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Data-driven NRQCD form factors for Bc decays to P-wave charmonia yield precise lepton-flavour ratios R(χc0)=0.185(3), R(χc1)=0.147(26) and R(hc)=0.068(2).

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2026-07-11 06:17 UTC pith:X3JRXMQT

load-bearing objection Data-driven P-wave wave-function derivatives give usable R ratios and BRs for B_c, but the quoted precision rides on an untested spin-symmetry transfer of S-wave slopes. the 2 major comments →

arxiv 2607.05527 v1 pith:X3JRXMQT submitted 2026-07-06 hep-ph hep-ex

Precision Study of Semileptonic and Non-Leptonic B_c Decays to η_c and P Wave Charmonia

Aritra Biswas , Soumitra Nandi , Shantanu Sahoo This is my paper
classification hep-ph hep-ex PACS 13.20.He12.39.Hg14.40.Nd
keywords Bc mesonP-wave charmoniasemileptonic decayslepton flavour universalityNRQCD form factorsradiative decaysR ratios
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.

The paper claims that the form factors governing Bc meson decays into the P-wave charmonia χc0, χc1 and hc can be fixed almost entirely by experiment once their analytic NRQCD expressions are adopted. Radiative-decay measurements of those charmonia are used to extract the derivatives of their radial wave functions at the origin; the resulting normalisations, combined with shapes taken from S-wave channels under heavy-quark spin symmetry, produce controlled predictions for semileptonic branching fractions and the lepton-flavour-universality ratios R. Because cascade decays involving P-wave states are important backgrounds to the cleaner J/ψ modes already under experimental scrutiny, these ratios supply a theoretically clean reference that future LHC measurements can test. The same wave-function inputs also update selected non-leptonic Bc rates and several production cross-sections of P-wave charmonia.

Core claim

By extracting the P-wave radial-wave-function derivatives at the origin from existing radiative-decay data and inserting them into NRQCD form-factor formulae, the authors obtain data-constrained Bc o(χc0,χc1,hc) form factors whose shapes are fixed by heavy-quark spin symmetry. These form factors yield the lepton-flavour ratios R(χc0)=0.185(3), R(χc1)=0.147(26) and R(hc)=0.068(2) together with the associated semileptonic branching fractions.

What carries the argument

NRQCD factorisation of the Bc o P-wave transition form factors, with normalisations set by the derivatives of the radial wave functions at the origin that are fitted directly to radiative-decay data and with q^{2} shapes taken from equal-J S-wave channels under heavy-quark spin symmetry.

Load-bearing premise

The q^{2}-shape parameters that control how the form factors vary with momentum transfer are assumed identical to those of the corresponding S-wave channels simply because the final states share the same total angular momentum.

What would settle it

A lattice-QCD determination of any of the Bc oχcJ or Bc o hc form factors at a few q^{2} points, or a first experimental measurement of one of the R(χcJ) or R(hc) ratios, that falls outside the quoted uncertainty bands.

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

If this is right

  • Future LHC measurements of R(χc0), R(χc1) or R(hc) can be compared directly with these Standard-Model benchmarks without large model-dependent theory errors.
  • Cascade backgrounds to the existing R(J/ψ) analyses can be estimated more reliably once the P-wave branching fractions are known.
  • The same wave-function derivatives update non-leptonic Bc o P-wave+light-meson rates and several e^{+}e^{-} and Z-decay production cross-sections for P-wave charmonia.
  • Absolute branching fractions remain limited by the large form-factor uncertainties, so ratio observables will be the first precision tests.

Where Pith is reading between the lines

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

  • Once lattice results for any of these form factors appear, the same radiative-decay fit can be repeated with the lattice points as additional constraints, converting the present hybrid prediction into a fully data-driven one.
  • The hierarchy of precision among the three R ratios already indicates which P-wave channel will give the cleanest new-physics probe when experimental data arrive.
  • The same extracted wave-function derivatives can be reused for any other exclusive process whose NRQCD factorisation involves the same long-distance matrix elements.

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

2 major / 5 minor

Summary. The paper computes semileptonic and non-leptonic B_c decays to η_c and the P-wave charmonia χ_c0, χ_c1 and h_c within NRQCD. Analytic form-factor expressions (including O(v^{2}) relativistic corrections) are taken from the literature; their normalisations at q^{2}=0 are fixed by extracting the radial wave-function derivatives ψ'_R(0) of the P-wave states from a global χ^{2} fit to radiative branching fractions (χ_c0→γγ, χ_c1→ργ/ϕγ/J/ψγ, h_c→η_cγ) together with lattice decay constants. The q^{2} shapes are obtained by a pole expansion whose slope parameters α_i and β are transferred from earlier B_c→J/ψ and B_c→η_c analyses under heavy-quark spin symmetry for equal total angular momentum J, then refined by a BCL z-expansion. The resulting form factors yield the LFU ratios R(χ_c0)=0.185(3), R(χ_c1)=0.147(26), R(h_c)=0.068(2), absolute branching fractions, selected non-leptonic rates, and production cross-sections in e^{+}e^{-} annihilation and Z decays.

Significance. If the spin-symmetry transfer of the shape parameters is reliable, the work supplies the first largely data-driven SM predictions for the P-wave LFU ratios with percent-level precision on R(χ_c0) and R(h_c). These ratios are experimentally relevant as backgrounds to R(J/ψ) and as independent tests of lepton-flavour universality in the heavy-heavy sector. The transparent χ^{2} extraction of the wave-function derivatives, the explicit quantification of BCL truncation errors, and the systematic exploitation of form-factor correlations that suppress the R uncertainties are genuine strengths. The same non-perturbative inputs are reused for non-leptonic B_c modes and for Z and e^{+}e^{-} production, giving a coherent set of falsifiable numbers that can be confronted with future LHCb, Belle II and lattice results.

major comments (2)
  1. [§3.4, Eq. (3.59), Table 7] §3.4 (paragraph after Eq. 3.59) and Table 7: the pole-expansion slopes α_i and the common β that control the entire q^{2} dependence of the B_c→P-wave form factors are taken unchanged from the B_c→J/ψ (J=1) and B_c→η_c (J=0) fits under the assumption that “an initial state decaying to different final states with the same total spin J have the same values for the shape parameters.” No lattice, LCSR or independent model check of this transfer is provided. Because the absolute normalisations already carry 50–70 % uncertainties (Tables 5–6), the quoted percent-level precision on R(χ_c0) and R(h_c) (Table 11) rests almost entirely on the correctness of the transferred slopes. A quantitative estimate of the residual spin-symmetry breaking (or a variation of α_i, β within a plausible range) is required before the R uncertainties can be regarded as robust.
  2. [§3.4, Table 6] §3.4 and Table 6: NLO QCD corrections in α_s are available only for the B_c→χ_c0 form factors. For the J=1 channels the authors assign an ad-hoc 20 % prior uncertainty to the LO results, motivated solely by the size of the NLO correction found for χ_c0. This choice is not derived from a power-counting argument or from a partial NLO calculation, and it is unclear whether it adequately covers the missing hard-scattering kernels for V, A0, A1 and A2. The absolute branching fractions in Table 10 (and the non-leptonic rates that depend on A0) inherit this uncontrolled theoretical error; a more systematic assessment or an explicit statement that the absolute rates remain LO+RC only is needed.
minor comments (5)
  1. [Abstract, §1] Abstract and §1 claim that shapes are constrained “without introducing any additional model-dependent inputs.” The spin-symmetry transfer of α_i, β is itself a model assumption; the wording should be softened to “with minimal additional model dependence.”
  2. [Table 4] Table 4: the p-value of the global fit is quoted as 0.94 for χ^{2}/dof = 1.705/4. A brief discussion of whether the large theory errors on χ_c1→ργ (∼71 %) dominate the goodness-of-fit would help the reader judge the robustness of the extracted ψ'_R(0).
  3. [§5.2] Eqs. (5.20)–(5.27) and Table 19: the double-charmonium cross-sections are given without a clear statement of the renormalisation-scale variation that is customarily used to estimate higher-order QCD uncertainty. Adding a short scale-variation band would make the comparison with Belle/BaBar more informative.
  4. [§4.2] Several numerical tables (e.g. Tables 13–15) list branching fractions with uncertainties larger than 100 %. While this is a consequence of the large form-factor errors, a one-sentence remark that only the ratios (or the relative hierarchy) are presently meaningful would prevent over-interpretation.
  5. [Throughout] Typographical inconsistencies appear in the notation for the radial wave-function derivatives (ψ'_R versus ψ'R) and in a few equation labels (e.g. the repeated “(5.4)” after Eq. (5.3)). A uniform notation pass would improve readability.

Circularity Check

2 steps flagged

Minor residual circularity from self-cited S-wave shapes and ψ_Bc(0) transferred under spin symmetry; R ratios and BRs retain independent content from radiative fits + external NRQCD.

specific steps
  1. self citation load bearing [§3.1 (after eqs. 3.13–3.19) and Tables 5–6]
    "Following our earlier analysis [48], we were able to obtain ψ_Bc(0) using lattice inputs on the B_c → J/ψ form factors [52] and the decay constants f_Bc. … using the fit results from table 4 and the value for the radial wave function of the B_c meson i.e. ψ_R_Bc(0) = 0.916 ± 0.124 from table VII of ref. [48]"

    Every absolute form-factor normalization (and therefore every absolute branching fraction) is proportional to this single self-extracted number. The present paper does not re-determine it; the scale is imported wholesale from the authors’ previous work.

  2. fitted input called prediction [§3.4 (paragraph after eq. 3.59) and Table 7]
    "Under this symmetry, an initial state (like the B_c meson) decaying to different final states with the same total spin J have the same values for the shape parameters [10, 27, 77]. … We then use the corresponding α_i and β for the B_c o J/ψ transition to estimate the B_c o χ_c1, h_c form factors since all of these final state charmonia have the same total spin J = 1. The α_i and β estimates for B_c o η_c transitions can similarly be used … for the B_c o χ_c0 form factors."

    The entire q^{2} dependence of the P-wave form factors is set equal, by construction, to the slopes previously fitted by the same authors to S-wave synthetic data. The subsequent BCL re-parametrization and the high-precision R ratios are therefore numerically forced by that transferred fit; only the overall normalizations differ.

full rationale

Wave-function derivatives ψ'_R(0) for χ_c0,1 and h_c are extracted by a genuine χ² fit to independent radiative branching fractions (Table 3) and are not tuned to any B_c observable; the NRQCD short-distance kernels are taken from the external literature. Absolute normalizations therefore carry new experimental information. The only load-bearing self-sourced pieces are (i) ψ_Bc(0) taken from the authors’ prior S-wave analysis and (ii) the pole-expansion slopes α_i, β fixed once and for all on B_c→J/ψ(η_c) synthetic data and then copied to the P-wave channels by the spin-symmetry assumption. Because the R ratios cancel the overall normalizations, their central values and tiny quoted errors are controlled almost entirely by those transferred shapes. This is residual circularity of the self-citation / transferred-fit kind, not a definitional identity, so the score remains moderate.

Axiom & Free-Parameter Ledger

5 free parameters · 3 axioms · 0 invented entities

The central predictions rest on a handful of fitted non-perturbative numbers (wave-function derivatives and shape parameters) together with standard NRQCD factorisation and heavy-quark spin symmetry; no new dynamical entities are postulated.

free parameters (5)
  • ψ'_R_χc0(0) = 0.143(45) GeV^{5/2}
    Fitted to B(χ_c0 oγγ) and related radiative data; controls overall normalisation of B_c oχ_c0 form factors.
  • ψ'_R_χc1(0) = 0.115(49) GeV^{5/2}
    Fitted simultaneously to χ_c1 radiative modes; sets size of B_c oχ_c1 form factors.
  • ψ'_R_hc(0) = 0.122(65) GeV^{5/2}
    Fitted to B(h_c oη_cγ); sets size of B_c o h_c form factors.
  • α_i, β (pole-expansion coefficients) = see Table 7
    Taken from B_c o J/ψ,η_c fits under spin symmetry and used for all P-wave form-factor shapes.
  • δ_corr (missing higher-order pieces) = 0 ± 0.1–0.2
    Nuisance parameters with 10–20 % priors that absorb unknown O(v^{4},α_s^{2}) corrections in the radiative widths.
axioms (3)
  • domain assumption NRQCD factorisation of B_c o P-wave form factors into short-distance coefficients times wave-function derivatives at the origin (Eq. 3.12).
    Taken from Zhu (2018) and used throughout §3.1; validity at the physical charm mass is assumed rather than proven.
  • domain assumption Heavy-quark spin symmetry equates the q^{2}-shape parameters of form factors for final states of equal total angular momentum J.
    Invoked explicitly after Eq. 3.59 to transfer α_i,β from S-wave to P-wave channels.
  • standard math BCL z-expansion truncated at linear order with a conservative 50 % estimate for the quadratic coefficient.
    Standard analyticity argument; truncation error quantified in §3.4.

pith-pipeline@v1.1.0-grok45 · 51813 in / 3038 out tokens · 25645 ms · 2026-07-11T06:17:58.553471+00:00 · methodology

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read the original abstract

We analyse semileptonic and non-leptonic decays of the $B_c$ meson into P wave charmonium states. The analytic expressions for the transition form factors are taken from NRQCD, while their normalisations and shapes are constrained directly using experimental data, without introducing any additional model-dependent inputs. Using radiative decay data of $\chi_{c0}$, $\chi_{c1}$, and $h_c$, we extract the derivatives of their radial wave functions at the origin and update the $B_c \to (\chi_{c0}, \chi_{c1}, h_c)$ form factors. We present predictions for the semileptonic branching fractions, the lepton flavour universality ratios $R(\chi_{c0})=0.185(3)$, $R(\chi_{c1})=0.147(26)$, and $R(h_c)=0.068(2)$, as well as selected non-leptonic $B_c$ decays and P-wave charmonium production in $e^+e^-$ annihilation and $Z$-boson decays.

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Works this paper leans on

84 extracted references · 75 linked inside Pith

  1. [1]

    Chang and X.-G

    C.-H. Chang and X.-G. Wu,Uncertainties in estimating hadronic production of the mesonB c and comparisons between TEVATRON and LHC,Eur. Phys. J. C38(2004) 267 [hep-ph/0309121]. [3]LHCbcollaboration,Measurement of the ratio of branching fractions B(B + c →J/ψτ +ντ)/B(B + c →J/ψµ +νµ),Phys. Rev. Lett.120(2018) 121801 [1711.05623]. [4]CMScollaboration,Test of...

    Pith/arXiv arXiv 2004

  2. [2]

    A. Y. Anisimov, I. M. Narodetsky, C. Semay and B. Silvestre-Brac,TheB c meson lifetime in the light front constituent quark model,Phys. Lett. B452(1999) 129 [hep-ph/9812514]. – 45 –

    Pith/arXiv arXiv 1999

  3. [3]

    V. V. Kiselev, A. K. Likhoded and A. I. Onishchenko,SemileptonicB c meson decays in sum rules of QCD and NRQCD,Nucl. Phys. B569(2000) 473 [hep-ph/9905359]

    Pith/arXiv arXiv 2000

  4. [4]

    V. V. Kiselev,Exclusive decays and lifetime ofB c meson in QCD sum rules,hep-ph/0211021

    Pith/arXiv arXiv

  5. [5]

    M. A. Ivanov, J. G. Korner and P. Santorelli,Exclusive semileptonic and nonleptonic decays of the Bc meson,Phys. Rev. D73(2006) 054024 [hep-ph/0602050]

    Pith/arXiv arXiv 2006

  6. [6]

    Hernandez, J

    E. Hernandez, J. Nieves and J. M. Verde-Velasco,Study of exclusive semileptonic and non-leptonic decays ofB c - in a nonrelativistic quark model,Phys. Rev. D74(2006) 074008 [hep-ph/0607150]

    Pith/arXiv arXiv 2006

  7. [7]

    Qiao and R.-L

    C.-F. Qiao and R.-L. Zhu,Estimation of semileptonic decays ofB c meson to S wave charmonia with nonrelativistic QCD,Phys. Rev. D87(2013) 014009 [1208.5916]

    Pith/arXiv arXiv 2013

  8. [8]

    Wang, Y.-Y

    W.-F. Wang, Y.-Y. Fan and Z.-J. Xiao,Semileptonic decaysB c →(η c, J/ψ)ℓνin the perturbative QCD approach,Chin. Phys. C37(2013) 093102 [1212.5903]

    Pith/arXiv arXiv 2013

  9. [9]

    Z. Rui, H. Li, G.-x. Wang and Y. Xiao,Semileptonic decays ofB c meson to S-wave charmonium states in the perturbative QCD approach,Eur. Phys. J. C76(2016) 564 [1602.08918]

    Pith/arXiv arXiv 2016

  10. [10]

    Dutta and A

    R. Dutta and A. Bhol,B c →(J/ψ, η c)τ νsemileptonic decays within the standard model and beyond, Phys. Rev. D96(2017) 076001 [1701.08598]

    Pith/arXiv arXiv 2017

  11. [11]

    Watanabe,New Physics effect onB c →J/ψτ¯νin relation to theR D(∗) anomaly,Phys

    R. Watanabe,New Physics effect onB c →J/ψτ¯νin relation to theR D(∗) anomaly,Phys. Lett. B 776(2018) 5 [1709.08644]

    Pith/arXiv arXiv 2018

  12. [12]

    Issadykov and M

    A. Issadykov and M. A. Ivanov,The decaysB c →J/ψ+ ¯ℓνℓ andB c →J/ψ+π(K)in covariant confined quark model,Phys. Lett. B783(2018) 178 [1804.00472]

    Pith/arXiv arXiv 2018

  13. [13]

    Leljak, B

    D. Leljak, B. Melic and M. Patra,On lepton flavour universality in semileptonicB c →η c, J/ψ decays,JHEP05(2019) 094 [1901.08368]

    Pith/arXiv arXiv 2019

  14. [14]

    T. D. Cohen, H. Lamm and R. F. Lebed,Model-independent bounds onR(J/ψ),JHEP09(2018) 168 [1807.02730]. [19]Particle Data Groupcollaboration,Review of Particle Physics,PTEP2020(2020) 083C01. [20]LHCbcollaboration,Study ofB + c decays to theK +K −π+ final state and evidence for the decay B+ c →χ c0π+,Phys. Rev. D94(2016) 091102 [1607.06134]

    Pith/arXiv arXiv 2018

  15. [15]

    Rui and Z.-T

    Z. Rui and Z.-T. Zou,S-wave ground state charmonium decays ofb c mesons in the perturbative qcd approach,Phys. Rev. D90(2014) 114030

    2014

  16. [16]

    Sun, D.-S

    J.-F. Sun, D.-S. Du and Y.-L. Yang,Study ofB c →J/ψπ,η cπdecays with perturbative QCD approach,Eur. Phys. J. C60(2009) 107 [0808.3619]

    Pith/arXiv arXiv 2009

  17. [17]

    Liu,B c-meson decays intoJ/ψplus a light meson in the improved perturbative QCD formalism, Phys

    X. Liu,B c-meson decays intoJ/ψplus a light meson in the improved perturbative QCD formalism, Phys. Rev. D108(2023) 096006 [2305.00713]

    Pith/arXiv arXiv 2023

  18. [18]

    Z. Rui, J. Zhang and L.-L. Zhang,Semileptonic decays ofB c meson toP-wave charmonium states, Phys. Rev. D98(2018) 033007 [1806.00796]

    Pith/arXiv arXiv 2018

  19. [19]

    M. A. Nobes and R. M. Woloshyn,Decays of theB c meson in a relativistic quark meson model,J. Phys. G26(2000) 1079 [hep-ph/0005056]

    Pith/arXiv arXiv 2000

  20. [20]

    Ebert, R

    D. Ebert, R. N. Faustov and V. O. Galkin,Weak decays of theB c meson to charmonium andD mesons in the relativistic quark model,Phys. Rev. D68(2003) 094020 [hep-ph/0306306]

    Pith/arXiv arXiv 2003

  21. [21]

    M. A. Ivanov, J. G. Korner and P. Santorelli,Semileptonic decays ofB c mesons into charmonium states in a relativistic quark model,Phys. Rev. D71(2005) 094006 [hep-ph/0501051]

    Pith/arXiv arXiv 2005

  22. [22]

    Ebert, R

    D. Ebert, R. N. Faustov and V. O. Galkin,Semileptonic and Nonleptonic Decays ofB c Mesons to Orbitally Excited Heavy Mesons in the Relativistic Quark Model,Phys. Rev. D82(2010) 034019 [1007.1369]. – 46 –

    Pith/arXiv arXiv 2010

  23. [23]

    Nayak, P

    L. Nayak, P. C. Dash, S. Kar and N. Barik,Exclusive semileptonicB c-meson decays to radially excited charmonium and charm meson states,Eur. Phys. J. C82(2022) 750 [2204.04453]

    Pith/arXiv arXiv 2022

  24. [24]

    Colangelo, G

    P. Colangelo, G. Nardulli and N. Paver,QCD sum rules calculation ofB c decays,Z. Phys. C57 (1993) 43

    1993

  25. [25]

    Azizi, H

    K. Azizi, H. Sundu and M. Bayar,SemileptonicB c to P-Wave Charmonia (χ c0, χc1, hc) Transitions within QCD Sum Rules,Phys. Rev. D79(2009) 116001 [0902.1467]

    Pith/arXiv arXiv 2009

  26. [26]

    Azizi, Y

    K. Azizi, Y. Sarac and H. Sundu,Investigation of theB c →χ c2ℓ¯νtransition via QCD sum rules, Eur. Phys. J. C73(2013) 2638 [1306.4095]

    Pith/arXiv arXiv 2013

  27. [27]

    Wang, Y.-L

    W. Wang, Y.-L. Shen and C.-D. Lu,Covariant Light-Front Approach forB c transition form factors, Phys. Rev. D79(2009) 054012 [0811.3748]

    Pith/arXiv arXiv 2009

  28. [28]

    H.-W. Ke, T. Liu and X.-Q. Li,Transitions ofB c →ψ(1S,2S)and the modified harmonic oscillator wave function in LFQM,Phys. Rev. D89(2014) 017501 [1307.5925]

    Pith/arXiv arXiv 2014

  29. [29]

    Brambilla, A

    N. Brambilla, A. Pineda, J. Soto and A. Vairo,Effective Field Theories for Heavy Quarkonium,Rev. Mod. Phys.77(2005) 1423 [hep-ph/0410047]

    Pith/arXiv arXiv 2005

  30. [30]

    G. T. Bodwin, E. Braaten and G. P. Lepage,Rigorous qcd analysis of inclusive annihilation and production of heavy quarkonium,Phys. Rev. D51(1995) 1125

    1995

  31. [31]

    G. T. Bodwin, D. Kang and J. Lee,Reconciling the light-cone and NRQCD approaches to calculating e+e− →J/ψ+η(c),Phys. Rev. D74(2006) 114028 [hep-ph/0603185]

    Pith/arXiv arXiv 2006

  32. [32]

    Brambilla et al.,Heavy Quarkonium: Progress, Puzzles, and Opportunities,Eur

    N. Brambilla et al.,Heavy Quarkonium: Progress, Puzzles, and Opportunities,Eur. Phys. J. C71 (2011) 1534 [1010.5827]

    Pith/arXiv arXiv 2011

  33. [33]

    V. V. Kiselev, O. N. Pakhomova and V. A. Saleev,Two particle decays ofB c meson into charmonium states,J. Phys. G28(2002) 595 [hep-ph/0110180]

    Pith/arXiv arXiv 2002

  34. [34]

    Bell and T

    G. Bell and T. Feldmann,Heavy-to-light form-factors for non-relativistic bound states,Nucl. Phys. B Proc. Suppl.164(2007) 189 [hep-ph/0509347]

    Pith/arXiv arXiv 2007

  35. [35]

    Bell,Higher order QCD corrections in exclusive charmless B decays, Ph.D

    G. Bell,Higher order QCD corrections in exclusive charmless B decays, Ph.D. thesis, Munich U., 2006.0705.3133

    arXiv 2006

  36. [36]

    Qiao and P

    C.-F. Qiao and P. Sun,NLO QCD Corrections toB c-to-Charmonium Form Factors,JHEP08 (2012) 087 [1103.2025]

    Pith/arXiv arXiv 2012

  37. [37]

    C.-F. Qiao, P. Sun, D. Yang and R.-L. Zhu,B c exclusive decays to charmonium and a light meson at next-to-leading order accuracy,Phys. Rev. D89(2014) 034008 [1209.5859]

    Pith/arXiv arXiv 2014

  38. [38]

    R. Zhu, Y. Ma, X.-L. Han and Z.-J. Xiao,Relativistic corrections to the form factors ofB c into S wave Charmonium,Phys. Rev. D95(2017) 094012 [1703.03875]

    Pith/arXiv arXiv 2017

  39. [39]

    Zhu,Relativistic corrections to the form factors ofB c intoP-wave orbitally excited charmonium, Nucl

    R. Zhu,Relativistic corrections to the form factors ofB c intoP-wave orbitally excited charmonium, Nucl. Phys. B931(2018) 359 [1710.07011]

    Pith/arXiv arXiv 2018

  40. [40]

    Tao, Z.-J

    W. Tao, Z.-J. Xiao and R. Zhu,Next-to-leading order QCD calculation ofB c to charmonium tensor form factors,Phys. Rev. D105(2022) 114026 [2204.06385]

    Pith/arXiv arXiv 2022

  41. [41]

    J. G. Korner and G. A. Schuler,Exclusive Semileptonic Heavy Meson Decays Including Lepton Mass Effects,Z. Phys. C46(1990) 93

    1990

  42. [42]

    Biswas, S

    A. Biswas, S. Nandi and S. Sahoo,Analyzing the semileptonic and nonleptonicB c →J/ψ, η c decays, 2311.00758

    Pith/arXiv arXiv

  43. [43]

    G. C. Donald, C. T. H. Davies, R. J. Dowdall, E. Follana, K. Hornbostel, J. Koponen et al., Precision tests of theJ/ψfrom full lattice QCD: mass, leptonic width and radiative decay rate toη c, Phys. Rev. D86(2012) 094501 [1208.2855]. – 47 –

    Pith/arXiv arXiv 2012

  44. [44]

    C. T. H. Davies, C. McNeile, E. Follana, G. P. Lepage, H. Na and J. Shigemitsu,Update: Precision Ds decay constant from full lattice QCD using very fine lattices,Phys. Rev. D82(2010) 114504 [1008.4018]. [51]HPQCDcollaboration,B-meson decay constants: a more complete picture from full lattice QCD, Phys. Rev. D91(2015) 114509 [1503.05762]. [52]HPQCDcollabor...

    Pith/arXiv arXiv 2010

  45. [45]

    Bourrely, I

    C. Bourrely, I. Caprini and L. Lellouch,Model-independent description ofB→πℓνdecays and a determination of|V ub|,Phys. Rev. D79(2009) 013008 [0807.2722]

    Pith/arXiv arXiv 2009

  46. [46]

    Mathur, M

    N. Mathur, M. Padmanath and S. Mondal,Precise predictions of charmed-bottom hadrons from lattice QCD,Phys. Rev. Lett.121(2018) 202002 [1806.04151]

    Pith/arXiv arXiv 2018

  47. [47]

    C. G. Boyd, B. Grinstein and R. F. Lebed,Constraints on form-factors for exclusive semileptonic heavy to light meson decays,Phys. Rev. Lett.74(1995) 4603 [hep-ph/9412324]

    Pith/arXiv arXiv 1995

  48. [48]

    C. G. Boyd, B. Grinstein and R. F. Lebed,Precision corrections to dispersive bounds on form-factors,Phys. Rev. D56(1997) 6895 [hep-ph/9705252]

    Pith/arXiv arXiv 1997

  49. [49]

    Ray and S

    I. Ray and S. Nandi,Test of new physics effects in ¯B→(D (∗), π)ℓ−¯νℓ decays with heavy and light leptons,2305.11855

    Pith/arXiv arXiv

  50. [50]

    Li, C.-D

    R.-H. Li, C.-D. Lu and W. Wang,Transition form factors of B decays into p-wave axial-vector mesons in the perturbative QCD approach,Phys. Rev. D79(2009) 034014 [0901.0307]

    Pith/arXiv arXiv 2009

  51. [51]

    Kivel and M

    N. Kivel and M. Vanderhaeghen,Radiative decaysχ cJ →V γwithin the QCD factorization framework,Phys. Rev. D96(2017) 054007 [1703.10383]

    Pith/arXiv arXiv 2017

  52. [52]

    H. S. Chung,P-wave quarkonium wavefunctions at the origin in the M Sscheme,JHEP09(2021) 195 [2106.15514]

    Pith/arXiv arXiv 2021

  53. [53]

    V. M. Braun et al.,Theρ-meson light-cone distribution amplitudes from lattice QCD,JHEP04 (2017) 082 [1612.02955]

    Pith/arXiv arXiv 2017

  54. [54]

    Ball and G

    P. Ball and G. W. Jones,Twist-3 distribution amplitudes ofK ∗ andϕmesons,JHEP03(2007) 069 [hep-ph/0702100]

    Pith/arXiv arXiv 2007

  55. [55]

    Ball and V

    P. Ball and V. M. Braun,The Rho meson light cone distribution amplitudes of leading twist revisited, Phys. Rev. D54(1996) 2182 [hep-ph/9602323]

    Pith/arXiv arXiv 1996

  56. [56]

    Ball and V

    P. Ball and V. M. Braun,Higher twist distribution amplitudes of vector mesons in QCD: Twist - 4 distributions and meson mass corrections,Nucl. Phys. B543(1999) 201 [hep-ph/9810475]

    Pith/arXiv arXiv 1999

  57. [57]

    P. Ball, V. M. Braun, Y. Koike and K. Tanaka,Higher twist distribution amplitudes of vector mesons in QCD: Formalism and twist - three distributions,Nucl. Phys. B529(1998) 323 [hep-ph/9802299]

    Pith/arXiv arXiv 1998

  58. [58]

    Brambilla, P

    N. Brambilla, P. Pietrulewicz and A. Vairo,Model-independent study of electric dipole transitions in quarkonium,Phys. Rev. D85(2012) 094005. [67]Quarkonium Working Groupcollaboration,Heavy quarkonium physics,hep-ph/0412158

    Pith/arXiv arXiv 2012

  59. [59]

    H. E. Mart´ ınez Neira,Phenomenology of the radiative E1 heavy quarkonium decay, Ph.D. thesis, Munich, Tech. U., 2017

    2017

  60. [60]

    G. T. Bodwin and A. Petrelli,Order-v 4 corrections toS-wave quarkonium decay,Phys. Rev. D66 (2002) 094011 [hep-ph/0205210]

    Pith/arXiv arXiv 2002

  61. [61]

    Guo, Y.-Q

    H.-K. Guo, Y.-Q. Ma and K.-T. Chao,O(α sv2)Corrections to Hadronic and Electromagnetic Decays of 1S0 Heavy Quarkonium,Phys. Rev. D83(2011) 114038 [1104.3138]

    Pith/arXiv arXiv 2011

  62. [62]

    J. Lee, J. H. Ee, U.-R. Kim and C. Yu,Quarkonium physics: NRQCD factorization formula for J/ψ→e +e−,CERN Yellow Rep. School Proc.2(2018) 69. – 48 –

    2018

  63. [63]

    Xu, Y.-J

    G.-Z. Xu, Y.-J. Li, K.-Y. Liu and Y.-J. Zhang,α sv2 corrections toη c andχ cJ production recoiled with a photon ate +e− colliders,JHEP10(2014) 071 [1407.3783]

    Pith/arXiv arXiv 2014

  64. [64]

    W.-L. Sang, F. Feng, Y. Jia and S.-R. Liang,Next-to-next-to-leading-order QCD corrections to χc0,2 →γγ,Phys. Rev. D94(2016) 111501 [1511.06288]

    Pith/arXiv arXiv 2016

  65. [65]

    E. J. Eichten and C. Quigg,Quarkonium wave functions at the origin,Phys. Rev. D52(1995) 1726 [hep-ph/9503356]

    Pith/arXiv arXiv 1995

  66. [66]

    Eichten, K

    E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane and T.-M. Yan,Charmonium: The Model,Phys. Rev. D17(1978) 3090

    1978

  67. [67]

    E. J. Eichten and C. Quigg,Quarkonium wave functions at the origin: an update,1904.11542

    Pith/arXiv arXiv 1904

  68. [68]

    Dey and S

    U. Dey and S. Nandi,Correlated study on someB c →PandB c →Swave channels in light of new inputs,2503.01693

    Pith/arXiv arXiv

  69. [69]

    S. K. Patra,OptEx, 2019

    2019

  70. [70]

    X.-X. Wang, W. Wang and C.-D. Lu,B c to P-Wave Charmonia Transitions in Covariant Light-Front Approach,Phys. Rev. D79(2009) 114018 [0901.1934]

    Pith/arXiv arXiv 2009

  71. [71]

    Chen and C.-F

    Z.-Q. Chen and C.-F. Qiao,B c meson exclusive decays to a P-wave charmonium and a pion at NLO accuracy,Phys. Rev. D104(2021) 016019 [2105.12066]

    Pith/arXiv arXiv 2021

  72. [72]

    Beyer and D

    M. Beyer and D. Melikhov,Form-factors of exclusive b→u transitions,Phys. Lett. B436(1998) 344 [hep-ph/9807223]

    Pith/arXiv arXiv 1998

  73. [73]

    Melikhov and B

    D. Melikhov and B. Stech,Weak form-factors for heavy meson decays: An Update,Phys. Rev. D62 (2000) 014006 [hep-ph/0001113]

    Pith/arXiv arXiv 2000

  74. [74]

    Wang and R

    W. Wang and R. Zhu,Model independent investigation of theR J/ψ,ηc and ratios of decay widths of semileptonicB c decays into a P-wave charmonium,Int. J. Mod. Phys. A34(2019) 1950195 [1808.10830]

    Pith/arXiv arXiv 2019

  75. [75]

    Chang, Y.-Q

    C.-H. Chang, Y.-Q. Chen, G.-L. Wang and H.-S. Zong,Decays of the mesonB c to a P wave charmonium stateχ c orh c,Phys. Rev. D65(2002) 014017 [hep-ph/0103036]

    Pith/arXiv arXiv 2002

  76. [76]

    Rui,Probing theP-wave charmonium decays ofB c meson,Phys

    Z. Rui,Probing theP-wave charmonium decays ofB c meson,Phys. Rev. D97(2018) 033001 [1712.08928]

    Pith/arXiv arXiv 2018

  77. [77]

    Losacco,NonleptonicB c decay rates from model independent relations,Mod

    N. Losacco,NonleptonicB c decay rates from model independent relations,Mod. Phys. Lett. A38 (2023) 2350027 [2302.12534]

    Pith/arXiv arXiv 2023

  78. [78]

    Wang, G.-L

    Z.-h. Wang, G.-L. Wang and C.-H. Chang,TheB c Decays toP-wave Charmonium by Improved Bethe-Salpeter Approach,J. Phys. G39(2012) 015009 [1107.0474]

    Pith/arXiv arXiv 2012

  79. [79]

    Buchalla, A

    G. Buchalla, A. J. Buras and M. E. Lautenbacher,Weak decays beyond leading logarithms,Rev. Mod. Phys.68(1996) 1125 [hep-ph/9512380]. [89]RQCDcollaboration,Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD, JHEP08(2019) 065 [1903.08038]

    Pith/arXiv arXiv 1996

  80. [80]

    A. K. Likhoded and A. V. Luchinsky,Double Charmonia Production in ExclusiveZBoson Decays, Mod. Phys. Lett. A33(2018) 1850078 [1712.03108]

    Pith/arXiv arXiv 2018

Showing first 80 references.