Pith. sign in

REVIEW 2 major objections 4 minor 62 references

Hadroproduction data support tetraquark hypothesis for $\chi_{c1} (3872)$

T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read A single color-octet channel, fixed by the wavefunction, reproduces χc1(3872) production at the LHC.

desk verdict One clean parameter-free ratio test, but the absolute cross sections are normalized to B-decay data, so the 'no unknown parameters' claim is overstated. read the letter →

arxiv 2505.06910 v2 pith:CRGSSLMN submitted 2025-05-11 hep-ph

Wai Kin Lai , Hee Sok Chung This is my paper · ORCID
classification hep-ph
keywords χc1(3872)tetraquarkNRQCDfactorizationcolor-octetmatrixelementhadroproductionnonpromptfractionpotential-modelwavefunctionthresholdresummationexotichadronproduction
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 tetraquark interpretation of $\chi_{c1}(3872)$ — a state in which the charm–anticharm pair sits in a color-octet $S$-wave at short distances — makes a parameter-free prediction for how often the particle is produced in high-energy proton collisions. In the nonrelativistic QCD (NRQCD) factorization formalism, only a single color-octet channel contributes at leading power, and its nonperturbative matrix element is determined by the $c\bar c$ wavefunction at the origin. The authors compute prompt and nonprompt cross sections at the LHC and find general agreement with CMS, ATLAS, and LHCb data, including the nonprompt fraction, which is predicted without any fitted parameter. If this agreement holds, hadroproduction data would support the tetraquark hypothesis over molecular, charmonium, and mixing pictures of $\chi_{c1}(3872)$.

What carries the argument

The central object is the NRQCD color-octet matrix element $\langle O^{\chi_{c1}(3872)}({}^3S_1^{[8]}) \rangle$, which measures the probability that the charm–anticharm pair inside $\chi_{c1}(3872)$ is in the color-octet spin-triplet $S$-wave state. The argument works because the tetraquark hypothesis places the $c\bar c$ pair in exactly this Fock state at short distances, so only this one matrix element appears at leading power; the color-singlet $P$-wave and octet $D$-wave contributions are suppressed by powers of the ratio of the hadronic scale to the charm mass. The calculation then uses potential-model wavefunctions to convert this matrix element into $3|\varphi(0)|^2$, with $\varphi$ the $c\bar c$ wavefunction at zero separation, so the production rate carries no unknown nonperturbative parameters once the tetraquark potential is specified.

What would settle it

Compute the color-octet $c\bar c$ wavefunction at the origin from first-principles QCD, for instance on the lattice or in the effective-field-theory tetraquark picture, and check whether $|\varphi(0)|^2$ falls within the range $0.69\times 10^{-3}$ to $2.0\times 10^{-3}\,\text{GeV}^3$ spanned by the potential models used here; a value outside that range would eliminate the agreement with the measured absolute cross sections.

Watch

Extended reading notes

Core claim

Under the tetraquark hypothesis examined here, the dominant Fock state of $\chi_{c1}(3872)$ is a color-octet spin-triplet $S$-wave $c\bar c$ pair, so at leading power in the nonrelativistic expansion the inclusive cross section factorizes as $\sigma_{\chi_{c1}(3872)} = \sigma_{c\bar c}({}^3S_1^{[8]}) \times \langle O({}^3S_1^{[8]}) \rangle$, with no competing channels. The paper establishes that this single-channel structure makes the nonprompt fraction independent of the nonperturbative matrix element, and that the matrix element itself is $\langle O({}^3S_1^{[8]}) \rangle = 3|\varphi(0)|^2$, computable from the wavefunction of the tetraquark potential model. Using a value of $|\varphi(0)|^2$ within the potential-model range and fixed to LHCb $b$-decay data, the authors obtain prompt and nonprompt cross sections consistent with CMS, ATLAS, and LHCb measurements; the resummed predictions describe the nonprompt fraction well, whereas fixed-order results lie below data. The conclusion is that hadroproduction data support the tetraquark hypothesis.

Load-bearing premise

The calculation assumes that the $c\bar c$ wavefunction obtained from a wave equation with potentials tuned to the tetraquark spectrum gives the true NRQCD matrix element through $\langle O({}^3S_1^{[8]}) \rangle = 3|\varphi(0)|^2$; if those potentials are not reliable, the parameter-free cross-section predictions lose their meaning.

Editorial extensions

If this is right

  • The nonprompt fraction of $\chi_{c1}(3872)$ production is predicted with no fitted parameter, because the matrix element cancels in the ratio; the resummed prediction agrees with CMS and ATLAS data.
  • Prompt hadroproduction cross sections at LHC energies are reproduced by a single color-octet channel, with resummation of threshold logarithms essential at large transverse momentum.
  • Nonprompt rates from $b$-hadron decays agree with ATLAS and LHCb measurements when the matrix element is fixed to the LHCb branching-fraction data.
  • The mixing model, which requires two nonperturbative unknowns, predicts $b$-decay production branching fractions more than three times smaller than LHCb observes, so the tetraquark picture fits the nonprompt data better.
  • If the tetraquark picture is right, $\chi_{c1}(3872)$ production becomes a direct probe of perturbative color-octet $c\bar c$ production in QCD.

Reading between the lines

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

  • A natural extension is to apply the same single-channel, wavefunction-determined formalism to other exotic candidates whose dominant Fock state is an $S$-wave color-octet heavy-quark pair, such as certain hybrid mesons.
  • The claim of no unknown parameters is conditional on the effective potentials tuned to the tetraquark spectrum; a first-principles calculation of the octet wavefunction at the origin would test it directly.
  • High-precision measurements of the nonprompt fraction at very large transverse momentum could discriminate the production mechanism even without absolute normalization, because the resummed and fixed-order predictions separate there.
  • Since the absolute normalization is tied to $|\varphi(0)|^2$, more precise measurements of $\chi_{c1}(3872)$ production could indirectly constrain the effective tetraquark potential.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper argues that the tetraquark (c\bar c q\bar q) interpretation of \chi_{c1}(3872) proposed in Refs. [29-31] leads to an NRQCD factorization formula in which inclusive production is dominated by a single color-octet ^3S_1^{[8]} c\bar c channel (Eq. (1)). The authors further claim that the corresponding nonperturbative matrix element \langle O(^3S_1^{[8]}) \rangle is fixed by the c\bar c wavefunction at the origin through Eq. (9), leaving no unknown parameters. Using this setup, they compute the nonprompt fraction (Sec. III), prompt cross sections (Fig. 2), and nonprompt cross sections (Fig. 3) at LHC energies, with both fixed-order and threshold-resummed ingredients, and report agreement with CMS, ATLAS, and LHCb data, concluding that hadroproduction data support the tetraquark hypothesis.

Significance. The parameter-free test in Sec. III is genuinely valuable: because the matrix element cancels in Eq. (2), the nonprompt fraction is a direct prediction of the single-channel hypothesis, and its fair agreement with CMS and ATLAS data (Fig. 1) is a nontrivial success. The single-channel dominance itself is an interesting structural consequence of the tetraquark scenario. However, the broader claim that the formalism has no unknown parameters and that the absolute cross sections independently support the tetraquark hypothesis is not realized: the matrix element used in Figs. 2 and 3 is not taken from the potential-model wavefunction but is fixed to the measured b-decay branching-fraction product in Sec. IV.B. The paper's independent phenomenological content therefore rests mainly on the nonprompt fraction; the absolute cross-section agreement is a consistency check conditional on that input. This distinction substantially changes the strength of the conclusion.

major comments (2)
  1. [Sec. IV.B and Eq. (9)] The claim that the production formalism has no unknown parameters is not matched by the numerical procedure. Eq. (9) states \langle O(^3S_1^{[8]}) \rangle = 3|\phi(0)|^2, and Sec. IV.A says the wavefunction is computable from a Schr\"odinger equation. But Sec. IV.B reports that the potential models of Refs. [29-31] give |\phi(0)|^2 values between 0.69\times10^{-3} and 2.0\times10^{-3} GeV^3, and then "for obtaining phenomenological results in this work we choose to fix |\phi(0)|^2 against the experimental value" Br(b\to\chi_{c1}(3872)+X)\times Br(\chi_{c1}(3872)\to J/\psi\pi^+\pi^-) = (4.3\pm0.5)\times10^{-5}, leading to |\phi(0)|^2=1.8\times10^{-3} GeV^3. Consequently the absolute prompt and nonprompt cross sections in Figs. 2 and 3 are normalized to a hadronic B-decay measurement rather than predicted from the tetraquark potentials. The agreement of those curves with hadroproduction data is therefore partly built in and does not independently test the tetraquark hypothesis in the way the abstract and Sec. I claim. The authors should either (a) quote the full potential-model spread as the prediction and compare it to data, or (b) explicitly demote the absolute cross sections to consistency checks and state that the no-unknown-parameters formalism has not yet been numerically realized.
  2. [Sec. V, Limitations] The concluding section itself concedes: "the nonperturbative matrix element fixed against LHCb data [24] used in this work is within the range of potential model calculations based on Refs. [29-31]". This admission confirms that the computation is not parameter-free and that the potential-model prediction is not precise enough to be used directly. The abstract and introduction should therefore not claim that the absolute cross sections provide a parameter-free test. What is currently demonstrated as parameter-free is the nonprompt fraction of Eq. (2), plus the single-channel dominance structure; the absolute rates are consistency checks conditioned on the measured B-decay branching-fraction product.
minor comments (4)
  1. [Fig. 1 caption] The caption of Fig. 1 does not define the meaning of the curves (FO versus resummed, and whether the nonprompt part uses FONLL with nonperturbative fragmentation). Please add a sentence describing the theoretical curves and the uncertainty band.
  2. [Sec. III, FONLL description] The text says "We take the fixed order+next-to-leading log (FONLL) result for \sigma_b [43,44], in which we include the correction from the nonperturbative fragmentation function". Please clarify which nonperturbative fragmentation function is used and how it is matched to the NLO short-distance coefficient C(b\to c\bar c(^3S_1^{[8]})+X).
  3. [Sec. IV.C, Mixing model] The statement that the mixing model of Refs. [27,28] leads to Br(b\to\chi_{c1}(3872)+X)Br(\chi_{c1}(3872)\to J/\psi\pi^+\pi^-) less than about 1.1\times10^{-5} is not accompanied by the derivation or the input values. Please include a brief explanation or a reference to where this bound is obtained.
  4. [Eq. (8)] The dimensionless quantity S defined by the vacuum expectation value of adjoint Wilson lines should have its renormalization scale and scheme specified, since the text states S=1+O(\alpha_s^2) and the NLO correction vanishes [46].

Circularity Check

1 steps flagged · score 6.0 of 10

Absolute cross sections are not parameter-free: |phi(0)|^2 is fixed to LHCb branching data in Sec. IV.B, so absolute-rate agreement is partly built in; only the nonprompt fraction is an independent prediction.

  1. fitted input called prediction [Section IV.B ('Prediction of cross sections'), after Eq. (9); consequential for Figs. 2 and 3 and Sec. V.]
    "In practice, however, we find that the result varies depending on the choice of potentials and parameters of the Schrödinger equation; we obtain values of |φ(0)|^2 that range from 0.69×10^-3 to 2.0×10^-3 GeV^3 from Refs. [29–31]. As our knowledge of the tetraquark potential is currently limited, for obtaining phenomenological results in this work we choose to fix |φ(0)|^2 against the experimental value Br(b→ χ_{c1}(3872)+X)× Br(χ_{c1}(3872)→ J/ψπ^+π^-) = (4.3±0.5)×10^-5 from LHCb [24] ..."

    Eq. (1) makes every absolute cross section proportional to ⟨O^{χc1(3872)}(3S1[8])⟩ = 3|φ(0)|^2, and Eq. (3) sets Br(b→χc1(3872)+X) = C(b→c-cbar(3S1[8])+X)⟨O⟩. Fixing |φ(0)|^2 to the LHCb product of this b-decay branching fraction times the χc1(3872)→J/ψπ^+π^- branching fraction fixes ⟨O⟩ from the inclusive nonprompt rate itself. The predicted nonprompt cross section is then proportional to that same measured product, so its overall normalization agrees with data by construction, and the prompt cross section inherits the same fitted normalization. Thus the absolute-rate 'predictions' in Figs. 2 and 3 are not parameter-free tests of the tetraquark hypothesis; only the nonprompt fraction of Sec. III, where ⟨O⟩ cancels, is independent. The paper concedes this in Sec.

full rationale

The core nonprompt-fraction prediction (Sec. III) is genuinely non-circular: in Eq. (2) the NRQCD matrix element cancels, and the result depends only on perturbatively computed short-distance coefficients and FONLL b-quark production, with no fitted parameter. That part provides independent support for the tetraquark scenario. However, the paper's headline claim of 'no unknown parameters' and the absolute prompt/nonprompt cross-section comparison are compromised by the procedure in Sec. IV.B: although Eq. (9) formally expresses the matrix element through the potential-model wavefunction, the central value |φ(0)|^2 = 1.8×10^-3 GeV^3 is not obtained from the Schrödinger equation but is 'fix[ed] ... against the experimental value' of the LHCb branching-fraction product. The same product controls the normalization of the nonprompt cross section through Eq. (3), so part of the agreement shown in Figs. 2 and 3 is built in rather than predicted. There is no load-bearing self-citation chain: the cited potential-model papers [29–31] and resummation results [46] are external or methodologically independent, and the nonprompt fraction does not rely on the fitted matrix element. The circularity is partial and localized: the matrix-element cancellation saves the nonprompt fraction, but the absolute-cross-section test advertised as parameter-free reduces, at the normalization level, to the branching-fraction input used to set |φ(0)|^2.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central free parameter is the wavefunction at the origin, used to set the NRQCD matrix element. The tetraquark potential model and the wavefunction mapping are domain assumptions that are not yet derived from first principles. No new particles or interactions are introduced.

free parameters (2)
  • |φ(0)|^2 (c-cbar wavefunction at origin) = 1.8e-3 GeV^3
    Fixed to reproduce the measured Br(b→χc1(3872)+X)*Br(χc1(3872)→J/ψπ+π-) = 4.3e-5 (LHCb + PDG); potential models give a range 0.69e-3 to 2.0e-3 GeV^3.
  • NRQCD matrix element ⟨O(3S1[8])⟩ = 5.5e-3 GeV^-3
    Derived from |φ(0)|^2 via Eq. (9); same fitted status as the wavefunction input.
assumptions (5)
  • domain assumption NRQCD factorization for inclusive quarkonium production
    Used in Eq. (1) to write the cross section as short-distance × long-distance matrix element; standard in quarkonium phenomenology but an assumption.
  • ad hoc to paper Tetraquark BOEFT potential model from Refs [29-31] accurately describes the χc1(3872) c-cbar wavefunction
    The potentials are tuned to the spectrum, not derived from first principles; admitted in the Introduction and Section V. The central value of |φ(0)|^2 is chosen within this range.
  • domain assumption Heavy-quark spin symmetry decouples c-cbar spin from light degrees of freedom
    Used in Section IV.A to write the projector, leading to Eq. (7).
  • domain assumption The c-cbar wavefunction in the tetraquark state satisfies a nonrelativistic Schrödinger equation
    Standard for potential models; used to compute |φ(0)|^2.
  • domain assumption Perturbative value S = 1 + O(α_s^2) for the adjoint Wilson loop
    Used after Eq. (8); NLO correction vanishes, so they set S=1 in the numerical predictions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Hadroproduction data support tetraquark hypothesis for $\chi_{c1} (3872)$." pith.science (2026). https://pith.science/paper/CRGSSLMN

@misc{pith2026250506910,
  author       = {Pith},
  title        = {Pith review of: Hadroproduction data support tetraquark hypothesis for $\chi_c1 (3872)$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CRGSSLMN}},
  note         = {Machine review of arXiv:2505.06910}
}
abstract

We show that the recently proposed tetraquark hypothesis for the nature of the $\chi_{c1}(3872)$ results in a formalism for inclusive production rates that has no unknown parameters. We employ this formalism to compute hadroproduction rates of $\chi_{c1}(3872)$ at the Large Hadron Collider, which agree with measured prompt and nonprompt cross sections. Thus we find that the tetraquark hypothesis for $\chi_{c1}(3872)$ is well supported by hadroproduction data.

Figures

Figures reproduced from arXiv: 2505.06910 by the authors.

Figure 1
Figure 1. FIG. 1. Nonprompt fractions for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Prompt production rates of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Nonprompt production rates of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

62 extracted references · 7 canonical work pages

  1. [8]

    Aaij et al

    R. Aaij et al. (LHCb), Quantum numbers of theX(3872) state and orbital angular momentum in its ρ0Jψ decay, Phys. Rev. D 92, 011102 (2015), arXiv:1504.06339 [hep- ex]

    arXiv 2015

  2. [24]

    Aaij et al

    R. Aaij et al. (LHCb), Measurement ofχc1(3872) produc- tion in proton-proton collisions at √s = 8 and 13 TeV, JHEP 01, 131, arXiv:2109.07360 [hep-ex]

    arXiv

  3. [1]

    S. K. Choi et al. (Belle), Observation of a narrow charmonium-like state in exclusive B±→ K±π+π−J/ψ decays, Phys. Rev. Lett. 91, 262001 (2003), arXiv:hep- ex/0309032

    arXiv 2003

  4. [2]

    Acosta et al

    D. Acosta et al. (CDF), Observation of the narrow state X(3872) → J/ψπ +π− in ¯pp collisions at √s = 1 .96 TeV, Phys. Rev. Lett. 93, 072001 (2004), arXiv:hep- ex/0312021

    arXiv 2004

  5. [3]

    V. M. Abazov et al. (D0), Observation and properties of the X(3872) decaying to J/ψπ +π− in p¯p collisions at√s = 1.96 TeV, Phys. Rev. Lett. 93, 162002 (2004), arXiv:hep-ex/0405004

    arXiv 2004

  6. [4]

    Aubert et al

    B. Aubert et al. (BaBar), Study of the B → J/ψK−π+π− decay and measurement of the B → X(3872)K− branching fraction, Phys. Rev. D71, 071103 (2005), arXiv:hep-ex/0406022

    arXiv 2005

  7. [5]

    Gell-Mann, A Schematic Model of Baryons and Mesons, Phys

    M. Gell-Mann, A Schematic Model of Baryons and Mesons, Phys. Lett. 8, 214 (1964). 6

    work page 1964

  8. [6]

    Zweig, An SU(3) model for strong interaction symme- try and its breaking

    G. Zweig, An SU(3) model for strong interaction symme- try and its breaking. Version 1 10.17181/CERN-TH-401 (1964)

    doi:10.17181/cern-th-401 1964

Show all 62 references
  1. [7]

    Aaij et al

    R. Aaij et al. (LHCb), Determination of the X(3872) meson quantum numbers, Phys. Rev. Lett. 110, 222001 (2013), arXiv:1302.6269 [hep-ex]

    2013 arXiv

  2. [9]

    Barnes and S

    T. Barnes and S. Godfrey, Charmonium options for the X(3872), Phys. Rev. D 69, 054008 (2004), arXiv:hep- ph/0311162

    2004

  3. [10]

    N. A. Tornqvist, Isospin breaking of the narrow charmo- nium state of Belle at 3872-MeV as a deuson, Phys. Lett. B 590, 209 (2004), arXiv:hep-ph/0402237

    2004 arXiv

  4. [11]

    M. B. Voloshin, Interference and binding effects in decays of possible molecular component of X(3872), Phys. Lett. B 579, 316 (2004), arXiv:hep-ph/0309307

    2004 arXiv

  5. [12]

    F. E. Close and P. R. Page, The D*0 anti-D0 thresh- old resonance, Phys. Lett. B 578, 119 (2004), arXiv:hep- ph/0309253

    2004

  6. [13]

    Wong, Molecular states of heavy quark mesons, Phys

    C.-Y. Wong, Molecular states of heavy quark mesons, Phys. Rev. C 69, 055202 (2004), arXiv:hep-ph/0311088

    2004 arXiv

  7. [14]

    Braaten and M

    E. Braaten and M. Kusunoki, Low-energy universality and the new charmonium resonance at 3870-MeV, Phys. Rev. D 69, 074005 (2004), arXiv:hep-ph/0311147

    2004 arXiv

  8. [15]

    E. S. Swanson, Short range structure in the X(3872), Phys. Lett. B 588, 189 (2004), arXiv:hep-ph/0311229

    2004 arXiv

  9. [16]

    F. E. Close and S. Godfrey, Charmonium hybrid produc- tion in exclusive B meson decays, Phys. Lett. B 574, 210 (2003), arXiv:hep-ph/0305285

    2003 arXiv

  10. [17]

    B. A. Li, Is X(3872) a possible candidate of hybrid meson, Phys. Lett. B 605, 306 (2005), arXiv:hep-ph/0410264

    2005 arXiv

  11. [18]

    Maiani, F

    L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer, Diquark-antidiquarks with hidden or open charm and the nature of X(3872), Phys. Rev. D 71, 014028 (2005), arXiv:hep-ph/0412098

    2005 arXiv

  12. [19]

    E. J. Eichten, K. Lane, and C. Quigg, B Meson Gate- ways to Missing Charmonium Levels, Phys. Rev. Lett. 89, 162002 (2002), arXiv:hep-ph/0206018

    2002 arXiv

  13. [20]

    E. J. Eichten, K. Lane, and C. Quigg, Charmonium levels near threshold and the narrow state X(3872)→ π+π−J/ψ, Phys. Rev. D 69, 094019 (2004), arXiv:hep- ph/0401210

    2004

  14. [21]

    Bignamini, B

    C. Bignamini, B. Grinstein, F. Piccinini, A. D. Polosa, and C. Sabelli, Is the X(3872) Production Cross Sec- tion at Tevatron Compatible with a Hadron Molecule Interpretation?, Phys. Rev. Lett. 103, 162001 (2009), arXiv:0906.0882 [hep-ph]

    2009 arXiv

  15. [22]

    Chatrchyan et al

    S. Chatrchyan et al. (CMS), Measurement of theX(3872) Production Cross Section Via Decays to J/ψπ +π− inpp collisions at√s = 7 TeV, JHEP04, 154, arXiv:1302.3968 [hep-ex]

    arXiv

  16. [23]

    Aaboud et al

    M. Aaboud et al. (ATLAS), Measurements ofψ(2S) and X(3872) → J/ψπ +π− production in pp collisions at√s = 8 TeV with the ATLAS detector, JHEP 01, 117, arXiv:1610.09303 [hep-ex]

    arXiv

  17. [25]

    Artoisenet and E

    P. Artoisenet and E. Braaten, Production of the X(3872) at the Tevatron and the LHC, Phys. Rev. D 81, 114018 (2010), arXiv:0911.2016 [hep-ph]

    2010 arXiv

  18. [26]

    Butenschoen, Z.-G

    M. Butenschoen, Z.-G. He, and B. A. Kniehl, NLO NRQCD disfavors the interpretation of X(3872) as χc1(2P ), Phys. Rev. D 88, 011501 (2013), arXiv:1303.6524 [hep-ph]

    2013 arXiv

  19. [27]

    Meng, Y.-J

    C. Meng, Y.-J. Gao, and K.-T. Chao, B →χc1(1P,2P)K decays in QCD factorization and X(3872), Phys. Rev. D 87, 074035 (2013), arXiv:hep-ph/0506222

    2013 arXiv

  20. [28]

    C. Meng, H. Han, and K.-T. Chao, X(3872) and its pro- duction at hadron colliders, Phys. Rev. D 96, 074014 (2017), arXiv:1304.6710 [hep-ph]

    2017 arXiv

  21. [29]

    Grinstein, L

    B. Grinstein, L. Maiani, and A. D. Polosa, Radiative decays of X(3872) discriminate between the molecular and compact interpretations, Phys. Rev. D 109, 074009 (2024), arXiv:2401.11623 [hep-ph]

    2024 arXiv

  22. [30]

    Braaten and R

    E. Braaten and R. Bruschini, Exotic hidden-heavy hadrons and where to find them, Phys. Lett. B 863, 139386 (2025), arXiv:2409.08002 [hep-ph]

    2025 arXiv

  23. [31]

    Brambilla, A

    N. Brambilla, A. Mohapatra, T. Scirpa, and A. Vairo, The nature of χc1 (3872) and T + cc (3875), (2024), arXiv:2411.14306 [hep-ph]

    2024

  24. [32]

    Born and R

    M. Born and R. Oppenheimer, Zur Quantentheorie der Molekeln, Annalen Phys. 389, 457 (1927)

    1927

  25. [33]

    K. J. Juge, J. Kuti, and C. J. Morningstar, Ab initio study of hybrid anti-b g b mesons, Phys. Rev. Lett. 82, 4400 (1999), arXiv:hep-ph/9902336

    1999 arXiv

  26. [34]

    Braaten, C

    E. Braaten, C. Langmack, and D. H. Smith, Born- Oppenheimer Approximation for the XYZ Mesons, Phys. Rev. D 90, 014044 (2014), arXiv:1402.0438 [hep-ph]

    2014 arXiv

  27. [35]

    Berwein, N

    M. Berwein, N. Brambilla, J. Tarr´ us Castell` a, and A. Vairo, Quarkonium Hybrids with Nonrelativistic Ef- fective Field Theories, Phys. Rev. D 92, 114019 (2015), arXiv:1510.04299 [hep-ph]

    2015 arXiv

  28. [36]

    Oncala and J

    R. Oncala and J. Soto, Heavy Quarkonium Hybrids: Spectrum, Decay and Mixing, Phys. Rev. D 96, 014004 (2017), arXiv:1702.03900 [hep-ph]

    2017 arXiv

  29. [37]

    Brambilla, W

    N. Brambilla, W. K. Lai, J. Segovia, J. Tarr´ us Castell` a, and A. Vairo, Spin structure of heavy-quark hybrids, Phys. Rev. D 99, 014017 (2019), [Erratum: Phys.Rev.D 101, 099902 (2020)], arXiv:1805.07713 [hep-ph]

    2019 arXiv

  30. [38]

    Brambilla, W

    N. Brambilla, W. K. Lai, J. Segovia, and J. Tarr´ us Castell` a, QCD spin effects in the heavy hybrid potentials and spectra, Phys. Rev. D 101, 054040 (2020), arXiv:1908.11699 [hep-ph]

    2020 arXiv

  31. [39]

    Maiani, A

    L. Maiani, A. D. Polosa, and V. Riquer, Hydrogen bond of QCD, Phys. Rev. D 100, 014002 (2019), arXiv:1903.10253 [hep-ph]

    2019 arXiv

  32. [40]

    Berwein, N

    M. Berwein, N. Brambilla, A. Mohapatra, and A. Vairo, Hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia in Born-Oppenheimer effective theory, Phys. Rev. D 110, 094040 (2024), arXiv:2408.04719 [hep-ph]

    2024 arXiv

  33. [41]

    G. T. Bodwin, E. Braaten, and G. P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51, 1125 (1995), [Erratum: Phys.Rev.D 55, 5853 (1997)], arXiv:hep- ph/9407339

    1995

  34. [42]

    Beneke, F

    M. Beneke, F. Maltoni, and I. Z. Rothstein, QCD analysis of inclusive B decay into charmonium, Phys. Rev. D 59, 054003 (1999), arXiv:hep-ph/9808360

    1999 arXiv

  35. [43]

    Cacciari, M

    M. Cacciari, M. Greco, and P. Nason, The pT spec- trum in heavy-flavour hadroproduction., JHEP 05, 007, arXiv:hep-ph/9803400

    arXiv

  36. [44]

    Cacciari, S

    M. Cacciari, S. Frixione, and P. Nason, The p(T) spec- trum in heavy flavor photoproduction, JHEP 03, 006, 7 arXiv:hep-ph/0102134

    arXiv

  37. [45]

    Wan and J.-X

    L.-P. Wan and J.-X. Wang, FDCHQHP: A Fortran pack- age for heavy quarkonium hadroproduction, Comput. Phys. Commun. 185, 2939 (2014), arXiv:1405.2143 [hep- ph]

    2014 arXiv

  38. [46]

    H. S. Chung, U.-R. Kim, and J. Lee, Resummation of Threshold Double Logarithms in Hadroproduction of Heavy Quarkonium, Phys. Rev. Lett.134, 071902 (2025), arXiv:2408.04255 [hep-ph]

    2025 arXiv

  39. [47]

    V. N. Gribov and L. N. Lipatov, Deep inelastic e p scat- tering in perturbation theory, Sov. J. Nucl. Phys.15, 438 (1972)

    1972

  40. [48]

    L. N. Lipatov, The parton model and perturbation the- ory, Yad. Fiz. 20, 181 (1974), Sov. J. Nucl. Phys. 20, 94 (1975)

    1974

  41. [49]

    Y. L. Dokshitzer, Calculation of the Structure Func- tions for Deep Inelastic Scattering and e+ e- Annihilation by Perturbation Theory in Quantum Chromodynamics., Sov. Phys. JETP 46, 641 (1977)

    1977

  42. [50]

    Altarelli and G

    G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126, 298 (1977)

    1977

  43. [51]

    Brambilla, H

    N. Brambilla, H. S. Chung, and A. Vairo, Inclusive Hadroproduction of P -Wave Heavy Quarkonia in Poten- tial Nonrelativistic QCD, Phys. Rev. Lett. 126, 082003 (2021), arXiv:2007.07613 [hep-ph]

    2021 arXiv

  44. [52]

    Brambilla, H

    N. Brambilla, H. S. Chung, and A. Vairo, Inclusive pro- duction of heavy quarkonia in pNRQCD, JHEP 09, 032, arXiv:2106.09417 [hep-ph]

    arXiv

  45. [53]

    Brambilla, H

    N. Brambilla, H. S. Chung, A. Vairo, and X.-P. Wang, Production and polarization of S-wave quarkonia in po- tential nonrelativistic QCD, Phys. Rev. D 105, L111503 (2022), arXiv:2203.07778 [hep-ph]

    2022 arXiv

  46. [54]

    Brambilla, H

    N. Brambilla, H. S. Chung, A. Vairo, and X.-P. Wang, Inclusive production of J/ψ, ψ(2S), and Υ states in pN- RQCD, JHEP 03, 242, arXiv:2210.17345 [hep-ph]

    arXiv

  47. [55]

    G. C. Nayak, J.-W. Qiu, and G. F. Sterman, Frag- mentation, factorization and infrared poles in heavy quarkonium production, Phys. Lett. B 613, 45 (2005), arXiv:hep-ph/0501235

    2005 arXiv

  48. [56]

    Navas et al

    S. Navas et al. (Particle Data Group), Review of Particle Physics, Phys. Rev. D 110, 030001 (2024)

    2024

  49. [57]

    Braaten and S

    E. Braaten and S. Fleming, Color octet fragmentation and the psi-prime surplus at the Tevatron, Phys. Rev. Lett. 74, 3327 (1995), arXiv:hep-ph/9411365

    1995 arXiv

  50. [58]

    H. S. Chung, Review of quarkonium production: sta- tus and prospects, PoS Confinement2018, 007 (2018), arXiv:1811.12098 [hep-ph]

    2018 arXiv

  51. [59]

    H. S. Chung, Quarkonium production and polarization: where do we stand?, EPJ Web Conf. 274, 01011 (2022), arXiv:2211.10201 [hep-ph]

    2022 arXiv

  52. [60]

    G. T. Bodwin, H. S. Chung, U.-R. Kim, and J. Lee, Frag- mentation contributions to J/ψ production at the Teva- tron and the LHC, Phys. Rev. Lett. 113, 022001 (2014), arXiv:1403.3612 [hep-ph]

    2014 arXiv

  53. [61]

    G. T. Bodwin, K.-T. Chao, H. S. Chung, U.-R. Kim, J. Lee, and Y.-Q. Ma, Fragmentation contributions to hadroproduction of prompt J/ψ, χcJ, and ψ(2S) states, Phys. Rev. D 93, 034041 (2016), arXiv:1509.07904 [hep- ph]

    2016 arXiv

  54. [62]

    Chen, X.-B

    A.-P. Chen, X.-B. Jin, Y.-Q. Ma, and C. Meng, Frag- mentation function of g →QQ(3S[8] 1 ) in soft gluon fac- torization and threshold resummation, JHEP 06, 046, arXiv:2103.15121 [hep-ph]

    arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.