Pith. sign in

REVIEW 3 major objections 5 minor 60 references

Implications on CP violation of charmless three body decays of bottom baryon from the U-spin analysis

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read U-spin symmetry fixes partner-channel CP asymmetries, and LHCb data yield four testable predictions.

desk verdict Clean U-spin relations and concrete testable predictions, but the numerical outputs carry an unquantified symmetry-breaking systematic in the CP-odd numerator. read the letter →

arxiv 2411.18400 v1 pith:6EFBA4ZC submitted 2024-11-27 hep-ph hep-ex

Wei Wang , Zhi-Peng Xing , Zhen-Xing Zhao This is my paper · ORCID
classification hep-phhep-ex
keywords CPviolationbottombaryonsU-spinsymmetrythree-bodydecaysdirectasymmetryStandardModelnulltestCKMphaseLHCb
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 U-spin symmetry, the flavor symmetry between down and strange quarks, fixes the direct CP asymmetries of partner charmless three-body bottom-baryon decays without a dynamical calculation of strong phases. It derives exact U-spin relations such as $A_{\rm CP}(\Lambda_b \to \Lambda K^+K^-) = -R\, A_{\rm CP}(\Xi_b^0 \to \Lambda \pi^+\pi^-)$, where $R$ is a known ratio of branching fractions and lifetimes, and uses LHCb's recent asymmetry and branching-ratio measurements to predict four unmeasured or newly measured channel asymmetries. If the relations hold, the predictions in Eq. (29) become direct experimental targets, and the quantity $\Delta$ in Eq. (31) provides a clean Standard Model null test.

What carries the argument

The central object is the U-spin representation of the anti-triplet bottom baryons, light baryon octet, and meson octet as SU(2) matrices, together with a U-spin doublet decomposition of the effective weak Hamiltonian into $H_u$ and $H_c$. Expanding the allowed three-body decay amplitudes in products of these matrices yields per-channel amplitudes of the form $A = V^*_{ub}V_{uq}A_u + V^*_{cb}V_{cq}A_c$. The direct-CP-asymmetry formula, which involves $\text{Im}(A_u A_c^*)$ divided by the summed rates, then converts amplitude equalities between partner channels into the ratio relations of Eqs. (24) through (27).

What would settle it

Measure $A_{\rm CP}(\Xi_b^0 \to \Lambda \pi^+\pi^-)$ at LHCb and compare it with the prediction $-0.090 \pm 0.051$ derived from $A_{\rm CP}(\Lambda_b \to \Lambda K^+K^-)$ through Eq. (24); disagreement beyond the quoted uncertainties would falsify the U-spin CPV relation, and additional data can also show whether $\Delta$ departs from zero.

Watch

Extended reading notes

Core claim

Under U-spin, a charmless three-body bottom-baryon decay amplitude separates into two CKM parts, $A = V^*_{ub}V_{uq}A_u + V^*_{cb}V_{cq}A_c$. U-spin partner channels, related by $d\leftrightarrow s$, have identical $A_u$ and $A_c$ up to trivial factors, so the imaginary part $\text{Im}(A_u A_c^*)$ is the same, while the CKM prefactor flips sign by unitarity. The paper shows that the direct CP asymmetry of one channel is therefore the negative of its partner's asymmetry times the ratio of the two channels' lifetimes and branching fractions. Combining these relations with LHCb's measured $\Lambda_b$ asymmetries produces predicted CP asymmetries for four partner channels and a null-test variable $\Delta$ that vanishes in the Standard Model if U-spin is exact.

Load-bearing premise

The load-bearing premise is that U-spin symmetry between down and strange quarks holds well enough for CP-asymmetry combinations even though it is known to break for absolute rates; if the breaking or phase-space averaging is as large as the measured asymmetries, the predicted values and $\Delta$ shift outside the stated errors.

Editorial extensions

If this is right

  • Equation (29) gives concrete, testable predictions: $A_{\rm CP}(\Lambda_b \to \Sigma^0 K^+K^-) = 0.083 \pm 0.028$, $A_{\rm CP}(\Xi_b^0 \to \Lambda \pi^+\pi^-) = -0.090 \pm 0.051$, $A_{\rm CP}(\Lambda_b \to \Sigma^0 K^+\pi^-) = -0.118 \pm 0.058$, and $A_{\rm CP}(\Xi_b^0 \to \Sigma K^-\pi^+) = 0.27 \pm 0.13$.
  • Any U-spin partner pair in Eqs. (27) and (28) obeys the same ratio relation, so one well-measured asymmetry predicts its partner without additional dynamical input.
  • The variable $\Delta$ in Eq. (31) is a Standard Model null test; its current value $-1.8 \pm 1.6$ is consistent with zero at about $1.1\sigma$, so improved LHCb data can sharpen the search for new physics.
  • Because the relations involve only CP asymmetries and known ratios of branching fractions and lifetimes, they sidestep the U-spin breaking that affects absolute rate predictions.

Reading between the lines

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

  • An extension not developed in the paper is to test the same relations differentially in invariant-mass bins, where resonance and final-state-interaction effects averaged over the full phase space would reveal themselves as local violations.
  • The U-spin doublet construction is general enough to extend to other bottom-baryon initial states and other three-meson final states beyond those tabulated; any partner pair sharing $A_u$ and $A_c$ would inherit a similar ratio rule.
  • The null-test variable $\Delta$ could be converted into a quantitative bound on U-spin breaking by measuring both partner asymmetries independently and attributing any residual to the symmetry-breaking parameter.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper applies U-spin symmetry to charmless three-body decays of bottom baryons and derives exact-looking relations between direct CP asymmetries of U-spin partner channels. Using the recent LHCb measurements of A_CP in four charmless baryon decays together with measured branching ratios and lifetimes, it predicts CP asymmetries for four additional channels, Eq. (29), and proposes the combination Delta in Eq. (31) as a Standard Model null test. The algebraic framework in Table I is explicit, the weak/strong phase decomposition in Eqs. (17)-(20) is standard, and the relations do not reduce to the inputs by construction. The central limitations are that U-spin breaking in the CP-odd numerator and the use of phase-space-integrated observables are not quantified, and the null test is not exactly calibrated once the large measured asymmetry in the Xi_b channel is taken into account.

Significance. If the U-spin relations hold at the precision claimed, the paper offers a clean, model-independent way to turn the first LHCb measurements of CP violation in bottom-baryon three-body decays into testable predictions for partner channels, plus a falsifiable null test. Strengths of the paper are that no hadronic parameters are fitted, the amplitude algebra leading to Table I is internally consistent, the numerical predictions propagate the experimental inputs in a transparent way, and the predicted channels are in principle measurable at LHCb. The significance is conditional, however, on a quantitative control of U-spin breaking and phase-space corrections; without such an estimate the quoted numerical errors in Eqs. (29) and (32) are incomplete.

major comments (3)
  1. [III, Eq. (24)] The replacement of |A|^2+|Abar|^2 by 2|A|^2 in Eq. (24) is not accurate for the input A_CP(Xi_b^0 -> Lambda K- pi+) = 0.27. Using the exact identity |A|^2+|Abar|^2 = 2 Gamma_i/(1+A_i), the correct partner relation is A_CP(Lambda_b -> Lambda K+K-)/A_CP(Xi_b^0 -> Lambda pi+pi-) = - R(Xi/Lambda) * (1+A_Lambda)/(1+A_Xi), not -R(Xi/Lambda). For the pair used in the Delta null test the omitted factor is (1-0.118)/(1+0.27) ~ 0.69, so under exact U-spin and exact numerator equality Delta in Eq. (31) equals (A_Lambda - A_Xi)/[R(Lambda/Xi)(1+A_Lambda)], which is of order -0.4 for R of order unity, not zero. The statement that the data agree with the Standard Model at 1.1 sigma is therefore not calibrated; the relation should be corrected or the approximation error should be quantified explicitly.
  2. [I and III, Eq. (20)] U-spin breaking in the CP-odd numerator is not estimated. The argument in Sec. I that U-spin breaking is less pronounced for CP violation because the weak phase originates in the CKM matrix protects only the CKM prefactor in Eq. (20); the numerator Im(A_u A_c^*) depends on the strong-phase difference, which U-spin breaking can modify. The errors quoted in Eq. (29) and Eq. (32) propagate only the experimental inputs. A 20-30% breaking in the integrated numerator would shift the central value 0.083 by roughly 0.02, comparable to the quoted uncertainty of 0.028. The authors should add a quantitative estimate of U-spin breaking, for example from the measured SU(3) breaking in the partner branching ratios or from the size of the d-s mass splittings, and include it as a theoretical uncertainty, or explicitly state that the predictions are valid only up to an unquantified U-spin-breaking correction.
  3. [III, Eqs. (15)-(23)] Eq. (15) is a pointwise equality of reduced amplitudes, but Eq. (23) and the subsequent CP asymmetry relations are applied to observables integrated over the three-body phase space. The paper never defines this integration in Eq. (16). The partner channels Lambda_b -> Lambda K+K- and Xi_b^0 -> Lambda pi+pi- have different Dalitz-plot boundaries because m_K differs from m_pi and m_Lambda_b differs from m_Xi_b, and their strong phases receive contributions from different resonances and final-state interactions. Equality of the integrated quantities Im(A_u A_c^*) therefore does not follow from the pointwise U-spin relations. The authors should state the phase-space integration explicitly and either justify the equality or estimate the correction from the different Dalitz-plot boundaries and resonance content.
minor comments (5)
  1. [III, Eq. (29)] The channel Xi_b^0 -> Sigma K- pi+ should specify Sigma^0; the superscript is missing in the abstract and in Eq. (29), and the notation is ambiguous because Sigma^+ states also appear in Table I.
  2. [III, Eqs. (24)-(29)] The numerical inputs used to evaluate R are incomplete: the branching fractions B(Lambda_b -> Lambda K+K-), B(Lambda_b -> Lambda K+pi-) and the lifetimes tau_Lambda_b, tau_Xi_b are not listed, so the reader cannot reproduce the values in Eq. (29) without consulting the experimental paper.
  3. [III, Eq. (31)] The measured input in Eq. (1) is quoted as A_CP(Xi_b^0 -> Lambda K- pi+), but the formula in Eq. (31) uses A_CP(Xi_b^0 -> Lambda pi+ K-); the equivalence of these orderings should be stated explicitly.
  4. [Table I] There are several typographical errors in Table I, for example the Lambda_b -> n pi+ pi- amplitude contains an unmatched closing parenthesis and the Xi_b^0 -> Xi^0 K+ K- entry has a dangling '+' at the end of the expression.
  5. [Appendix A] The appendix switches between 'u-spin' and 'U-spin', and the step from Eq. (A4) to Eq. (A5) is too compressed; a sentence explaining how phi_3 defines the matrix in Eq. (A5) would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: CPV relations are derived from U-spin and CKM unitarity; predictions propagate independent measurements rather than fitting the target quantities.

full rationale

The paper's central relations (Eqs. 24-27) follow from the U-spin amplitude identities in Table I/Eq. (15) combined with CKM unitarity. No hadronic parameter is fitted to the CP asymmetry being predicted; the numerical outputs in Eq. (29) are obtained by inserting the independently measured LHCb asymmetries of Eq. (1) and measured branching ratios/lifetimes into the derived relations. The null-test Delta compares two measured asymmetries and is not forced to zero by construction. The acknowledged U-spin breaking for absolute rates is a model-uncertainty caveat, not a circular step; the paper explicitly avoids using the U-spin relations to predict branching ratios. Self-citations appear only as background methodology references and are not load-bearing. Hence no circularity.

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

No hadronic parameters are fitted. The amplitude coefficients in Table I are undetermined but cancel in the CPV relations; numerical outputs use only experimental inputs (measured ACPs, branching ratios, lifetimes) and standard CKM parameters. The main axiomatic input is U-spin symmetry, applied to integrated three-body observables without a quantitative breaking estimate.

assumptions (5)
  • domain assumption U-spin (d-s flavor) symmetry is exact for the three-body decay amplitudes, including weak and strong phases.
    Assumed throughout Sec II and III; acknowledged as approximate in Sec I, but the size of the breaking is not quantified.
  • domain assumption The amplitude factorizes into two CKM components with process-independent strong amplitudes A_u and A_c and no additional weak-phase structures.
    Eq (17)-(20) assume only SM tree and penguin operators with two weak phases; no new physics or additional amplitudes are included.
  • standard math CKM unitarity relation between d-type and s-type imaginary CKM products.
    Used in Eq (23) to relate Im(V_ub* V_us V_cb V_cs*) and Im(V_ub* V_ud V_cb V_cd*) with a relative minus sign.
  • domain assumption Lambda and Sigma^0 lie in the same U-spin triplet and therefore have equal CP asymmetries up to a constant normalization.
    Appendix A places Lambda and Sigma^0 in the same U-spin triplet; used to map measured Lambda channels to Sigma^0 predictions.
  • domain assumption Integrated three-body decay observables obey the same U-spin relations as point amplitudes.
    Table I amplitudes are applied to full three-body phase space; resonances, phase-space integrals, and final-state interactions are not modeled.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Implications on CP violation of charmless three body decays of bottom baryon from the U-spin analysis." pith.science (2026). https://pith.science/paper/6EFBA4ZC

@misc{pith2026241118400,
  author       = {Pith},
  title        = {Pith review of: Implications on CP violation of charmless three body decays of bottom baryon from the U-spin analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6EFBA4ZC}},
  note         = {Machine review of arXiv:2411.18400}
}
abstract

Motivated by recent LHCb measurements of CP violation in $\Lambda_b$ three-body decays, we conduct an analysis of CP asymmetry in three-body decays of bottom baryons utilizing U-spin symmetry. We first develop a convenient representation that facilitates the incorporation of U-spin symmetry into our analysis. By integrating weak and strong phases into the derived amplitude, we obtain the CP asymmetry and establish relationships between CP asymmetries in U-spin related decay channels. With the help of experimental measurements, we provide numerical predictions for the CP asymmetries for other decay channels, particularly $\Lambda_b \to \Sigma^0 K^+ K^-$, $\Xi^0_b \to \Lambda \pi^+ \pi^-$, $\Lambda_b \to \Sigma^0 K^+ \pi^-$, and $\Xi^0_b \to \Sigma K^- \pi^+$. Furthermore, we provide a quantity that can be used as a null test of standard model and deviations from 0 will reflect the possible new physics. These results are valuable for CPV measurements in baryon decays, and can be tested in future experiments.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

60 extracted references · 19 canonical work pages

  1. [1]

    J. H. Christenson, J. W. Cronin, V. L. Fitch and R. Turlay, Phys. Rev. Lett. 13, 138-140 (1964) doi:10.1103/PhysRevLett.13.138

    doi:10.1103/physrevlett.13.138 1964

  2. [2]

    Aubert et al

    B. Aubert et al. [BaBar], Phys. Rev. Lett. 86, 2515-2522 (2001) doi:10.1103/PhysRevLett.86.2515 [arXiv:hep-ex/0102030 [hep-ex]]

    arXiv 2001

  3. [3]

    Abe et al

    K. Abe et al. [Belle], Phys. Rev. Lett. 87, 091802 (2001) doi:10.1103/PhysRevLett.87.091802 [arXiv:hep-ex/0107061 [hep-ex]]

    arXiv 2001

  4. [4]

    Aaij et al

    R. Aaij et al. [LHCb], Phys. Rev. Lett. 122, no.21, 211803 (2019) doi:10.1103/PhysRevLett.122.211803 [arXiv:1903.08726 [hep-ex]]

    arXiv 2019

  5. [5]

    Measurements of Direct CP Violating Asymmetries in Charmless Decays of Strange Bottom Mesons and Bottom Baryons

    T. Aaltonen et al. [CDF], Phys. Rev. Lett. 106, 181802 (2011) doi:10.1103/PhysRevLett.106.181802 [arXiv:1103.5762 [hep-ex]]

    work page Pith review arXiv 2011

  6. [6]

    T. A. Aaltonen et al. [CDF], Phys. Rev. Lett. 113, no.24, 242001 (2014) doi:10.1103/PhysRevLett.113.242001 [arXiv:1403.5586 [hep-ex]]

    work page Pith review arXiv 2014

  7. [7]

    R. M. Wang, X. D. Cheng and X. B. Yuan, Phys. Rev. D 107, no.5, 053002 (2023) doi:10.1103/PhysRevD.107.053002 [arXiv:2212.01828 [hep-ph]]

    work page Pith review arXiv 2023

  8. [8]

    J. P. Wang and F. S. Yu, Phys. Lett. B 849, 138460 (2024) doi:10.1016/j.physletb.2024.138460 [arXiv:2208.01589 [hep-ph]]

    arXiv 2024

Show all 60 references
  1. [9]

    C. Q. Geng, X. N. Jin, C. W. Liu, Z. Y. Wei and J. Zhang, Phys. Lett. B 834, 137429 (2022) doi:10.1016/j.physletb.2022.137429 [arXiv:2206.00348 [hep-ph]]

    2022

  2. [10]

    L. K. Li et al. [Belle], [arXiv:2305.12806 [hep-ex]]

    arXiv

  3. [11]

    X. Dai, M. Saur, Y. Shang, X. Yang and Y. Zhang, Sym- metry 15, no.2, 522 (2023) doi:10.3390/sym15020522 [arXiv:2302.00180 [hep-ex]]

    2023 arXiv

  4. [12]

    W. J. Song, Y. F. Shen and Q. Qin, Eur. Phys. J. C 84, no.10, 1030 (2024) doi:10.1140/epjc/s10052-024-13350-z [arXiv:2403.01904 [hep-ph]]

    2024 arXiv

  5. [13]

    Aaij et al

    R. Aaij et al. [LHCb], [arXiv:2411.15441 [hep-ex]]

  6. [14]

    C. D. Lu, Y. M. Wang, H. Zou, A. Ali and G. Kramer, Phys. Rev. D 80, 034011 (2009) doi:10.1103/PhysRevD.80.034011 [arXiv:0906.1479 [hep- ph]]

    2009 arXiv

  7. [15]

    Z. Rui, J. M. Li and C. Q. Zhang, Phys. Rev. D 107, no.5, 053009 (2023) doi:10.1103/PhysRevD.107.053009 [arXiv:2210.15357 [hep-ph]]

    2023 arXiv

  8. [16]

    C. Q. Zhang, J. M. Li, M. K. Jia and Z. Rui, Phys. Rev. D 105, no.7, 073005 (2022) doi:10.1103/PhysRevD.105.073005 [arXiv:2202.09181 [hep-ph]]

    2022 arXiv

  9. [17]

    Z. Rui, C. Q. Zhang, J. M. Li and M. K. Jia, Phys. Rev. D 106, no.5, 053005 (2022) doi:10.1103/PhysRevD.106.053005 [arXiv:2206.04501 [hep-ph]]

    2022 arXiv

  10. [18]

    Rui and Z

    Z. Rui and Z. T. Zou, Phys. Rev. D 109, no.3, 033013 (2024) doi:10.1103/PhysRevD.109.033013 [arXiv:2310.19031 [hep-ph]]

    2024 arXiv

  11. [19]

    J. X. Yu, J. J. Han, Y. Li, H. n. Li, Z. J. Xiao and F. S. Yu, [arXiv:2409.02821 [hep-ph]]

    arXiv

  12. [20]

    Bediaga, T

    I. Bediaga, T. Frederico and P. C. Magalh˜ aes, Phys. Rev. Lett. 131, no.5, 051802 (2023) doi:10.1103/PhysRevLett.131.051802 [arXiv:2203.04056 [hep-ph]]

    2023 arXiv

  13. [21]

    J. P. Wang and F. S. Yu, Chin. Phys. C 48, no.10, 101002 (2024) doi:10.1088/1674-1137/ad75f4 [arXiv:2407.04110 [hep-ph]]

    2024 arXiv

  14. [22]

    C. P. Jia, H. Y. Jiang, J. P. Wang and F. S. Yu, JHEP 11, 072 (2024) doi:10.1007/JHEP11(2024)072 [arXiv:2408.14959 [hep-ph]]

    2024 arXiv

  15. [23]

    X. G. He and C. W. Liu, [arXiv:2404.19166 [hep-ph]]

    arXiv

  16. [24]

    Gronau and J

    M. Gronau and J. L. Rosner, Phys. Rev. D 89, no.3, 037501 (2014) [erratum: Phys. Rev. D 91, no.11, 119902 (2015)] doi:10.1103/PhysRevD.89.037501 [arXiv:1312.5730 [hep-ph]]

    2014 arXiv

  17. [25]

    M. He, X. G. He and G. N. Li, Phys. Rev. D 92, no.3, 036010 (2015) doi:10.1103/PhysRevD.92.036010 [arXiv:1507.07990 [hep-ph]]

    2015 arXiv

  18. [26]

    X. G. He, Y. J. Shi and W. Wang, Eur. Phys. J. C 80, no.5, 359 (2020) doi:10.1140/epjc/s10052-020-7862-5 [arXiv:1811.03480 [hep-ph]]

    2020 arXiv

  19. [27]

    S. Roy, R. Sinha and N. G. Deshpande, Phys. Rev. D 101, no.3, 036018 (2020) doi:10.1103/PhysRevD.101.036018 [arXiv:1911.01121 [hep-ph]]

    2020 arXiv

  20. [28]

    Wang, Eur

    D. Wang, Eur. Phys. J. C 79, no.5, 429 (2019) doi:10.1140/epjc/s10052-019-6925-y [arXiv:1901.01776 [hep-ph]]

    2019 arXiv

  21. [29]

    S. Roy, R. Sinha and N. G. Deshpande, Phys. Rev. D 102, no.5, 053007 (2020) doi:10.1103/PhysRevD.102.053007 [arXiv:2006.16813 [hep-ph]]

    2020 arXiv

  22. [30]

    Wang, Eur

    D. Wang, Eur. Phys. J. C 83, 279 (2023) doi:10.1140/epjc/s10052-023-11439-5 [arXiv:2207.1105 3 [hep-ph]]

    2023

  23. [31]

    J. Sun, R. Zhu and Z. P. Xing, [arXiv:2407.00426 [hep- ph]]

    arXiv

  24. [32]

    Y. K. Hsiao and C. Q. Geng, Phys. Rev. D 91, no.11, 116007 (2015) doi:10.1103/PhysRevD.91.116007 [arXiv:1412.1899 [hep-ph]]

    2015 arXiv

  25. [33]

    J. Zhu, H. W. Ke and Z. T. Wei, Eur. Phys. J. C 76, no.5, 284 (2016) doi:10.1140/epjc/s10052-016-4134-5 [arXiv:1603.02800 [hep-ph]]

    2016 arXiv

  26. [34]

    A. Dery, Y. Grossman, S. Schacht and D. Tonelli, [arXiv:2209.07429 [hep-ph]]

    arXiv

  27. [35]

    Y. F. Shen, J. P. Wang and Q. Qin, Phys. Rev. D 108, no.11, L111901 (2023) doi:10.1103/PhysRevD.108.L111901 [arXiv:2309.09854 [hep-ph]]

    2023 arXiv

  28. [36]

    Y. F. Shen, W. J. Song and Q. Qin, Phys. Rev. D 110, no.3, L031301 (2024) 8 doi:10.1103/PhysRevD.110.L031301 [arXiv:2301.05848 [hep-ph]]

    2024 arXiv

  29. [37]

    G. S. Bali, V. M. Braun, M. G¨ ockeler, M. Gru- ber, F. Hutzler, A. Sch¨ afer, R. W. Schiel, J. Simeth, W. S¨ oldner and A. Sternbeck, et al. JHEP 02, 070 (2016) doi:10.1007/JHEP02(2016)070 [arXiv:1512.02050 [hep-lat]]

    2016 arXiv

  30. [38]

    G. S. Bali et al. [RQCD], Eur. Phys. J. A 55, no.7, 116 (2019) doi:10.1140/epja/i2019-12803-6 [arXiv:1903.12590 [hep-lat]]

    2019 arXiv

  31. [39]

    Z. F. Deng, C. Han, W. Wang, J. Zeng and J. L. Zhang, JHEP 07, 191 (2023) doi:10.1007/JHEP07(2023)191 [arXiv:2304.09004 [hep-ph]]

    2023 arXiv

  32. [40]

    C. Han, Y. Su, W. Wang and J. L. Zhang, JHEP 12, 044 (2023) doi:10.1007/JHEP12(2023)044 [arXiv:2308.16793 [hep-ph]]

    2023 arXiv

  33. [41]

    Han and J

    C. Han and J. Zhang, Phys. Rev. D 109, no.1, 014034 (2024) doi:10.1103/PhysRevD.109.014034 [arXiv:2311.02669 [hep-ph]]

    2024 arXiv

  34. [42]

    C. Han, W. Wang, J. Zeng and J. L. Zhang, JHEP 07, 019 (2024) doi:10.1007/JHEP07(2024)019 [arXiv:2404.04855 [hep-ph]]

    2024 arXiv

  35. [43]

    M. H. Chu, H. Bai, J. Hua, J. Liang, X. Ji, A. Schafer, Y. Su, W. Wang, Y. B. Yang and J. Zeng, et al. [arXiv:2411.12554 [hep-lat]]

    arXiv

  36. [44]

    X. G. He and G. N. Li, Phys. Lett. B 750, 82-88 (2015) doi:10.1016/j.physletb.2015.08.048 [arXiv:1501.00646 [hep-ph]]

    2015 arXiv

  37. [45]

    C. D. L¨ u, W. Wang and F. S. Yu, Phys. Rev. D 93, no.5, 056008 (2016) doi:10.1103/PhysRevD.93.056008 [arXiv:1601.04241 [hep-ph]]

    2016 arXiv

  38. [46]

    C. Q. Geng, Y. K. Hsiao, C. W. Liu and T. H. Tsai, JHEP 11, 147 (2017) doi:10.1007/JHEP11(2017)147 [arXiv:1709.00808 [hep-ph]]

    2017 arXiv

  39. [47]

    W. Wang, Z. P. Xing and J. Xu, Eur. Phys. J. C 77, no.11, 800 (2017) doi:10.1140/epjc/s10052-017-5363- y [arXiv:1707.06570 [hep-ph]]

    2017 arXiv

  40. [48]

    A. Dery, M. Ghosh, Y. Grossman and S. Schacht, JHEP 03, 165 (2020) doi:10.1007/JHEP03(2020)165 [arXiv:2001.05397 [hep-ph]]

    2020 arXiv

  41. [49]

    Y. K. Hsiao, Y. L. Wang and H. J. Zhao, JHEP 09, 035 (2022) doi:10.1007/JHEP09(2022)035 [arXiv:2111.04124 [hep-ph]]

    2022 arXiv

  42. [50]

    Huang, Z

    F. Huang, Z. P. Xing and X. G. He, JHEP 03, 143 (2022) [erratum: JHEP 09, 087 (2022)] doi:10.1007/JHEP03(2022)143 [arXiv:2112.10556 [hep- ph]]

    2022 arXiv

  43. [51]

    Gronau, Phys

    M. Gronau, Phys. Lett. B 492, 297-302 (2000) doi:10.1016/S0370-2693(00)01119-9 [arXiv:hep-ph/0008292 [hep-ph]]

    2000 arXiv

  44. [52]

    Gronau, Phys

    M. Gronau, Phys. Lett. B 727, 136-140 (2013) doi:10.1016/j.physletb.2013.09.056 [arXiv:1308.3448 [hep-ph]]

    2013 arXiv

  45. [53]

    Bhattacharya and D

    B. Bhattacharya and D. London, JHEP 04, 154 (2015) doi:10.1007/JHEP04(2015)154 [arXiv:1503.00737 [hep- ph]]

    2015 arXiv

  46. [54]

    Grossman and S

    Y. Grossman and S. Schacht, Phys. Rev. D 99, no.3, 033005 (2019) doi:10.1103/PhysRevD.99.033005 [arXiv:1811.11188 [hep-ph]]

    2019 arXiv

  47. [55]

    A. Dery, Y. Grossman, S. Schacht and A. Soffer, JHEP 05, 179 (2021) doi:10.1007/JHEP05(2021)179 [arXiv:2101.02560 [hep-ph]]

    2021 arXiv

  48. [56]

    Gavrilova, Y

    M. Gavrilova, Y. Grossman and S. Schacht, JHEP 08, 278 (2022) doi:10.1007/JHEP08(2022)278 [arXiv:2205.12975 [hep-ph]]

    2022 arXiv

  49. [57]

    Schacht, JHEP 03, 205 (2023) doi:10.1007/JHEP03(2023)205 [arXiv:2207.08539 [hep- ph]]

    S. Schacht, JHEP 03, 205 (2023) doi:10.1007/JHEP03(2023)205 [arXiv:2207.08539 [hep- ph]]

    2023 arXiv

  50. [58]

    Wang and J

    D. Wang and J. F. Luo, Phys. Rev. D 110, no.9, 093001 (2024) doi:10.1103/PhysRevD.110.093001 [arXiv:2406.14061 [hep-ph]]

    2024 arXiv

  51. [59]

    Buchalla, A

    G. Buchalla, A. J. Buras and M. E. Laut- enbacher, Rev. Mod. Phys. 68, 1125- 1144 (1996) doi:10.1103/RevModPhys.68.1125 [arXiv:hep-ph/9512380 [hep-ph]]

    1996 arXiv

  52. [60]

    Navas et al

    S. Navas et al. [Particle Data Group], Phys. Rev. D 110, no.3, 030001 (2024) doi:10.1103/PhysRevD.110.030001

    2024 doi

Pith tools

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