted nonleptonic $D_{s1}\pi$ rate could be tested by refitting $\beta$ separately for each p-wave meson to its own decay constant.
  • If the $D'_{s1}$ semileptonic discrepancy survives remeasurement, comparing the muon and tau modes of the same transition would help separate form-factor effects from possible new physics, though the paper does not explore that comparison.
  • The same form factors can be recycled directly for other $b\to c\ell\bar{\nu}$ transitions in heavy-light systems, so the method's reliability is testable across a broader set of decays beyond $\bar{B}_s\to D_{sJ}$.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. This paper computes the \bar{B}_s \to D_{sJ} transition form factors (D_{sJ} = D_s, D_s^*, D_{s0}, D_{s1}, D'_{s1}, D_{s2}) in the covariant light-front quark model. The two axial-vector mesons are identified with the heavy-quark-limit eigenstates via Eq. (20), form factors are fitted to the pole forms of Eqs. (24)-(25) with parameters in Table I, and the results are used to predict semileptonic (\bar{B}_s \to D_{sJ}\ell\bar{\nu}) and nonleptonic (\bar{B}_s \to D_{sJ}\pi/K) branching fractions under naive factorization. The s-wave semileptonic predictions agree with experiment (D_s\mu\bar{\nu}: 2.66e-2 vs (2.31 +/- 0.21)e-2; D_s^*\mu\bar{\nu}: 5.11e-2 vs (5.2 +/- 0.5)e-2). The p-wave predictions scatter widely relative to the literature; notably \bar{B}_s \to D'_{s1}\mu\bar{\nu} = 11.1e-3 exceeds the measured (2.7 +/- 0.7)e-3 by a factor of four. The paper concludes that \bar{B}_s \to D_{sJ}\pi with J = 0, 1', 2 have sizable branching fractions and are promising LHC targets. The authors explicitly flag in Sects. III.C and III.D the fragility of the p-wave assumptions: zero axial-vector mixing despite a charm quark that may not be heavy enough, a single shared shape parameter \beta = 0.3483 GeV for all four p-wave mesons that may be too small, and naive factorization over-predicting the measured s-wave nonleptonic channels by factors of 1.6-2.2.

Significance. The s-wave sector is a genuine success: the two semileptonic rates agree with experiment without being fitted, establishing that the form-factor machinery and standard inputs (masses, V_cb, \tau_{B_s}) are reliable at the 10-15% level. The analytic expressions in Appendix A and the explicit fit parameters in Table I make the calculation essentially reproducible, and the comparisons in Tables II and III are careful and extensive. The significance of the p-wave sector is conditional. If the mixing and shape-parameter assumptions survive scrutiny, the paper supplies a complete set of LFQM predictions for channels testable at LHCb, including several at the 10^-3 level and a fourfold tension with the measured \bar{B}_s \to D'_{s1}\mu\bar{\nu} rate that would be phenomenologically notable. At present, however, that tension is not interpretable: because the physical axial-vector states are mixtures of the |P_1^{1/2}\rangle and |P_1^{3/2}\rangle states, a nonzero mixing angle shifts the D_{s1} and D'_{s1} rates in opposite directions, and no scan over the mixing angle is given.

major comments (3)
  1. [Section III.C, Eq. (20)] The identification of D_{s1}(2460) as the pure heavy-quark-limit eigenstate |P_1^{1/2}\rangle and D_{s1}(2536) as |P_1^{3/2}\rangle is load-bearing for every axial-vector prediction, in particular for the fourfold excess of the predicted \bar{B}_s \to D'_{s1}\mu\bar{\nu} rate (11.1e-3) over the measured (2.7 +/- 0.7)e-3. The authors themselves state in Sect. III.C that the charm quark mass is not large enough and that a relatively large mixing angle may exist. Under a nonzero mixing angle the D_{s1} and D'_{s1} form factors become linear combinations of the |P_1^{1/2}\rangle and |P_1^{3/2}\rangle form factors, and the two semileptonic rates move in opposite directions. As it stands, the reader cannot tell whether the factor-of-four discrepancy is an artifact of the zero-mixing ansatz, a form-factor error, or a real effect, so the suggestion in Sect. III.C that the measurement be repeated is premature. Please provide a scan of the D_{s1} and D'_{s1} semileptonic rates versus the mixing angle, state the mixing angle needed to reproduce the experimental rate, and propagate that scan into the affected entries of Table II.
  2. [Section III.A, Eq. (23), and Section III.D] All four p-wave mesons are assigned the single shape parameter \beta = 0.3483 GeV, fixed through f_{D_{s0}} = 74.4 MeV taken from the quark-model paper Ref. [4]; no measured input anchors the p-wave \beta. The authors concede in Sect. III.D that this value may be too small and that their p-wave nonleptonic rates are consequently underestimated. The effect is severe for D_{s1}: \bar{B}_s \to D_{s1}\pi is predicted at 4.39e-6, up to about two orders of magnitude below the other predictions listed in Table III (Refs. [33, 34, 3]). Because the small D_{s1} form factors in Table I result from near-cancellations, they are maximally sensitive to \beta. Please add a sensitivity study varying the p-wave shape parameter (uniformly, and per meson if possible), and quote how the p-wave entries in Tables II and III change under that variation.
  3. [Section III.D, Eqs. (36)-(40)] The headline claim that \bar{B}_s \to D_{sJ}\pi with J = 0, 1', 2 are promising candidates for observation rests on naive factorization with a_1 = 1.02. The same framework over-predicts the measured s-wave channels by factors of about 1.6 (\bar{B}_s \to D_s\pi: 4.62e-3 vs (2.98 +/- 0.14)e-3) and about 2.2 (\bar{B}_s \to D_s^*\pi: 4.12e-3 vs (1.9^{+0.5}_{-0.4})e-3), as the authors acknowledge in the text. This implies an unquantified normalization uncertainty of order a factor of two that propagates directly into the absolute scale of the p-wave nonleptonic predictions on which the paper's conclusion rests. Please state an uncertainty on the nonleptonic predictions, for example by varying a_1 over a plausible range or by showing the sensitivity to the 1/N_c-suppressed amplitudes, and temper the corresponding conclusions accordingly.
minor comments (3)
  1. [Reference list, Ref. [42]] Ref. [42] is listed as E. V. Linder, New Astron. Rev. 49, 93 (2005), arXiv:astro-ph/0404032, which is an astronomy/dark-energy review rather than a source for the \bar{B}_s \to D'_{s1} semileptonic prediction (0.8-1.0e-3) attributed to it in Table II. Please verify and replace this citation.
  2. [Tables II and III] All entries in Tables II and III are quoted without uncertainties. Once the mixing-angle scan and \beta-sensitivity study requested above are performed, please propagate those uncertainties into the tabulated values so that the comparisons with experiment, in particular the D'_{s1} semileptonic channel, can be judged quantitatively.
  3. [Abstract and Conclusions] The concluding sentence repeats the abstract's claim that some branching fractions are sizable and promising without the caveats on axial-vector mixing and on naive factorization that are stated in Sects. III.C and III.D. I suggest carrying those caveats into the abstract and conclusions, since the size of the p-wave rates is sensitive to both assumptions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the branching fractions are genuine LFQM outputs, and no prediction reduces by construction to a fitted input or self-citation.

full rationale

The central derivation is self-contained. The form factors are computed in the covariant LFQM from explicitly stated inputs: constituent quark masses (Eq. 21), meson masses from PDG (Eq. 22), and shape parameters β fixed by decay constants (Eq. 23). The branching fractions are obtained by integrating the q^2-dependent form factors over phase space (Eqs. 27–33), so they are genuine outputs. The s-wave semileptonic rates agreeing with data are external benchmarks, not fit targets; the paper compares rather than fits. The D_s1(2460)/D_s1(2536) identification with heavy-quark-limit eigenstates (Eq. 20) is stated as an approximation, and the authors explicitly acknowledge that a relatively large mixing angle may exist, so this is an uncertainty claim, not a hidden input. The shared p-wave shape parameter β = 0.3483 GeV is an openly stated assumption ('we have assumed that the shape parameters ... are approximately equal to that of D_s0'), and the paper even concedes it may be too small; it is not a fitted parameter renamed as a prediction. Self-citations (Refs. [5], [44], [22]) appear as standard formalism references, comparison values, or a remark about the nature of hadron mixing, and none of them is load-bearing in the sense of forcing a result by appeal to an unverified uniqueness theorem. The paper's most notable number, B(B̄_s → D'_s1 μν̄) = 11.1×10^-3, is a prediction derived from the model plus the zero-mixing approximation; the factor-of-four discrepancy with experiment is presented as a genuine mismatch that the authors suggest deserves further study and remeasurement. No equation is shown to reduce to its own input, and no fitted quantity is relabeled as a prediction. Therefore the derivation chain is not circular.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the inherited LFQM machinery of Jaus (1999) and Cheng, Chua and Hwang (2004), a Gaussian wave function with one shape parameter per meson, with a single shared β for all four p-wave states, the zero-mixing HQET identification of the two axial mesons, and naive factorization for nonleptonic modes. Four shape parameters are fitted to external decay constants; the shared p-wave β is the weakest link because four distinct mesons depend on it, and its anchor, f_Ds0 = 74.4 MeV, comes from a similar class of quark-model calculation. No entities are invented.

free parameters (7)
  • β_B̄s (light-front shape parameter for B̄s) = 0.6209 GeV
    Fixed by matching f_B̄s = 230.3 MeV from FLAG (Ref. [30]); calibrates the Gaussian wave function for the initial meson.
  • β_Ds = 0.5416 GeV
    Fixed by matching f_Ds = 249.9 MeV from PDG (Eq. 23).
  • β_D*s = 0.4364 GeV
    Fixed by matching f_D*s = 272 MeV from Verma (Ref. [4]).
  • β_p-wave shared by D_s0, D_s1, D'_s1, D_s2 = 0.3483 GeV
    Fixed by matching f_Ds0 = 74.4 MeV from Ref. [4], then assumed equal for the other three p-wave mesons by hand; the paper concedes it may be too small (Sect. III.D). All p-wave form factors inherit this one number.
  • Constituent quark masses m_s, m_c, m_b = 0.37, 1.4, 4.64 GeV
    Taken unchanged from Ref. [2]; model inputs to which form factors are sensitive, not re-fitted here.
  • Naive factorization coefficient a1 = 1.02
    Borrowed from Refs. [5,29,34,45] for the nonleptonic amplitudes; scale- and scheme-dependent in general.
  • q²-fit coefficients F(0), m_fit, δ per form factor = Table I (20 form factors)
    Fitted to the model's own computed F(q²) points; seven form factors use the sign-flipped formula Eq. (25) because m²_fit from Eq. (24) is negative. This is parametrization of model output, not physics input, but it sets the q² extrapolation used in the decay integrals.
assumptions (6)
  • standard math LFQM master formulas for decay constants and form factors, including zero-mode contributions, from Jaus (1999) and Cheng, Chua and Hwang (2004)
    Eqs. (4)-(9) and Appendix A are inherited verbatim from Refs. [1,2]; the paper applies rather than re-derives the framework.
  • domain assumption Gaussian light-front momentum wave function with shape parameter β for every meson
    Eq. (8) and Eq. (A9); the functional form is chosen, not derived from QCD.
  • domain assumption Heavy-quark-limit identification D_s1(2460) ≈ |P^{1/2}_1⟩ and D_s1(2536) ≈ |P^{3/2}_1⟩ with zero mixing
    Eq. (20) and Sect. III.C; the paper acknowledges the charm quark may not be heavy enough and the mixing angle may be large.
  • domain assumption Naive factorization of two-body nonleptonic amplitudes with constant a1 = 1.02
    Eqs. (35)-(40); the paper itself notes the s-wave π/K rates overshoot data by about 50 percent, signaling factorization breakdown.
  • domain assumption Decay constants f_D*s = 272 MeV and f_Ds0 = 74.4 MeV from Ref. [4] are reliable anchors
    Ref. [4] is a 2012 quark-model calculation; its f_Ds0 value determines the entire p-wave β.
  • domain assumption Spectator anti-strange quark approximation: b → c transition inside B̄_s leaves the s quark untouched
    Introductory statement of the mechanism; standard in LFQM but not exact (no explicit s-quark binding corrections beyond constituent masses).

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Cite this review

Pith. "Pith review of Semileptonic and nonleptonic $\bar{B}_{s}\to D_{sJ}$ decays in covariant light-front approach." pith.science (2026). https://pith.science/paper/6F2KGQHO

@misc{pith2026250415056,
  author       = {Pith},
  title        = {Pith review of: Semileptonic and nonleptonic $\barB_s\to D_sJ$ decays in covariant light-front approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6F2KGQHO}},
  note         = {Machine review of arXiv:2504.15056}
}
abstract

In this work, we investigate the $\bar{B}_{s}\to D_{sJ}$ transitions in covariant light-front approach, where $D_{sJ}$ denotes an s-wave or p-wave $c\bar{s}$ meson state. We first obtain the transition form factors within the framework of the quark model, and then apply the obtained form factors to obtain the branching fractions of semileptonic and nonleptonic decays. We also compare our results with experimental data and other theoretical predictions. We find that some branching fractions are sizable and might be accessible at the LHC and future $e^{+}$-$e^{-}$ colliders. Our work is expected to be of great value for establishing corresponding decay channels, and also be helpful in understanding the non-perturbative QCD dynamics.

Figures

Figures reproduced from arXiv: 2504.15056 by the authors.

Figure 1
Figure 1. FIG. 1: Feynman diagram for the meson weak transitions, wher [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

68 extracted references · 35 canonical work pages · cited by 2 Pith papers

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    Y. S. Li, X. Liu and F. S. Yu, Phys. Rev. D 104, no.1, 013005 (2021) doi:10.1103/PhysRevD.104.013005 [a rXiv:2104.04962 [hep-ph]]

    arXiv 2021

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    16 × 10−2 4

    3 × 10−3[35] ¯Bs → D∗ s e¯νe 5. 16 × 10−2 4. 42 × 10−2[32], 6 . 26 × 10−2[33], 5 . 3 × 10−2[34], -

    work page

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    (19) In the above equation, ˆN ′(′′) 1 = x1(M ′(′′)2 − M ′(′′)2 0 ), and h′(′′) P can be found in Eq

    + x2q2 − x2(m′ 1 − m′′ 1 )2 − x1(m′ 1 − m2)2 − x1(m′′ 1 − m2)2] , f−(q2) = Nc 16π3 ∫ dx2d2p′ ⊥ 2h′ P h′′ P x2 ˆN ′ 1 ˆN ′′ 1 { − x1x2M ′2 − p′2 ⊥ − m′ 1m2 + (m′′ 1 − m2) × (x2m′ 1 + x1m2) + 2 q · P q2 ( p′2 ⊥ + 2 (p′ ⊥ · q⊥)2 q2 ) + 2 (p′ ⊥ · q⊥)2 q2 − p′ ⊥ · q⊥ q2 [ M ′′2 − x2(q2 + q · P ) − (x2 − x1)M ′2 + 2x1M ′2 0 − 2(m′ 1 − m2)(m′ 1 + m′′ 1 ) ] } . (...

    work page

  4. [1]

    (6) The explicit form of h′ P is given by h′ P =(M ′2 − M ′2 0) √ x1x2 Nc 1√ 2~M ′ 0 ϕ′, (7) where ϕ′ is the light-front momentum distribution amplitude for an s-wave mes on

    4(m′ 1x2 + m2x1). (6) The explicit form of h′ P is given by h′ P =(M ′2 − M ′2 0) √ x1x2 Nc 1√ 2~M ′ 0 ϕ′, (7) where ϕ′ is the light-front momentum distribution amplitude for an s-wave mes on. In practice, the following Gaussian- type wave function is usually adopted: ϕ′ = ϕ′(x2, p′ ⊥) =4 ( π β′2 )3/4 √ e′ 1e2 x1x2M ′ 0 exp ( − p′2 z + p′2 ⊥ 2β′2 ) , (8) ...

    work page

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    4(m′ 1x2 − m2x1), fV = Nc 4π3M ′ ∫ dx2d2p′ ⊥ h′ V x1x2(M ′2 − M ′2 0) × [ x1M ′2 0 − m′ 1(m′ 1 − m2) − p′2 ⊥ + m′ 1 + m2 ω′ V p′2 ⊥ ] , f3A = − Nc 4π3M ′ ∫ dx2d2p′ ⊥ h′ 3A x1x2(M ′2 − M ′2 0) × [ x1M ′2 0 − m′ 1(m′ 1 + m2) − p′2 ⊥ − m′ 1 − m2 ω′ 3A p′2 ⊥ ] , f1A = Nc 4π3M ′ ∫ dx2d2p′ ⊥ h′ 1A x1x2(M ′2 − M ′2

    work page

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    (9) The explicit forms of h′ M and ω′ M can be found in Appendix A

    ( m′ 1 − m2 ω′ 1A p′2 ⊥). (9) The explicit forms of h′ M and ω′ M can be found in Appendix A. In practice, the decay constant is used to determine the shape pa rameter β′ in the light-front momentum distribution amplitude, see, for example, Eq. (8). C. Form factors The semileptonic decays ¯Bs → DsJ l¯ν are induced at the quark level through b → cl¯ν, and ...

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    0 × 10−2[35], 2

    1 × 10−2[34], 1 . 0 × 10−2[35], 2 . 8 ∼ 3. 5 × 10−2[36] ¯Bs → Dsµ ¯νµ 2. 66 × 10−2 2. 32 × 10−2[33], 1 . 0 × 10−2[35] (2. 31 ± 0. 21) × 10−2 ¯Bs → Dsτ ¯ντ 8. 00 × 10−3 6. 3 × 10−3[32], 6 . 7 × 10−3[33], 6 . 2 × 10−3[34], -

    work page

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    09 × 10−2[37], 1 . 89 ∼ 6. 61 × 10−2[38] ¯Bs → D∗ s µ ¯νµ 5. 11 × 10−2 6. 26 × 10−2[33] (5. 2 ± 0. 5) × 10−2 ¯Bs → D∗ s τ ¯ντ 1. 18 × 10−2 1. 20 × 10−2[32], 1 . 53 × 10−2[33], 1 . 3 × 10−2[34] - ¯Bs → Ds0e¯νe 1. 19 × 10−3 1. 26 × 10−3[6], 0 . 72 × 10−3[39], 1 . 3 × 10−3[40], -

    work page

Show all 68 references
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    6 × 10−3[34], 6

    9 × 10−3[33], 3 . 6 × 10−3[34], 6 . 0 × 10−3[41],

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    3 × 10−3[35], 0 . 9 ∼ 2. 0 × 10−3[42] ¯Bs → Ds0µ ¯νµ 1. 18 × 10−3 1. 25 × 10−3[6], 0 . 71 × 10−3[39], 3 . 9 × 10−3[33], -

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    3 × 10−3[35] ¯Bs → Ds0τ ¯ντ 3

    0 × 10−3[41], 2 . 3 × 10−3[35] ¯Bs → Ds0τ ¯ντ 3. 04 × 10−4 1. 8 × 10−4[6], 0 . 57 × 10−4[39], 4 × 10−4[33], -

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    2 × 10−4[41], 5

    9 × 10−4[34], 8 . 2 × 10−4[41], 5 . 7 × 10−4[35] ¯Bs → Ds1e¯νe 2. 79 × 10−3 1. 8 × 10−4[6], 6 . 48 × 10−4[39], 3 . 2 × 10−3[33], -

  5. [12]

    67 × 10−3 1

    9 × 10−3[34] ¯Bs → Ds1µ ¯νµ 2. 67 × 10−3 1. 8 × 10−4[6], 6 . 42 × 10−4[39], 3 . 2 × 10−3[33], -

  6. [13]

    47 × 10−5 2

    5 × 10−4[3] ¯Bs → Ds1τ ¯ντ 3. 47 × 10−5 2. 0 × 10−5[6], 5 . 4 × 10−5[39], 3 . 0 × 10−4[33], -

  7. [14]

    9 × 10−6[3] ¯Bs → D′ s1e¯νe 11

    5 × 10−4[34], 9 . 9 × 10−6[3] ¯Bs → D′ s1e¯νe 11. 4 × 10−3 6. 17 × 10−3[6], 6 . 31 × 10−3[39], 4 . 7 × 10−3[33], -

  8. [15]

    9 × 10−3[43], 0

    4 × 10−3[34], 4 . 9 × 10−3[43], 0 . 8 ∼ 1. 0 × 10−3[42] ¯Bs → D′ s1µ ¯νµ 11. 1 × 10−3 6. 13 × 10−3[6], 6 . 25 × 10−3[39], 4 . 7 × 10−3[33], (2. 7 ± 0. 7) × 10−3

  9. [16]

    9 × 10−3[43] ¯Bs → D′ s1τ ¯ντ 5

    0 × 10−3[3], 4 . 9 × 10−3[43] ¯Bs → D′ s1τ ¯ντ 5. 18 × 10−4 6. 3 × 10−4[6], 3 . 8 × 10−4[39], 4 . 0 × 10−4[33], -

  10. [17]

    7 × 10−5[3] ¯Bs → Ds2e¯νe 5

    9 × 10−4[34], 9 . 7 × 10−5[3] ¯Bs → Ds2e¯νe 5. 91 × 10−3 3. 77 × 10−3[39], 4 . 4 × 10−3[33], 6 . 7 × 10−3[34] - ¯Bs → Ds2µ ¯νµ 5. 76 × 10−3 3. 73 × 10−3[39], 4 . 4 × 10−3[33] - ¯Bs → Ds2τ ¯ντ 2. 62 × 10−4 2. 4 × 10−4[39], 3 . 0 × 10−4[33], 2 . 9 × 10−4[34] - D. Nonleptonic ¯Bs...

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    52 × 10−4 2

    13 × 10−3[46] ¯Bs → DsK 3. 52 × 10−4 2. 8 × 10−4[34], 2 . 1 × 10−4[45], 1 . 3 × 10−4[35], (2. 25 ± 0. 12) × 10−4

  12. [19]

    12 × 10−3 2

    71 × 10−4[46] ¯Bs → D∗ s π 4. 12 × 10−3 2. 7 × 10−3[34], 3 . 0 × 10−3[45], 2 . 8 × 10−3[3], (1. 9+0. 5 −0. 4) × 10−3

  13. [20]

    09 × 10−4 2

    11 × 10−3[47] ¯Bs → D∗ s K 3. 09 × 10−4 2. 1 × 10−4[34], 2 . 4 × 10−4[45], 4 . 8 × 10−4[3] (1. 32+0. 40 −0. 32) × 10−4 ¯Bs → Ds0π 3. 02 × 10−4 1. 0 × 10−3[33], 9 × 10−4[34], 5 . 2 × 10−4[35] - ¯Bs → Ds0K 2. 38 × 10−5 9 × 10−5[33], 1 . 2 × 10−4[34], 4 × 10−5[35] - ¯Bs → Ds1π 4....

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.