Pith. sign in

REVIEW 4 major objections 4 minor 164 references

This paper argues that the exotic resonances T_c̄s̄0(2870) and T_cs̄0(2900) are compact tetraquarks, matching their masses and fall-apart widths with a hybrid quark potential model.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 02:33 UTC pith:2FAEAM6J

load-bearing objection A careful, honest constituent-model survey; the 2870/2900 assignments are plausible but the OBE short-range cutoff leaves a ~100 MeV systematic uncertainty the paper does not quantify. the 4 major comments →

arxiv 2607.25401 v1 pith:2FAEAM6J submitted 2026-07-28 hep-ph

Singly heavy tetraquarks

Jun-Jie Liu , Zhi-Biao Liang , Feng-Xiao Liu , Mu-Yang Chen , Xian-Hui Zhong , Qiang Zhao This is my paper
classification hep-ph
keywords singly heavy tetraquarkshybrid quark potential modelone-gluon exchangeone-boson exchangefall-apart decaycharmed-strange exoticsquark-exchange modeltetraquark spectra
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 tries to settle what two recently observed exotic states are made of. It argues that T_c̄s̄0(2870) and T_cs̄0(2900) are compact tetraquarks—four quarks bound together—rather than loose meson molecules or kinematical effects. The evidence is a systematic calculation of all singly-heavy tetraquark spectra and decays: after adding meson-exchange forces to the usual gluon-exchange forces, the predicted masses and widths of the two states land within tens of MeV of the measured values. If correct, this turns a catalog of about a hundred predicted states into a concrete search program, and rules out the tetraquark interpretation for several older candidates like Ds0(2317), Ds1(2460), Tbs(5568), and Tcs(2327).

Core claim

On the paper's own terms, the central claim is that the 2870 and 2900 resonances are the lowest scalar tetraquarks of the c̄s̄ud and cn s̄n̄ systems, with quantum numbers 00+ and 10+, predicted at 2919 and 2922 MeV. The 2919 state's computed fall-apart width (71 MeV) and dominant D*K* decay channel match the measured width of 67±24 MeV; the 2922 state's mass matches 2900 MeV, though the computed width (~53 MeV) is narrower than the observed O(100) MeV. The paper further claims that all obtained 1S-wave tetraquarks lie far above their dissociation thresholds yet decay with narrow fall-apart widths of 1–120 MeV, making them observable, while the Ds0(2317), Ds1(2460), Tbs(5568), and Tcs(2327) s

What carries the argument

The machinery is a semi-relativistic Hamiltonian for four quarks that combines one-gluon-exchange (OGE) potentials—confinement, color-Coulomb, and color-magnetic spin-spin terms—with one-boson-exchange (OBE) potentials from π, K, η, η′, σ, ρ, ω, K*, and φ mesons. The OBE terms, especially ρ and ω exchange, supply −100 to −200 MeV of attraction per configuration, pushing low-lying masses 300–400 MeV below the authors' earlier gluon-only results; that shift is what brings the 2919/2922 predictions into line with the observed resonances. Masses are obtained by diagonalizing the Hamiltonian in an explicitly correlated Gaussian basis, and fall-apart widths are computed with a quark-exchange model

Load-bearing premise

The load-bearing premise is that meson-exchange forces calibrated on ordinary baryons and mesons, cut off ad hoc at 0.30 fm to tame their short-range divergence, operate unchanged inside a compact four-quark system; if that cutoff or coupling is wrong at the ~100 MeV level, the mass matches that identify the resonances disappear.

What would settle it

Measure the D*K* branching fraction of the T_c̄s̄0(2870) candidate: the paper predicts it carries about 90% of the total fall-apart width (DK/D*K* ≈ 0.12), so observing a comparable DK and D*K* rate, or no D*K* at all, would falsify the compact-tetraquark assignment. Similarly, a lattice or model-independent determination of the lowest 00+ c̄s̄ud mass below ~2.6 GeV would contradict the predicted 2919 MeV.

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

If this is right

  • If the assignments hold, T_c̄s̄0(2870) should have a dominant D*K* decay mode, roughly eight times its DK rate, providing a direct experimental check.
  • The low-mass partners T^0(c̄s̄[ud])0+(2510) and T^1(cn[s̄n̄])0+(2527) become concrete search targets in the D−K+ and D+sπ− channels.
  • The predicted narrow tensor states (widths of order 1 MeV) across the six systems give near-background-free discovery channels such as D*sρ and B*sφ.
  • The bottom partners T^1(bn{s̄n̄})0+(6263) and T^0(bs[ūd])0+(6252) offer flavor analogues to confirm the pattern.
  • Older candidates Ds0(2317), Ds1(2460), Tbs(5568), and Tcs(2327) are excluded as compact tetraquarks, redirecting their interpretations to conventional mesons or other structures.

Where Pith is reading between the lines

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

  • The strongest single corroboration would be measuring the D*K* dominance of the 2870 candidate and the DK/Dsπ ratio of the 2900 candidate simultaneously, because those two ratios are the paper's most distinctive quantitative fingerprints.
  • The paper's mass-overlap observations for D1(2420) and B1(5721) suggest a broader test: if tetraquark and conventional meson states coexist at nearly the same mass, decay widths and radiative transitions—not masses—will be the discriminating observables.
  • One could extend the model to compute production rates of the predicted states in B decays, since the paper gives only decay patterns; a state with a narrow fall-apart width could still be unobservable if produced weakly.
  • The predicted near-degeneracies of high-lying axial and tensor states imply that experimental separation will require partial-wave analysis; the paper's branching-fraction tables are the natural input for such fits.

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

4 major / 4 minor

Summary. This paper presents a systematic constituent-quark-model study of the 1S-wave spectra and fall-apart decays of all singly-heavy tetraquark systems (Qn\bar n\bar n, Qs\bar n\bar n, Qn\bar s\bar n, Qs\bar s\bar n, Qn\bar s\bar s, Qs\bar s\bar s) using a semi-relativistic Hamiltonian with OGE and OBE interactions, solved with explicitly correlated Gaussians. Parameters are fixed to the meson spectrum and to external baryon/photoproduction data, then applied unfitted to the tetraquarks. The main physical claim is that the LHCb states T_{\bar c\bar s0}(2870) and T_{c\bar s0}(2900) are compact tetraquarks with IJ^P=00^+ and 10^+, identified as the predicted T^0_{(\bar c\bar s[ud])0+}(2919) and T^1_{(cn\{\bar s\bar n\})0+}(2922), with comparable widths. The paper also reports that D_{s0}(2317), D_{s1}(2460), T_{b\bar s}(5568), and T_{c\bar s}(2327) are not reproduced as compact tetraquarks, and it provides a survey of narrow states and preferred decay channels as a search roadmap.

Significance. If the central assignment holds, the paper would establish that at least two open-flavor LHCb exotics are compact tetraquarks and would provide a comprehensive ~100-state spectrum with decay widths as a guide. The systematic scope—six flavor sectors, unified treatment of mass and decay, externally calibrated parameters with no tetraquark tuning—is a genuine strength. The reporting of negative results for several claimed exotics is honest and useful. The paper also makes falsifiable predictions, e.g., the dominant D*K* decay of the 2870 candidate and specific D_sπ/DK ratios for the 2900 candidate. However, the reliability of the central identification is limited by the absence of any uncertainty or sensitivity analysis, as detailed in the major comments.

major comments (4)
  1. [Sec. II.B.2, Eqs. (15)–(17); Tables XVII–XXII] The short-range OBE potentials are cut off at r^{π/ρ/ω}_{ij}=0.30 fm, chosen 'by the measured masses of the ω meson and Λc baryon.' The OBE terms supply −100 to −200 MeV for the configurations of interest and are the main mechanism lowering the low-lying masses 300–400 MeV below the OGE-only results (Secs. III.B.1, III.C.1). The central identification of T̄c̄s0(2870) and Tc̄s0(2900) as compact tetraquarks relies on mass matches of 25–50 MeV (2919 vs 2872±16; 2922 vs 2900). No cutoff-variation study or uncertainty estimate is provided. Since a 50–100 MeV systematic shift from the cutoff prescription or the Gaussian/Yukawa short-range form would erase these matches, this is a load-bearing gap. Please provide a sensitivity scan of r_{ij} (e.g., ±0.1–0.2 fm) and of the regulator, reporting the resulting shifts of the 2919/2922 states.
  2. [Sec. III, discussion following Tables XVII–XXII] The paper states that ⟨V_σ⟩ ∼ −(60±10) MeV 'can be absorbed in the other parameters, such as constituent quark mass and zero energy,' and that g_σ = g_π is an approximation. This is an internal admission that a sizable piece of the OBE attraction has no independent calibrating power. Because the central claim depends on the OBE sector's magnitude, please demonstrate the absorption explicitly: recompute the spectra with the σ term removed while refitting the zero-point energies C_{ij}, and show that the 2919/2922 masses (and their difference) are stable. If they are not stable, quantify the ambiguity and propagate it into the identification.
  3. [Tables III and IV] The parameter fit to the meson spectrum has residuals up to ~50 MeV (e.g., ω: 731 vs 783). These fitted parameters determine the tetraquark masses, but no uncertainties are propagated from the fit to any of the ~100 predicted masses or widths. Given that the central identifications rest on 25–50 MeV agreement, the lack of any error estimate makes the significance of the agreements impossible to assess. Please provide a sensitivity study (e.g., refitting within the meson residuals and recomputing the candidate masses) or a conservative theoretical uncertainty for the mass predictions.
  4. [Sec. II.C, Eq. (27); Tables XII–XIII] The fall-apart widths used to support the identities are computed with the OGE potential only, while the masses are obtained from the OGE+OBE Hamiltonian; the final meson wave functions are single SHO forms matched to RMS radii. The paper gives no estimate of the model dependence of the widths. In particular, the 53 MeV width for T^1_{(cn\{\bar s\bar n\})0+}(2922) is admitted to be narrower than the measured O(100) MeV. Please either quantify the uncertainty in the width calculation or downgrade the width agreement from a quantitative discriminant to a qualitative consistency check.
minor comments (4)
  1. [Sec. II.B.2] The sentence 'determined by the measured masses of the ω meson and Λc baryon' should specify which observables and how the cutoff was adjusted; as written, the procedure is not reproducible.
  2. [Table IV] The 52 MeV residual for the ω mass deserves explicit discussion, since it exceeds the mass differences used for identification in several places.
  3. [Figs. 3–6] Overlapping labels and identical line styles make individual states hard to distinguish; listing the predicted masses in the caption would improve readability.
  4. [Sec. III.B.1] The authors note that the 2900 assignment changed from the ¯3F state in their OGE-only study [83] to the 6F state here. This model dependence is important and should be stated in the abstract or summary as a caution.

Circularity Check

0 steps flagged

No significant circularity: model parameters are fitted to meson and baryon data, then applied unfitted to tetraquark predictions; the 2870/2900 identifications are nontrivial postdictions.

full rationale

The derivation chain is a genuine application of a Hamiltonian (Eq. 10) with OGE (Eq. 12) and OBE (Eqs. 14-17) potentials. The model parameters (Table III) are determined by fitting the 1S/2S meson spectrum (Table IV) and by baryon decay/photoproduction analyses (delta=0.576, g_v=1.7, Lambda=0.66/0.85 GeV). The tetraquark spectra in Tables V-X are then computed with no tetraquark observable used as input. The central identifications (T^0(bar-c-bar-s[ud])0+(2919) with T-bar-c-bar-s0(2870) and T^1(cn{s-bar-n})0+(2922) with T_c-bar-s0(2900)) are postdictions: no fit was performed to the 2870/2900 masses or widths. The paper also reports failures (Ds0(2317), Ds1(2460), Tb-bar-s(5568), Tc-bar-s(2327)) rather than tuning them away, and it admits the 2922 width is slightly narrower than data (Sec. III.B.1). Flagged limitations, weighed here but not circular: the ad hoc OBE short-range cutoff r^{pi/rho/omega}_{ij}=0.30 fm introduced in Sec. II.B.2, and the statement in Sec. III that <V_sigma> ~ -(60 +/- 10) MeV 'can be absorbed in the other parameters, such as constituent quark mass and zero energy.' These affect robustness of the OBE sector, but the cutoff and couplings are calibrated to non-tetraquark observables and do not include the target masses or widths. Self-citations (refs. 83, 120, 139-141) provide parameter provenance and prior baryon/meson fits; they are external, falsifiable calibrations rather than load-bearing self-referential reductions. No equation reduces to another by construction, and no fitted tetraquark input is renamed as a prediction.

Axiom & Free-Parameter Ledger

7 free parameters · 6 axioms · 0 invented entities

The model is calibrated entirely on mesons (Table IV), baryon decays (δ), and photoproduction (g_v): ~20 fitted parameters against ~18 meson observables with residuals up to ~50 MeV. The tetraquark predictions are parameter-free in the narrow sense — no tetraquark datum is fitted — but with no error bars, the quoted ~MeV precision is nominal; the paper's own cross-model comparisons imply a several-hundred-MeV systematic spread. The σ-exchange absorbability note shows part of the OBE sector is redundant with fitted constants, so the 'crucial' OBE role resides in the flavor/spin-dependent π, ρ, ω, K exchanges, which are regulated by the hand-imposed 0.30 fm cutoff. No new physical entities are postulated: the ~100 tetraquark states are model outputs with falsifiable handles (masses, widths, channels), not ad hoc inputs.

free parameters (7)
  • Constituent quark masses mn, ms, mc, mb = 0.3221, 0.4747, 1.4736, 4.7976 GeV
    Fitted to reproduce the 1S and 2S meson spectrum (Table IV).
  • OGE couplings gn, gs, gc, gb = 0.7100, 0.6271, 0.5600, 0.5000
    Fitted to the meson spectrum; the flavor-dependent parameterization αij = gi·gj is a designed degree of freedom.
  • Confinement strength b and zero-point energies Cij = b=0.2134 GeV²; Cnn=-0.6530, Cns=-0.6680, Cnc=-0.4374, Cnb=-0.3460, Css=-0.6535, Csc=-0.4663, Csb=-0.3773 GeV
    Fitted to the meson spectrum; the paper notes the σ-exchange OBE background (~-60 MeV) is absorbable into such constants, so the Cij partially re-absorb OBE strength.
  • r0 mass-dependence parameters A, B = A=1.0627 GeV^(B-1), B=0.4966
    Fitted to the meson spectrum using the Silvestre-Brac form (ref 137).
  • Chiral couplings δ, g_v, and g_σ = g_π = δ=0.576; g_v=1.7; g_σ=g_π
    Taken from baryon resonance decays (refs 139-141) and vector-meson photoproduction (ref 142); gσ=gπ is a stated approximation.
  • Cutoffs Λ (pseudoscalar/σ) and Λ_v (vector) = 0.66 GeV, 0.85 GeV
    From the light-meson spectrum fit and prior group work (ref 120).
  • Short-range cutoff distances r^{π/ρ/ω}_ij = 0.30 fm
    Imposed to cure the short-range divergence of π, ρ, ω exchange, 'determined by the measured masses of the ω meson and Λc baryon' (Sec. II.B.2). This cutoff sits below the tetraquark RMS radii (0.4-0.7 fm) and regulates the OBE attractions (-100 to -200 MeV) that drive the low masses.
axioms (6)
  • domain assumption Constituent-quark-model validity: static quarks with effective masses and pairwise potentials describe multiquark states; confinement is saturated by pairwise linear potentials.
    Foundational to the whole Hamiltonian (Eq. 10); standard in the literature but unproved here.
  • domain assumption OBE couplings and cutoffs determined in baryon/meson systems apply unchanged inside a compact tetraquark at interquark distances ~0.3-0.7 fm.
    Needed for the OBE shifts of -100 to -200 MeV (Tables XVII-XXII); the truncation at 0.30 fm is the regularization for the divergent short-range OBE.
  • domain assumption Tensor and spin-orbit forces are negligible for the low-lying 1S-wave states.
    Stated in Sec. II.B.1; tensor forces can mix S with D waves even in ground-state multiplets.
  • domain assumption Fall-apart decays are induced by OGE only (Eq. 27), with final mesons in single SHO wavefunctions.
    Sec. II.C: 'the exchange process is assumed to be induced by the OGE potential'; the final-state wavefunction approximation is stated.
  • domain assumption The ECG variational basis with 64 Gaussians converges; the geometric-progression parameters (ra1, qa, nmax) are chosen to give 'stable' results.
    Sec. II.B.3; no convergence study or detailed basis parameters are shown, only a stability assertion.
  • domain assumption The same Hamiltonian reproduces the meson spectrum well enough to calibrate tetraquark masses, despite ~50 MeV residuals in the 1S meson fit (ω: 731 vs 783 MeV).
    Parameter determination in Sec. II.B.2 and Table IV; the tetraquark claims demand ~25-50 MeV accuracy from a fit with up to ~50 MeV residuals.

pith-pipeline@v1.3.0-alltime-deepseek · 85806 in / 22538 out tokens · 233106 ms · 2026-08-01T02:33:23.449559+00:00 · methodology

0 comments
read the original abstract

In this work, we carry out a systematic study of the spectra of the $1S$-wave states for the whole singly-heavy tetraquark systems within a semi-relativistic hybrid quark potential model, in which both the one-gluon exchange (OGE) and one-boson exchange (OBE) interactions are included. Furthermore, the fall-apart decays are evaluated with the quark exchange model by combining the obtained spectra. It is found that besides the OGE potentials, the OBE potentials play crucial roles for describing the spectrum. All of our obtained states lie far above the lowest dissociation meson-meson threshold. They are compact states with relatively narrow fall-apart widths $\sim 1-120$~MeV. The $D_{s0}(2317)$, $D_{s1}(2460)$, $T_{b\bar{s}}(5568)$, and $T_{c\bar{s}}(2327)$ resonances reported from experiments cannot be explained as compact tetraquarks. While the $T_{\bar{c}\bar{s}0}(2870)$ and $T_{c\bar{s}0}(2900)$ favor the tetraquark states with $IJ^P=00^+$ and $10^+$, i.e. $T_{(\bar{c}\bar{s}[ud])0^+}^0(2919)$ and $T_{(cn\{\bar{s}\bar{n}\})0^+}^{1}(2922)$, respectively. More singly-heavy tetraquark states have good potentials to be observed in some of their dominant decay channels in experiments.

Figures

Figures reproduced from arXiv: 2607.25401 by Feng-Xiao Liu, Jun-Jie Liu, Mu-Yang Chen, Qiang Zhao, Xian-Hui Zhong, Zhi-Biao Liang.

Figure 1
Figure 1. Figure 1: FIG. 1: The illustration of the Jacobi coordinates taken for [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The fall-apart decays of a singly-heavy tetraquark s [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Mass spectra of the 1 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Mass spectra of the 1 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Mass spectra of the 1 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: A few studies of the css¯s¯ system can be found in the literature [31, 33, 80, 81, 86, 94]. Our predicted mass spec￾trum of the 1S -wave states lies about 100 MeV below that predicted in Ref. [80], while about 100 − 600 MeV above that predicted in Refs. [31, 33, 54, 81, 94]. The two scalar states, T 0 (cs{s¯s¯})0+ (3196) and T 0 (cs{s¯s¯})0+ (3406), are mixed states between |(cs) 6 0 {s¯s¯} 6¯ 0 i0 and |(c… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

164 extracted references · 132 linked inside Pith

  1. [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 [hep-ex]]

    2003

  2. [2]

    Navas et al

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

    2024

  3. [3]

    H. X. Chen, W. Chen, X. Liu and S. L. Zhu, The hidden- charm pentaquark and tetraquark states, Phys. Rept. 639, 1- 121 (2016) [arXiv:1601.02092 [hep-ph]]

    Pith/arXiv arXiv 2016

  4. [4]

    H. X. Chen, W. Chen, X. Liu, Y . R. Liu and S. L. Zhu, A re- view of the open charm and open bottom systems, Rept. Prog. Phys. 80, no.7, 076201 (2017) [arXiv:1609.08928 [hep-ph]]

    Pith/arXiv arXiv 2017

  5. [5]

    Esposito, A

    A. Esposito, A. Pilloni and A. D. Polosa, Multiquark Reso - nances, Phys. Rept. 668, 1-97 (2017) [arXiv:1611.07920 [hep- ph]]

    Pith/arXiv arXiv 2017

  6. [6]

    F. K. Guo, C. Hanhart, U. G. Meißner, Q. Wang, Q. Zhao and B. S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, no.1, 015004 (2018) [erratum: Rev. Mod. Phys. 94, no.2, 029901 (2022)] [arXiv:1705.00141 [hep-ph]]

    Pith/arXiv arXiv 2018

  7. [7]

    S. L. Olsen, T. Skwarnicki and D. Zieminska, Nonstandard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys. 90, no.1, 015003 (2018) [arXiv:1708.04012 [hep- ph]]

    Pith/arXiv arXiv 2018

  8. [8]

    R. F. Lebed, R. E. Mitchell and E. S. Swanson, Heavy-Quark QCD Exotica, Prog. Part. Nucl. Phys. 93, 143-194 (2017) [arXiv:1610.04528 [hep-ph]]

    Pith/arXiv arXiv 2017

  9. [9]

    A. Ali, J. S. Lange and S. Stone, Exotics: Heavy Pentaquar ks and Tetraquarks, Prog. Part. Nucl. Phys. 97, 123-198 (2017) [arXiv:1706.00610 [hep-ph]]

    Pith/arXiv arXiv 2017

  10. [10]

    Y . R. Liu, H. X. Chen, W. Chen, X. Liu and S. L. Zhu, Pen- taquark and Tetraquark states, Prog. Part. Nucl. Phys. 107, 237-320 (2019) [arXiv:1903.11976 [hep-ph]]

    Pith/arXiv arXiv 2019

  11. [11]

    Brambilla, S

    N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C. P . Shen, C. E. Thomas, A. V airo and C. Z. Y uan, The XYZ states: experimental and theoretical status and perspecti ves, Phys. Rept. 873, 1-154 (2020) [arXiv:1907.07583 [hep-ex]]

    Pith/arXiv arXiv 2020

  12. [12]

    H. X. Chen, W. Chen, X. Liu, Y . R. Liu and S. L. Zhu, An updated review of the new hadron states, Rept. Prog. Phys. 86 , no.2, 026201 (2023) [arXiv:2204.02649 [hep-ph]]

    Pith/arXiv arXiv 2023

  13. [13]

    X. Dai, S. Jia, A. Nefediev, J. Nieves, C. Shen and L. Zhan g, Exotic hadrons associated with b-quark, Phys. Rept. 1191, 1- 62 (2026) [arXiv:2603.09315 [hep-ph]]

    Pith/arXiv arXiv 2026

  14. [14]

    Aubert et al

    B. Aubert et al. [BaBar], Observation of a narrow meson de- caying to D+ sπ0 at a mass of 2.32-GeV /c2, Phys. Rev. Lett. 90, 242001 (2003) [arXiv:hep-ex/0304021 [hep-ex]]

    Pith/arXiv arXiv 2003

  15. [15]

    Krokovny et al

    P . Krokovny et al. [Belle], Observation of the DsJ (2317) and DsJ (2457) in B decays, Phys. Rev. Lett. 91, 262002 (2003) [arXiv:hep-ex/0308019 [hep-ex]]

    Pith/arXiv arXiv 2003

  16. [16]

    Besson et al

    D. Besson et al. [CLEO], Observation of a narrow resonance of mass 2.46-GeV /c2 decaying to D∗+ s π0 and confirmation of the D∗ sJ (2317) state, Phys. Rev. D 68, 032002 (2003) [erra- tum: Phys. Rev. D 75, 119908 (2007)] [arXiv:hep-ex/0305100 [hep-ex]]

    Pith/arXiv arXiv 2003

  17. [17]

    H. Y . Cheng and W. S. Hou, B decays as spectroscope for charmed four quark states, Phys. Lett. B 566, 193-200 (2003) [arXiv:hep-ph/0305038 [hep-ph]]

    Pith/arXiv arXiv 2003

  18. [18]

    Y . Q. Chen and X. Q. Li, A Comprehensive four-quark in- terpretation of Ds(2317), Ds(2457) and Ds(2632), Phys. Rev. Lett. 93, 232001 (2004) [arXiv:hep-ph /0407062 [hep-ph]]

    2004

  19. [19]

    Dmitrasinovic, D∗+ s (2317) and D∗+ s (2460): Tetraquarks bound by the t Hooft instanton-induced interaction?, Phys

    V . Dmitrasinovic, D∗+ s (2317) and D∗+ s (2460): Tetraquarks bound by the t Hooft instanton-induced interaction?, Phys. Rev. D 70, 096011 (2004)

    2004

  20. [20]

    Dmitrasinovic, D+ s0(2317)-D0(2308) mass di fference as ev- idence for tetraquarks, Phys

    V . Dmitrasinovic, D+ s0(2317)-D0(2308) mass di fference as ev- idence for tetraquarks, Phys. Rev. Lett. 94, 162002 (2005)

    2005

  21. [21]

    M. E. Bracco, A. Lozea, R. D. Matheus, F. S. Navarra and M. Nielsen, Disentangling two- and four-quark state pictur es of the charmed scalar mesons, Phys. Lett. B 624, 217-222 (2005) [arXiv:hep-ph/0503137 [hep-ph]]

    Pith/arXiv arXiv 2005

  22. [22]

    Nielsen, D+ sJ (2317) → D+ sπ0 decay width, Phys

    M. Nielsen, D+ sJ (2317) → D+ sπ0 decay width, Phys. Lett. B 634, 35-38 (2006) [arXiv:hep-ph /0510277 [hep-ph]]

    2006

  23. [23]

    Kim and Y

    H. Kim and Y . Oh, Ds(2317) as a four-quark state in QCD sum rules, Phys. Rev. D 72, 074012 (2005) [arXiv:hep-ph/0508251 [hep-ph]]

    Pith/arXiv arXiv 2005

  24. [24]

    Z. G. Wang and S. L. Wan, Ds(2317) as a tetraquark state with QCD sum rules in heavy quark limit, Nucl. Phys. A 778, 22-29 (2006) [arXiv:hep-ph/0602080 [hep-ph]]

    Pith/arXiv arXiv 2006

  25. [25]

    Maiani, F

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

    arXiv 2005

  26. [26]

    Terasaki, BABAR resonance as a new window of hadron physics, Phys

    K. Terasaki, BABAR resonance as a new window of hadron physics, Phys. Rev. D 68, 011501 (2003) [arXiv:hep- ph/0305213 [hep-ph]]

    arXiv 2003

  27. [27]

    Hayashigaki and K

    A. Hayashigaki and K. Terasaki, Isospin quantum number of D+ s0(2317), Prog. Theor. Phys. 114, 1191-1200 (2006) [arXiv:hep-ph/0410393 [hep-ph]]

    Pith/arXiv arXiv 2006

  28. [28]

    Terasaki, Charmed scalar mesons and related, [arXiv :hep- ph/0405146 [hep-ph]]

    K. Terasaki, Charmed scalar mesons and related, [arXiv :hep- ph/0405146 [hep-ph]]

    arXiv

  29. [29]

    V . B. Jovanovic, Masses and Mixing of cq¯q ¯q Tetraquarks Us- ing Glozman-Riska Hyperfine Interaction, Phys. Rev. D 76, 105011 (2007) [arXiv:0711.2299 [hep-ph]]

    Pith/arXiv arXiv 2007

  30. [30]

    Terasaki, Production of neutral and doubly charged p art- ners of D+ s0(2317), Prog

    K. Terasaki, Production of neutral and doubly charged p art- ners of D+ s0(2317), Prog. Theor. Phys. 116, 435-440 (2006) [arXiv:hep-ph/0604207 [hep-ph]]

    Pith/arXiv arXiv 2006

  31. [31]

    Ebert, R

    D. Ebert, R. N. Faustov and V . O. Galkin, Masses of tetraquarks with open charm and bottom, Phys. Lett. B 696, 241-245 (2011) [arXiv:1011.2677 [hep-ph]]

    Pith/arXiv arXiv 2011

  32. [32]

    S. M. Gerasyuta and V . I. Kochkin, Tetraquarks with char m in coupled-channel formalism, Phys. Rev. D 78, 116004 (2008) [arXiv:0804.4567 [hep-ph]]

    Pith/arXiv arXiv 2008

  33. [33]

    H. X. Zhang, W. L. Wang, Y . B. Dai and Z. Y . Zhang, Chi- ral SU(3) quark model study of tetraquark states: cn¯n ¯s/cs ¯s ¯s, Commun. Theor. Phys. 49, 414-420 (2008) [arXiv:hep- ph/0607207 [hep-ph]]

    arXiv 2008

  34. [34]

    V . M. Abazovet al. [D0], Evidence for a B0 sπ± state, Phys. Rev. Lett. 117, no.2, 022003 (2016) [arXiv:1602.07588 [hep-ex] ]

    Pith/arXiv arXiv 2016

  35. [35]

    Wang and R

    W. Wang and R. Zhu, Can X(5568) be a tetraquark state?, Chin. Phys. C 40, no.9, 093101 (2016) [arXiv:1602.08806 [hep-ph]]

    Pith/arXiv arXiv 2016

  36. [36]

    W. Chen, H. X. Chen, X. Liu, T. G. Steele and S. L. Zhu, Decoding the X(5568) as a fully open-flavor su¯b ¯d tetraquark state,” Phys. Rev. Lett. 117, no.2, 022002 (2016 ) [arXiv:1602.08916 [hep-ph]]

    Pith/arXiv arXiv 2016

  37. [37]

    S. S. Agaev, K. Azizi and H. Sundu, Mass and decay constan t of the newly observed exotic X(5568) state, Phys. Rev. D 93, no.7, 074024 (2016) [arXiv:1602.08642 [hep-ph]]

    Pith/arXiv arXiv 2016

  38. [38]

    Z. G. Wang, Analysis of the X(5568) as scalar tetraquark state in the diquark-antidiquark model with QCD sum rules,” Commun. Theor. Phys. 66, no.3, 335-339 (2016) [arXiv:1602.08711 [hep-ph]]

    Pith/arXiv arXiv 2016

  39. [39]

    C. M. Zanetti, M. Nielsen and K. P . Khemchandani, QCD sum rule study of a charged bottom-strange scalar meson,” Phys. 34 Rev. D 93, no.9, 096011 (2016) [arXiv:1602.09041 [hep-ph]]

    Pith/arXiv arXiv 2016

  40. [40]

    S. S. Agaev, K. Azizi and H. Sundu, Width of the exotic Xb(5568) state through its strong decay to B0 sπ+, Phys. Rev. D 93, no.11, 114007 (2016) [arXiv:1603.00290 [hep-ph]]

    Pith/arXiv arXiv 2016

  41. [41]

    Y . R. Liu, X. Liu and S. L. Zhu, X(5568) and its partner states, Phys. Rev. D 93, no.7, 074023 (2016) [arXiv:1603.01131 [hep-ph]]

    Pith/arXiv arXiv 2016

  42. [42]

    J. M. Dias, K. P . Khemchandani, A. Mart´ ınez Torres, M. Nielsen and C. M. Zanetti, A QCD sum rule calculation of the X±(5568) → B0 sπ± decay width, Phys. Lett. B 758, 235- 238 (2016) [arXiv:1603.02249 [hep-ph]]

    Pith/arXiv arXiv 2016

  43. [43]

    Z. G. Wang, Analysis of the strong decay X(5568) → B0 sπ+ with QCD sum rules, Eur. Phys. J. C 76, no.5, 279 (2016) [arXiv:1603.02498 [hep-ph]]

    Pith/arXiv arXiv 2016

  44. [44]

    Stancu, X(5568) as a su ¯d ¯b tetraquark in a sim- ple quark model, J

    F. Stancu, X(5568) as a su ¯d ¯b tetraquark in a sim- ple quark model, J. Phys. G 43, no.10, 105001 (2016) [arXiv:1603.03322 [hep-ph]]

    Pith/arXiv arXiv 2016

  45. [45]

    Tang and C

    L. Tang and C. F. Qiao, Tetraquark States with Open Flavo rs, Eur. Phys. J. C 76, no.10, 558 (2016) [arXiv:1603.04761 [hep- ph]]

    Pith/arXiv arXiv 2016

  46. [46]

    C. B. Lang, D. Mohler and S. Prelovsek, Bsπ+ scattering and search for X(5568) with lattice QCD, Phys. Rev. D 94, 074509 (2016) [arXiv:1607.03185 [hep-lat]]

    Pith/arXiv arXiv 2016

  47. [47]

    Goerke, T

    F. Goerke, T. Gutsche, M. A. Ivanov, J. G. Korner, V . E. Lyubovitskij and P . Santorelli, Four-quark structure of Zc(3900), Z(4430) and Xb(5568) states, Phys. Rev. D 94, no.9, 094017 (2016) [arXiv:1608.04656 [hep-ph]]

    Pith/arXiv arXiv 2016

  48. [48]

    S. S. Agaev, K. Azizi, B. Barsbay and H. Sundu, Resonance X(5568) as an exotic axial-vector state, Eur. Phys. J. A 53, no.1, 11 (2017) [arXiv:1608.04785 [hep-ph]]

    Pith/arXiv arXiv 2017

  49. [49]

    Lucha, D

    W. Lucha, D. Melikhov and H. Sazdjian, Are there narrow flavor-exotic tetraquarks in large- Nc QCD?, Phys. Rev. D 98, no.9, 094011 (2018) [arXiv:1810.09986 [hep-ph]]

    Pith/arXiv arXiv 2018

  50. [50]

    J. R. Zhang, J. L. Zou and J. Y . Wu, 0 + tetraquark states from improved QCD sum rules: delving into X(5568), Chin. Phys. C 42, no.4, 043101 (2018) [arXiv:1705.03741 [hep-ph]]

    Pith/arXiv arXiv 2018

  51. [51]

    Mutuk, Mass Spectrum of Exotic X(5568) State via Artifi- cial Neural Network, Int

    H. Mutuk, Mass Spectrum of Exotic X(5568) State via Artifi- cial Neural Network, Int. J. Mod. Phys. A 34, no.28, 1950167 (2019) [arXiv:1901.01154 [hep-ph]]

    Pith/arXiv arXiv 2019

  52. [52]

    Z. Yang, Q. Wang and U. G. Meißner, Where does the X(5568) structure come from?, Phys. Lett. B 767, 470-473 (2017) [arXiv:1609.08807 [hep-ph]]

    Pith/arXiv arXiv 2017

  53. [53]

    F. K. Guo, U. G. Meißner and B. S. Zou, How the X(5568) challenges our understanding of QCD, Commun. Theor. Phys. 65, no.5, 593-595 (2016) [arXiv:1603.06316 [hep-ph]]

    Pith/arXiv arXiv 2016

  54. [54]

    Q. F. L¨ u and Y . B. Dong, Masses of open charm and bottom tetraquark states in a relativized quark model, Phys. Rev. D 94, no.9, 094041 (2016) [arXiv:1603.06417 [hep-ph]]

    Pith/arXiv arXiv 2016

  55. [55]

    S. S. Agaev, K. Azizi and H. Sundu, Charmed partner of the exotic X(5568) state and its properties, Phys. Rev. D 93, no.9, 094006 (2016) [arXiv:1603.01471 [hep-ph]]

    Pith/arXiv arXiv 2016

  56. [56]

    A. K. Agamaliev, T. M. Aliev and M. Savcı, Magnetic moment of XQ state with JPC = 1+± in light cone QCD sum rules, Phys. Rev. D 95, no.3, 036015 (2017) [arXiv:1610.03980 [hep-ph]]

    Pith/arXiv arXiv 2017

  57. [57]

    S. S. Agaev, K. Azizi and H. Sundu, Testing the doubly charged charm-strange tetraquarks, Eur. Phys. J. C 78, no.2 , 141 (2018) [arXiv:1710.01971 [hep-ph]]

    Pith/arXiv arXiv 2018

  58. [58]

    W. Chen, H. X. Chen, X. Liu, T. G. Steele and S. L. Zhu, Open-flavor charm and bottom sq ¯q ¯Q and qq¯q ¯Q tetraquark states, Phys. Rev. D 95, no.11, 114005 (2017) [arXiv:1705.10088 [hep-ph]]

    Pith/arXiv arXiv 2017

  59. [59]

    Chen and J

    X. Chen and J. Ping, Looking for a ud ¯s¯b bound state in the chiral quark model, Phys. Rev. D 98, no.5, 054022 (2018) [arXiv:1807.10505 [hep-ph]]

    Pith/arXiv arXiv 2018

  60. [60]

    Huang and J

    H. Huang and J. Ping, Investigating tetraquarks compos ed of us ¯d ¯b and ud ¯s¯b, Eur. Phys. J. C 79, no.7, 556 (2019) [arXiv:1902.05778 [hep-ph]]

    Pith/arXiv arXiv 2019

  61. [61]

    J. Y . S¨ ung¨ u, A. T¨ urkan and E. V eli V eliev, In the Pursuit of X(5568) and its Charmed Partner, Acta Phys. Polon. B 50, 1501 (2019) [arXiv:1909.06149 [hep-ph]]

    Pith/arXiv arXiv 2019

  62. [62]

    J. B. Cheng, S. Y . Li, Y . R. Liu, Y . N. Liu, Z. G. Si and T. Yao, Spectrum and rearrangement decays of tetraquark states wit h four different flavors, Phys. Rev. D 101, no.11, 114017 (2020) [arXiv:2001.05287 [hep-ph]]

    Pith/arXiv arXiv 2020

  63. [63]

    S. S. Agaev, K. Azizi and H. Sundu, Decay modes of the scal ar exotic meson Tbs ¯u ¯d, Phys. Rev. D 100, no.9, 094020 (2019) [arXiv:1907.04017 [hep-ph]]

    Pith/arXiv arXiv 2019

  64. [64]

    Y . Xing, F. S. Y u and R. Zhu, Weak Decays of Stable Open- bottom Tetraquark by SU(3) Symmetry Analysis, Eur. Phys. J. C 79, no.5, 373 (2019) [arXiv:1903.05973 [hep-ph]]

    Pith/arXiv arXiv 2019

  65. [65]

    F. S. Y u, Weak-decay searches for Qs ¯u ¯d tetraquarks, Eur. Phys. J. C 82, no.7, 641 (2022) [arXiv:1709.02571 [hep-ph]]

    Pith/arXiv arXiv 2022

  66. [66]

    X. G. He, W. Wang and R. L. Zhu, Production of Charmed Tetraquarks from Bc and B decays, J. Phys. G 44, no.1, 014003 (2017) [arXiv:1606.00097 [hep-ph]]

    Pith/arXiv arXiv 2017

  67. [67]

    A. Ali, L. Maiani, A. D. Polosa and V . Riquer, B± c de- cays into tetraquarks, Phys. Rev. D 94, no.3, 034036 (2016) [arXiv:1604.01731 [hep-ph]]

    Pith/arXiv arXiv 2016

  68. [68]

    Aaij et al

    R. Aaij et al. [LHCb], Search for Structure in the B0 sπ± In- variant Mass Spectrum, Phys. Rev. Lett. 117, no.15, 152003 (2016) [arXiv:1608.00435 [hep-ex]]

    Pith/arXiv arXiv 2016

  69. [69]

    A. M. Sirunyan et al. [CMS], Search for the X(5568) state decaying into B0 sπ± in proton-proton collisions at √ s = 8 TeV , Phys. Rev. Lett. 120, no.20, 202005 (2018) [arXiv:1712.06144 [hep-ex]]

    Pith/arXiv arXiv 2018

  70. [70]

    Aaboud et al

    M. Aaboud et al. [A TLAS], Search for a Structure in the B0 sπ± Invariant Mass Spectrum with the A TLAS Experiment, Phys. Rev. Lett. 120, no.20, 202007 (2018) [arXiv:1802.01840 [hep- ex]]

    Pith/arXiv arXiv 2018

  71. [71]

    Aaltonen et al

    T. Aaltonen et al. [CDF], A search for the exotic meson X(5568) with the Collider Detector at Fermilab, Phys. Rev. Lett. 120, no.20, 202006 (2018) [arXiv:1712.09620 [hep-ex ]]

    Pith/arXiv arXiv 2018

  72. [72]

    Aaij et al

    R. Aaij et al. [LHCb], A model-independent study of reso- nant structure in B+ → D+D−K+ decays, Phys. Rev. Lett. 125, 242001 (2020) [arXiv:2009.00025 [hep-ex]]

    arXiv 2020

  73. [73]

    Aaij et al

    R. Aaij et al. [LHCb], Amplitude analysis of the B+ → D+D−K+ decay, Phys. Rev. D 102, 112003 (2020) [arXiv:2009.00026 [hep-ex]]

    arXiv 2020

  74. [74]

    Aaij et al

    R. Aaij et al. [LHCb], Observation of New Charmonium or Charmoniumlike States in B+ → D∗±D∓K+ Decays, Phys. Rev. Lett. 133, no.13, 131902 (2024) [arXiv:2406.03156 [hep- ex]]

    arXiv 2024

  75. [75]

    Aaij et al

    R. Aaij et al. [LHCb], First Observation of a Doubly Charged Tetraquark and Its Neutral Partner, Phys. Rev. Lett. 131, no .4, 041902 (2023) [arXiv:2212.02716 [hep-ex]]

    arXiv 2023

  76. [76]

    Aaij et al

    R. Aaij et al. [LHCb], Amplitude analysis of B0 → ¯D0D+ sπ− and B+ → D−D+ sπ+ decays, Phys. Rev. D 108, no.1, 012017 (2023) [arXiv:2212.02717 [hep-ex]]

    arXiv 2023

  77. [77]

    Aaij et al

    R. Aaij et al. [LHCb], Study of Ds1(2460)+ → D+ sπ+π− in B → ¯D(∗)D+ sπ+π− decays, Sci. Bull. 70, 1432-1444 (2025) [arXiv:2411.03399 [hep-ex]]

    arXiv 2025

  78. [78]

    Tan and J

    Y . Tan and J. Ping, X(2900) in a chiral quark model, Chin. Phys. C 45, no.9, 093104 (2021) [arXiv:2010.04045 [hep- ph]]

    Pith/arXiv arXiv 2021

  79. [79]

    G. Yang, J. Ping and J. Segovia, sQ ¯q ¯q (q = u, d; Q = c, b) tetraquarks in the chiral quark model, Phys. Rev. D 103, no.7 , 074011 (2021) [arXiv:2101.04933 [hep-ph]]

    Pith/arXiv arXiv 2021

  80. [80]

    Q. F. L¨ u, D. Y . Chen and Y . B. Dong, Open charm and bottom 35 tetraquarks in an extended relativized quark model, Phys. R ev. D 102, no.7, 074021 (2020) [arXiv:2008.07340 [hep-ph]]

    Pith/arXiv arXiv 2020

Showing first 80 references.