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Analysis of the $B_{(s)}\rightarrow T(J^P=2^-)$ transition in light cone QCD sum rules

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Light-cone QCD sum rules give the form factors for $B_{(s)}$ to $J^P=2^-$ tensor-meson transitions and predict rare-decay branching ratios at $10^{-7}$ to $10^{-8}$.

desk verdict Competent LCSR extension to 2^- tensor mesons, but an unresolved a2 normalization ambiguity could halve the a2 branching ratios. read the letter →

arxiv 2411.15952 v2 pith:S6MD46S4 submitted 2024-11-24 hep-ph

T. M. Aliev , Y. Sarac This is my paper · ORCID
classification hep-ph
keywords lightconeQCDsumrulesBmesondecaystensormesonsformfactorsflavorchangingneutralcurrentsbranchingratiossemileptonicdistributionamplitudes
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 derives the form factors that control the rare semileptonic decays $B_{(s)}\to T\,\ell^+\ell^-$, where $T$ is a tensor meson with $J^P=2^-$: the $K_2$, $a_2$, $f_2$, and $\phi_2$. The calculation uses light-cone QCD sum rules with $B$-meson light-cone distribution amplitudes up to twist-4, working to leading order in $\alpha_s$. The paper's central result is a full set of seven form factors for each transition, extrapolated to the physical region, and the decay rates they imply. All obtained branching ratios lie at $10^{-7}\div 10^{-8}$, which the authors argue is within reach of future experiments. If the prediction is right, these modes provide Standard Model baselines for searching lepton-flavor-universality violation and other new-physics effects in channels with an extra tensor-meson polarization.

What carries the argument

The central object is the correlation function $\Pi_{\mu\nu\rho}(q,k)=\int d^4x\,e^{ik\cdot x}\langle 0|T\{J_{\mu\nu}(x),J_\rho(0)\}|B_{q_2}(p)\rangle$, where $J_{\mu\nu}$ is the interpolating current for the $2^-$ tensor meson and $J_\rho$ the weak transition current. The OPE side is written in terms of the $B$-meson light-cone distribution amplitudes $\phi_+$, $\bar\phi$, $g_+$, $g_-$ up to twist-4, and the hadronic side is written in terms of the tensor-meson decay constant and the seven form factors. A master Borel-transformed formula subtracts the continuum and higher-state contributions, and a $z$-series expansion transfers the sum-rule results, valid only at $q^2<0$, to the physical region.

What would settle it

Measure $\mathrm{BR}(B\to K_2\,\mu^+\mu^-)$: the paper predicts $(5.63\pm3.06)\times10^{-7}$. A precise measurement outside that range, or a lattice-QCD computation of the $B\to K_2$ form factors at spacelike $q^2$ that disagrees with the $z$-series fits of Table IV, would decide whether the central claim holds.

Watch

Extended reading notes

Core claim

The paper claims that the hadronic matrix elements of the weak currents $\bar q_1 \gamma_\rho \gamma_5 b$, $\bar q_1 \gamma_\rho b$, and $\bar q_1 \sigma_{\rho\alpha} q_\alpha (\gamma_5) b$ between a $B_{(s)}$ meson and a $J^P=2^-$ tensor meson can be extracted from the light-cone OPE of a correlation function, and that the resulting form factors $A$, $V_0$, $V_1$, $V_2$, $T_1$, $T_2$, $T_3$ are reliably parameterized by a two-parameter $z$-series fit. Feeding these into the Standard Model effective Hamiltonian gives $\mathrm{BR}(B\to K_2\ell^+\ell^-)$ around $10^{-7}$, $\mathrm{BR}(B_s\to\phi_2\ell^+\ell^-)$ around $10^{-6}$ to $10^{-7}$, and $\mathrm{BR}(B\to a_2/f_2\,\ell^+\ell^-)$ around $10^{-8}$, with the electron modes slightly larger than the muon modes. The paper treats these as usable Standard Model predictions for a set of decays that have not yet been measured.

Load-bearing premise

The load-bearing premise is that the interpolating currents with the quark content of Table I, together with the masses and decay constants taken from [40], faithfully describe the physical $K_2$, $a_2$, $f_2$, and $\phi_2$ states; if those states are contaminated or the inputs are off, every form factor and branching ratio shifts.

Editorial extensions

If this is right

  • The $B\to K_2$ modes are predicted at $\mathrm{BR}\sim 10^{-7}$, making them plausible discovery channels at experiments with large $B$-meson samples.
  • The $B_s\to\phi_2$ modes are predicted to be the most abundant of the four channels, reaching $\mathrm{BR}(B_s\to\phi_2\,e^+e^-)=(1.43\pm0.70)\times10^{-6}$.
  • The $B\to a_2$ and $B\to f_2$ modes are predicted at $10^{-8}$, roughly ten times rarer than the $K_2$ modes.
  • Electron and muon modes differ only by phase-space and lepton-mass terms, so a ratio $\mathrm{BR}(T\,e^+e^-)/\mathrm{BR}(T\,\mu^+\mu^-)$ different from the predicted values would signal lepton-flavor-universality violation.
  • The tabulated $z$-series fit parameters give a compact, ready-to-use parametrization of the form factors for other $B_{(s)}\to T(2^-)$ studies.

Reading between the lines

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

  • The extra tensor polarization adds helicity observables beyond those of vector-meson modes; an angular analysis of $B\to K_2\ell^+\ell^-$ could be a more sensitive new-physics probe than the branching ratio alone.
  • The calculation keeps only two-particle $B$-meson distribution amplitudes and the leading order in $\alpha_s$; a lattice-QCD computation of the same form factors, or the inclusion of three-particle and $O(\alpha_s)$ corrections, would test how much of the $10^{-7}$--$10^{-8}$ rate is genuine rather than an artifact of the truncation.
  • The narrow-width approximation used for the tensor mesons may need revision once experimental precision grows, since $K_2$, $a_2$, $f_2$, and $\phi_2$ are broad states.
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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 / 4 minor

Summary. The paper presents a light-cone QCD sum rule (LCSR) calculation of the form factors for the semileptonic transitions B_(s) -> T with T = K2, phi2, f2, a2, where T denotes a tensor meson with J^P = 2^-. Using B-meson distribution amplitudes up to twist-4 and a master sum-rule formula, the authors extract seven form factors in the spacelike region and then extrapolate to the physical region with a truncated z-series. These form factors are inserted into the Standard Model effective Hamiltonian to compute branching ratios for B_(s) -> T l^+ l^- decays, obtaining values of order 10^-7 to 10^-8. The paper includes explicit analytic expressions for the sum-rule coefficients and a Monte Carlo uncertainty analysis of the fit parameters.

Significance. If the results are correct, they provide quantitative Standard Model predictions for rare FCNC decays that have not yet been measured, and they would be useful input for LHCb and Belle II searches. The paper is commendable for presenting the full set of coefficient functions in Appendix B, thereby making the calculation reproducible, and for propagating input uncertainties through a Monte Carlo procedure. However, the reliability of the a2 predictions is compromised by an unresolved normalization ambiguity, and the systematic uncertainties from the Wandzura-Wilczek approximation for g- and from the truncated z-series extrapolation are not quantified. These issues currently preclude an unqualified acceptance of the central numerical results.

major comments (3)
  1. [Sec. II, Eqs. (3), (4), (26); Table I; Table III; Table V] The master formula Eq. (26) sets N = sqrt(2) for both f2 and a2 meson states, but the interpolating current for a2 in Eq. (3) is a single-flavor current with no 1/sqrt(2) prefactor, in contrast to the f2 current in Eq. (4), which explicitly contains 1/sqrt(2) and a two-flavor sum. If the decay constant f_T in Table III is defined with the same single-flavor current as Eq. (3), the hadronic side of the sum rule already accounts for the current normalization, and the extra division by sqrt(2) in Eq. (26) artificially suppresses the a2 form factors by sqrt(2) and the a2 branching ratios by a factor of 2. If, instead, the f_T convention incorporates an isospin factor from a different current normalization, this convention must be stated explicitly and the charge state of the a2 mode specified. As written, the a2 columns of Tables IV and V are not unambiguously defined, and this issue directly affects the central predictions of the paper.
  2. [Appendix A, Eqs. (A4)-(A6)] The g- distribution amplitude is obtained through the Wandzura-Wilczek approximation because, as the authors state, no model expression for g- is available. This approximation is used without any estimate of its uncertainty. Since g- enters the OPE coefficients C^{...}_{g-} in Appendix B, the Monte Carlo errors of Table IV, which only sample the input parameters lambda_B, lambda_E, lambda_H, masses, and s0, necessarily miss the systematic error from the WW approximation. The authors should either justify the WW form quantitatively (for example, by comparing with an alternative model or by varying the functional form and observing the effect on the form factors) or explicitly list this as an omitted uncertainty in the error budget.
  3. [Sec. III, Eq. (34), Table IV] The LCSR results are used only for q^2 < 0, and the physical-region form factors are obtained by extrapolating a z-series truncated at n = 1 (two free parameters a0 and a1). The paper does not demonstrate that this truncation is sufficient for the large extrapolation from q^2 < 0 up to q^2 ~ (m_B - m_T)^2 ~ 12 GeV^2. The branching ratios in Table V depend entirely on this extrapolation, so the authors should provide evidence of stability, for instance by including an a2 term in the fit, by comparing with an alternative parameterization, or by quantifying the fit quality and the shift in the physical-region predictions when the order of truncation is changed. Without such a check, the numerical values in the physical region are not demonstrated to be robust.
minor comments (4)
  1. [Abstract and Sec. I] The abstract uses "flavor changing neural currents" where "neutral" is intended; the same typo appears in Sec. I. Please correct it.
  2. [Sec. II, Eq. (26) and Table III] The narrow-width approximation is stated in the text, but its practical impact on the broad 2^- states is not discussed. A brief estimate of the finite-width correction, or a reference justifying its neglect, would strengthen the paper.
  3. [Figs. 2-5] The axis labels for T2 and T3 are corrupted in the displayed version (appearing as "2" and "3" symbols); please ensure the LaTeX labels are rendered correctly.
  4. [Sec. III, input parameters] The CKM values are quoted with asymmetric errors only for V_tb; the propagation of the V_td and V_ts uncertainties into the branching ratios is not described, although it is presumably included in the Monte Carlo. A sentence clarifying this would be helpful.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; the LCSR form factors and branching ratios are computed from external inputs, with only minor non-load-bearing self-citations (Refs. [19], [40]).

full rationale

The paper's central derivation is a standard light-cone QCD sum rule calculation. The OPE side is evaluated using B-meson distribution amplitudes up to twist-4 taken from independent sources (e.g., Ref. [53] for the DA model, Refs. [43]-[47] for nonperturbative parameters), and the hadronic side uses meson masses from PDG and decay constants from Ref. [40]. The resulting form factors are calculated in the q2<0 region and then fitted to a two-parameter z-series, which is an interpolation/extrapolation of the sum-rule output rather than a fit to any experimental observable. The branching ratios in Table V are obtained from the effective Hamiltonian with Wilson coefficients from independent references and the computed form factors; no branching ratio or form factor is fitted to data. The main self-citations are Ref. [19] for the master formula and Ref. [40] for the tensor-meson decay constants. These are technical inputs or tools from prior work, not assertions equivalent to the present prediction, and neither is a uniqueness theorem or a fit to the target observable. The z-series fit to computed LCSR points does not constitute 'fitted input called prediction' because the fitted quantity is the sum-rule calculation itself, not the measured decay rate. The possible a2 normalization issue with N=sqrt(2) in Eq. (26) is a consistency/correctness concern, not a circularity, since it does not make any output equal to an input by construction. Overall, the derivation is self-contained against external inputs and contains only minor, non-load-bearing self-citations.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central computation rests on standard LCSR truncations and on the z-series fit parameters. The main free parameters are the Borel mass, continuum threshold, and z-series coefficients. No new particles, forces, or conserved quantities are introduced; the higher-dimensional spin-j operators mentioned in the introduction are explicitly neglected.

free parameters (3)
  • Borel parameter M^2 = 1.5-2.5 GeV^2 (per channel, Table III)
    Auxiliary LCSR parameter chosen by hand to suppress higher twists and continuum; the central values differ per channel but are not determined by data.
  • Continuum threshold s0 = 2.02-2.52 GeV^2 (per channel, Table III)
    Chosen so that mass sum rules reproduce experimental tensor meson masses within 5%; it is a model input in LCSR.
  • z-series fit parameters a0, a1 = Table IV values, e.g., A(B->K2): a0=-0.873 +/- 0.220, a1=5.770 +/- 3.050
    Fit to LCSR results in q2<0; the physical-region form factors and branching ratios depend on these fitted coefficients.
assumptions (5)
  • domain assumption The light-cone operator product expansion for the correlation function is dominated by the two-particle B-meson DAs up to twist-4; three-particle contributions are negligibly small.
    Invoked in Sec. II when the authors restrict to two-particle DAs, citing Ref [33] for the smallness of three-particle effects. The whole numerical result depends on this truncation.
  • ad hoc to paper The g- distribution amplitude can be approximated by the Wandzura-Wilczek expression (Eqs. A4-A6).
    Stated in Appendix A: since there is no available model expression for g-, the WW approximation is used. This approximation directly enters the form factor coefficients in Appendix B.
  • domain assumption The narrow-width approximation: tensor meson widths are set to zero.
    Explicitly stated in Sec. II after Eq. (26): 'we have used narrow-width approximation; i.e. the widths of the tensor mesons are taken zero.' Broad 2^- states may make this questionable.
  • domain assumption B-meson DAs of model II A from Ref [53] are valid and are combined with the quark-hadron duality ansatz and z-series extrapolation to physical q^2.
    The DAs are used in Eq. (20) and Appendix A; the z-series fit is used for q^2>=0 because LCSR is reliable only for q^2<0.
  • domain assumption Leading-order in alpha_s: radiative corrections to the LCSR are omitted.
    The abstract and Sec. I state the analysis is performed in leading order of O(alpha_s), which is standard but an approximation.

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Pith. "Pith review of Analysis of the $B_{(s)}\rightarrow T(J^P=2^-)$ transition in light cone QCD sum rules." pith.science (2026). https://pith.science/paper/S6MD46S4

@misc{pith2026241115952,
  author       = {Pith},
  title        = {Pith review of: Analysis of the $B_(s)\rightarrow T(J^P=2^-)$ transition in light cone QCD sum rules},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S6MD46S4}},
  note         = {Machine review of arXiv:2411.15952}
}
abstract

The semileptonic $B_{(s)} \rightarrow T(J^P=2^-)l^+l^-$ decays induced by flavor changing neural currents are investigated within the light cone QCD sum rule method. We apply the $B$ meson distribution amplitudes up to twist-4 and calculate the relevant form factors of the $B_{(s)} \rightarrow T$ transitions, where $T=K_2,~a_2,~f_2,~\phi_2$ with $J^P=2^-$. The obtained results of the form factors then adopted in the calculations of the corresponding widths. The present results can be used in future experiments for studying the properties of $J^P=2^-$ tensor mesons.

Figures

Figures reproduced from arXiv: 2411.15952 by the authors.

Figure 1
Figure 1. FIG. 1. The histograms of the fit parameters [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The variation of the form factors of [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The variation of the form factors of the [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The variation of the form factors of the [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The variation of the form factors of the [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]

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  1. Studying the tensor resonance contributions in $B \to PP\ell^+\ell^-$ and $B \to PV\ell^+\ell^-$ decays

    hep-ph 2026-07 conditional novelty 4.0 of 10

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Works this paper leans on

58 extracted references · 19 canonical work pages · cited by 1 Pith paper

  1. [33]

    Khodjamirian, T

    A. Khodjamirian, T. Mannel and N. Offen, Phys. Rev. D 75, 054013 (2007) [arXiv:hep-ph/0611193 [hep-ph]]

    arXiv 2007

  2. [1]

    Gratrex, M

    J. Gratrex, M. Hopfer and R. Zwicky, Phys. Rev. D 93, no.5, 054008 (2016) [arXiv:1506.03970 [hep-ph]]

    arXiv 2016

  3. [2]

    and Bs→ (K ∗ 2, f′ 2, D∗ s2), were considered and their corresponding form factors wer e calculated using the standard and covariant light-front quark model. In Ref. [19], B→T transition for the tensor mesonsD2, f2, a2, and K ∗ 2 were considered, and the corresponding form factors for the tree-level and flavor-changing neutral current transitions were obta...

    work page

  4. [3]

    The quark fields present in the interpolating currents Jµν and Jρ and Γ ρ 2 present in Jρ

    Γρ 2 Form factor B→K2 s d γργ5 γρ σρ{q}γ5 σρ{q} A V0, V1, V2 T1 T2, T3 Bs→φ2 s s B→f2 d(u) d(u) B→a2 d u TABLE I. The quark fields present in the interpolating currents Jµν and Jρ and Γ ρ 2 present in Jρ . the Appendix, supplementary materials, namely the two-par ticle DAs of the B meson and analytic results corresponding to the calculations are presented....

    work page

  5. [4]

    Heavy-to-Light Form Factors in the Final Hadron Large Energy Limit: Covariant Quark Model Approach

    J. Charles, A. Le Yaouanc, L. Oliver, O. Pene and J. C. Raynal, Phys. Lett. B 451, 187 (1999) [arXiv:hep-ph/9901378 [hep-ph]]

    work page Pith review arXiv 1999

  6. [5]

    and ( 19) define T23A and T23B

    work page

  7. [6]

    Ebert, R

    D. Ebert, R. N. Faustov and V. O. Galkin, Phys. Rev. D 64, 094022 (2001) [arXiv:hep-ph/0107065 [hep-ph]]

    arXiv 2001

  8. [7]

    Testing spin-2 mediator by angular observables in $b\rightarrow s \mu^+ \mu^-$

    S. Fajfer, B. Melic and M. Patra, Phys. Rev. D 97, no.9, 095036 (2018) [arXiv:1801.07115 [hep-ph]]

    work page Pith review arXiv 2018

Show all 58 references
  1. [8]

    Scora and N

    D. Scora and N. Isgur, Phys. Rev. D 52, 2783-2812 (1995) [arXiv:hep-ph/9503486 [hep-ph]]

    1995 arXiv

  2. [9]

    H. Y. Cheng and C. K. Chua, Phys. Rev. D 81, 114006 (2010) [erratum: Phys. Rev. D 82, 059904 (2010)] [arXiv:0909.4627 [hep-ph]]

    2010 arXiv

  3. [10]

    A. S. Safir, Eur. Phys. J. direct 3, no.1, 15 (2001) [arXiv:hep-ph/0109232 [hep-ph]]

    2001 arXiv

  4. [11]

    Sharma and R

    N. Sharma and R. C. Verma, Phys. Rev. D 82, 094014 (2010) [arXiv:1004.1928 [hep-ph]]

    2010 arXiv

  5. [12]

    H. Y. Cheng, C. K. Chua and C. W. Hwang, Phys. Rev. D 69, 074025 (2004) [arXiv:hep-ph/0310359 [hep-ph]]

    2004 arXiv

  6. [13]

    Datta, Y

    A. Datta, Y. Gao, A. V. Gritsan, D. London, M. Nagashima and A. Szynkman, Phys. Rev. D 77, 114025 (2008) [arXiv:0711.2107 [hep-ph]]

    2008 arXiv

  7. [14]

    K. C. Yang, Phys. Lett. B 695, 444-448 (2011) [arXiv:1010.2944 [hep-ph]] . 20

    2011 arXiv

  8. [15]

    H. Y. Cheng and C. K. Chua, Phys. Rev. D 82, 034014 (2010) [arXiv:1005.1968 [hep-ph]]

    2010 arXiv

  9. [16]

    Khosravi and S

    R. Khosravi and S. Sadeghi, Adv. High Energy Phys. 2016, 2352041 (2016) [arXiv:1503.02883 [hep-ph]]

    2016 arXiv

  10. [17]

    Wang, Phys

    W. Wang, Phys. Rev. D 83, 014008 (2011) [arXiv:1008.5326 [hep-ph]]

    2011 arXiv

  11. [18]

    Note that in the derivation of Eq

    and ( 19). Note that in the derivation of Eq. ( 26) we have used narrow-width approximation; i.e. the widths of the tensor mesons are taken zero. At the end of this section we present the expression for the de cay widths of the considered transitions. In the Standard Model the...

  12. [19]

    Z. G. Wang, Mod. Phys. Lett. A 26, 2761-2782 (2011) [arXiv:1011.3200 [hep-ph]]

    2011 arXiv

  13. [20]

    Azizi, H

    K. Azizi, H. Sundu and S. Sahin, Phys. Rev. D 88, no.3, 036004 (2013) [arXiv:1306.4098 [hep-ph]]

    2013 arXiv

  14. [21]

    L. Chen, Y. W. Ren, L. T. Wang and Q. Chang, Eur. Phys. J. C 82, no.5, 451 (2022) [arXiv:2112.08016 [hep-ph]]

    2022 arXiv

  15. [22]

    Emmerich, M

    M. Emmerich, M. Strohmaier and A. Sch¨ afer, Phys. Rev. D 98, no.1, 014008 (2018) [arXiv:1804.02953 [hep-ph]]

    2018 arXiv

  16. [23]

    F. U. Bernlochner, Z. Ligeti and D. J. Robinson, Phys. Rev. D 97, no.7, 075011 (2018) [arXiv:1711.03110 [hep-ph]]

    2018 arXiv

  17. [24]

    T. M. Aliev, H. Dag, A. Kokulu and A. Ozpineci, Phys. Rev. D 100, no.9, 094005 (2019) [arXiv:1908.00847 [hep-ph]]

    2019 arXiv

  18. [25]

    Y. B. Zuo, C. X. Yue, B. Yu, Y. H. Kou, Y. Chen and W. Ling, Eur. Phys. J. C 81, no.1, 30 (2021)

    2021

  19. [26]

    V. L. Chernyak and I. R. Zhitnitsky, Nucl. Phys. B 345, 137-172 (1990)

    1990

  20. [27]

    Y. B. Zuo, J. L. Zhu, S. S. Hu, C. C. Liu and J. Y. Zou, Eur. Phys. J. C 84, no.2, 109 (2024)

    2024

  21. [28]

    Vardani and R

    J. Vardani and R. Sain, [arXiv:2407.15577 [hep-ph]]

  22. [29]

    Q. M. U. Salam, I. Ahmed, R. Khalid and I. U. Rehman, [arXiv:2411.00912 [hep-ph]]

    arXiv

  23. [30]

    I. I. Balitsky, V. M. Braun and A. V. Kolesnichenko, Nucl. Phys. B 312, 509-550 (1989)

    1989

  24. [31]

    the λ means λ(m2 B,m 2 T,q 2) and is defined as λ(x,y,z ) = x2 +y2 +z2− 2xy− 2xz− 2yz, (32) and ˜Fi are ˜F1 = −Ceff 9 (µ) 2 mB +mT A(q2)−Ceff 7 (µ) 4mb q2 T1 ( q2) ˜F2 = − (mB +mT ) m2 B [ Ceff 9 (µ)V1(q2) +Ceff 7 (µ) 2mb(mB−mT ) q2 T2 ( q2)] ˜F3 = −Ceff 9 (µ) 1 mB +mT V2(q2)−C...

  25. [32]

    Colangelo and A

    P. Colangelo and A. Khodjamirian, [arXiv:hep-ph/0010175 [hep-ph]]

    arXiv

  26. [34]

    Faller, A

    S. Faller, A. Khodjamirian, C. Klein and T. Mannel, Eur. Phys. J. C 60, 603-615 (2009) [arXiv:0809.0222 [hep-ph]]

    2009 arXiv

  27. [35]

    Y. M. Wang and Y. L. Shen, Nucl. Phys. B 898, 563-604 (2015) [arXiv:1506.00667 [hep-ph]]

    2015 arXiv

  28. [36]

    Y. M. Wang and Y. L. Shen, JHEP 02, 179 (2016) [arXiv:1511.09036 [hep-ph]]

    2016 arXiv

  29. [37]

    Cheng, A

    S. Cheng, A. Khodjamirian and J. Virto, JHEP 05, 157 (2017) [arXiv:1701.01633 [hep-ph]]

    2017 arXiv

  30. [38]

    Gubernari, A

    N. Gubernari, A. Kokulu and D. van Dyk, JHEP 01, 150 (2019) [arXiv:1811.00983 [hep-ph]]

    2019 arXiv

  31. [39]

    J. Gao, C. D. L¨ u, Y. L. Shen, Y. M. Wang and Y. B. Wei, Phys. Rev. D 101, no.7, 074035 (2020) [arXiv:1907.11092 [hep-ph]]

    2020 arXiv

  32. [40]

    Cheng and J

    S. Cheng and J. M. Shen, Eur. Phys. J. C 80, no.6, 554 (2020) [arXiv:1907.08401 [hep-ph]]

    2020 arXiv

  33. [41]

    Descotes-Genon, A

    S. Descotes-Genon, A. Khodjamirian and J. Virto, JHEP 12, 083 (2019) [arXiv:1908.02267 [hep-ph]]

    2019 arXiv

  34. [42]

    A. J. Buras and M. Munz, Phys. Rev. D 52, 186-195 (1995) [arXiv:hep-ph/9501281 [hep-ph]]

    1995 arXiv

  35. [43]

    A. J. Buras, Phys. Rept. 1025, 1-64 (2023) [arXiv:1102.5650 [hep-ph]]

    2023 arXiv

  36. [44]

    Hurth and M

    T. Hurth and M. Nakao, Ann. Rev. Nucl. Part. Sci. 60, 645-677 (2010) [arXiv:1005.1224 [hep-ph]]

    2010 arXiv

  37. [45]

    T. M. Aliev, S. Bilmis and K. C. Yang, Nucl. Phys. B 931, 132-145 (2018) [arXiv:1706.05073 [hep-ph]]

    2018 arXiv

  38. [46]

    Navas et al

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

    2024

  39. [47]

    Bazavov, C

    A. Bazavov, C. Bernard, N. Brown, C. Detar, A. X. El-Khadra , E. G´ amiz, S. Gottlieb, U. M. Heller, J. Komijani and A. S. Kronfeld, et al. Phys. Rev. D 98, no.7, 074512 (2018) 21 [arXiv:1712.09262 [hep-lat]]

    2018 arXiv

  40. [48]

    Janowski, B

    T. Janowski, B. Pullin and R. Zwicky, JHEP 12, 008 (2021) [arXiv:2106.13616 [hep-ph]]

    2021 arXiv

  41. [49]

    Rahimi and M

    M. Rahimi and M. Wald, Phys. Rev. D 104, no.1, 016027 (2021) [arXiv:2012.12165 [hep-ph]]

    2021 arXiv

  42. [50]

    Nishikawa and K

    T. Nishikawa and K. Tanaka, Nucl. Phys. B 879, 110-142 (2014) [arXiv:1109.6786 [hep-ph]]

    2014 arXiv

  43. [51]

    V. M. Braun, D. Y. Ivanov and G. P. Korchemsky, Phys. Rev. D 69, 034014 (2004) [arXiv:hep-ph/0309330 [hep-ph]]

    2004 arXiv

  44. [52]

    Khodjamirian, R

    A. Khodjamirian, R. Mandal and T. Mannel, JHEP 10, 043 (2020) [arXiv:2008.03935 [hep-ph]]

    2020 arXiv

  45. [53]

    Sentitemsu Imsong, A

    I. Sentitemsu Imsong, A. Khodjamirian, T. Mannel and D. van D yk, JHEP 02, 126 (2015) [arXiv:1409.7816 [hep-ph]]

    2015 arXiv

  46. [54]

    Ball and R

    P. Ball and R. Zwicky, Phys. Rev. D 71, 014015 (2005) [arXiv:hep-ph/0406232 [hep-ph]]

    2005 arXiv

  47. [55]

    Jamin and B

    M. Jamin and B. O. Lange, Phys. Rev. D 65, 056005 (2002) [arXiv:hep-ph/0108135 [hep-ph]]

    2002 arXiv

  48. [56]

    Bharucha, D

    A. Bharucha, D. M. Straub and R. Zwicky, JHEP 08, 098 (2016) [arXiv:1503.05534 [hep-ph]]

    2016 arXiv

  49. [57]

    H. M. Asatrian, C. Greub and A. Kokulu, Phys. Rev. D 95, no.5, 053006 (2017) [arXiv:1611.08449 [hep-ph]]

    2017 arXiv

  50. [58]

    V. M. Braun, Y. Ji and A. N. Manashov, JHEP 05, 022 (2017) [arXiv:1703.02446 [hep-ph]]

    2017 arXiv

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Reviewed August 12, 2026 · model on record in the stance chip above.